From dc912fd15e51038c999625d7fb0ebfb909f7079a Mon Sep 17 00:00:00 2001 From: Emily Boudreaux Date: Tue, 4 Aug 2026 14:24:55 -0400 Subject: [PATCH] feat(libmeanfield): centrifugal + pressure --- CMakeLists.txt | 90 +- clang-format-styles/style | 296 + experiments/README.md | 30 + experiments/experiment_main.cpp | 211 + experiments/experiment_results.cppm | 65 + experiments/gravity_accuracy_budget.cpp | 616 + format | 3 + libmeanfield/impl/analysis/integral.cpp | 200 +- libmeanfield/impl/fem.cpp | 626 +- libmeanfield/impl/integrators/advection.cpp | 72 +- libmeanfield/impl/integrators/centrifugal.cpp | 111 +- libmeanfield/impl/integrators/coriolis.cpp | 118 +- libmeanfield/impl/integrators/gravity.cpp | 357 +- .../impl/integrators/mass_continuity.cpp | 241 +- libmeanfield/impl/integrators/viscosity.cpp | 91 +- libmeanfield/impl/mapping/coefficients.cpp | 115 +- .../impl/mapping/compactification/kelvin.cpp | 266 + libmeanfield/impl/mapping/domain_mapper.cpp | 293 +- .../impl/mapping/domain_mapper_new.cpp | 916 + libmeanfield/impl/mapping/transformations.cpp | 276 + ...rotropic_closure_linearization_context.cpp | 135 + .../contexts/gravity_field_context.cpp | 442 + .../hydrostatic_equilibrium_context.cpp | 309 + libmeanfield/impl/operators/gravity_field.cpp | 790 + .../impl/operators/gravity_field_jacobian.cpp | 317 + .../kernels/barotropic_closure_kernels.cpp | 811 + .../operators/kernels/gravity_kernels.cpp | 1030 + .../hydrostatic_equilibrium_kernels.cpp | 775 + .../kernels/pressure_force_kernels.cpp | 464 + .../operators/prepared_barotropic_closure.cpp | 718 + .../operators/prepared_gravity_source.cpp | 617 + .../impl/operators/prepared_hdiv_mass.cpp | 441 + .../prepared_hydrostatic_equilibrium.cpp | 1432 + libmeanfield/impl/physics/gravity.cpp | 501 +- libmeanfield/impl/physics/solid.cpp | 32 +- libmeanfield/impl/utils/domain.cpp | 40 +- libmeanfield/impl/utils/misc.cpp | 55 +- libmeanfield/include/profile.h | 194 + libmeanfield/interface/analysis/integral.cppm | 12 +- libmeanfield/interface/boundary/context.cppm | 20 +- libmeanfield/interface/fem.cppm | 194 +- libmeanfield/interface/field/field_base.cppm | 356 + libmeanfield/interface/field/field_mfem.cppm | 380 + .../interface/field/field_registry.cppm | 379 + .../interface/integrators/advection.cppm | 2 +- .../interface/integrators/centrifugal.cppm | 18 +- .../interface/integrators/coriolis.cppm | 30 +- .../interface/integrators/gravity.cppm | 32 +- .../integrators/mass_continuity.cppm | 23 +- .../integrators/pressure_gradient.cppm | 117 +- .../interface/integrators/viscosity.cppm | 13 +- .../interface/mapping/coefficients.cppm | 48 +- .../compactification/compactification.cppm | 46 + .../mapping/compactification/kelvin.cppm | 50 + .../mapping/compactification/options.cppm | 9 + .../interface/mapping/domain_mapper.cppm | 315 +- .../interface/mapping/transformations.cppm | 87 + libmeanfield/interface/mapping/types.cppm | 77 +- libmeanfield/interface/mean_field.cppm | 26 + ...otropic_closure_linearization_context.cppm | 76 + .../contexts/gravity_field_context.cppm | 157 + .../hydrostatic_equilibrium_context.cppm | 154 + .../interface/operators/gravity_field.cppm | 147 + .../operators/gravity_field_jacobian.cppm | 38 + .../kernels/barotropic_closure_kernels.cppm | 51 + .../operators/kernels/gravity_kernels.cppm | 42 + .../hydrostatic_equilibrium_kernels.cppm | 73 + .../kernels/pressure_force_kernels.cppm | 20 + .../prepared_barotropic_closure_operator.cppm | 90 + .../operators/prepared_gravity_source.cppm | 61 + .../operators/prepared_hdiv_mass.cppm | 40 + ...ared_hydrostatic_equilibrium_operator.cppm | 278 + libmeanfield/interface/physics/barotrope.cppm | 173 + libmeanfield/interface/physics/context.cppm | 5 +- libmeanfield/interface/physics/gravity.cppm | 16 +- .../interface/physics/rigid_rotation.cppm | 127 + libmeanfield/interface/physics/solid.cppm | 5 +- libmeanfield/interface/quadrature/mfem.cppm | 310 +- libmeanfield/interface/quadrature/policy.cppm | 217 +- libmeanfield/interface/solver/fields.cppm | 29 + libmeanfield/interface/utils/blocks.cppm | 493 + libmeanfield/interface/utils/domain.cppm | 2 +- libmeanfield/interface/utils/misc.cppm | 90 +- libmeanfield/interface/utils/user.cppm | 15 +- sandbox.smesh | 377501 +++++++++------ tests/geometry/volume.cpp | 22 +- tests/integrators/centrifugal.cpp | 1394 + tests/integrators/gravity.cpp | 931 + tests/mapping/compactification/kelvin.cpp | 922 + tests/mapping/domain_mapper.cpp | 3486 + tests/mapping/hdiv_mass_tensor.cpp | 454 + ...rotropic_closure_linearization_context.cpp | 297 + .../contexts/gravity_field_context.cpp | 306 + .../hydrostatic_equilibrium_context.cpp | 382 + tests/operators/gravity_field.cpp | 4483 + .../kernels/barotropic_closure_kernels.cpp | 628 + tests/operators/kernels/gravity_kernels.cpp | 0 .../hydrostatic_equilibrium_kernels.cpp | 1054 + .../kernels/pressure_force_kernels.cpp | 424 + .../operators/prepared_barotropic_closure.cpp | 995 + tests/operators/prepared_gravity_source.cpp | 157 + tests/operators/prepared_hdiv_mass.cpp | 164 + .../prepared_hydrostatic_equilibrium.cpp | 334 + ...rostatic_equilibrium_analytic_accuracy.cpp | 484 + ...rostatic_equilibrium_complete_jacobian.cpp | 436 + ...atic_equilibrium_displacement_jacobian.cpp | 423 + ...pared_hydrostatic_equilibrium_jacobian.cpp | 472 + tests/physics/barotrope.cpp | 144 + tests/physics/barotrope_pressure.cpp | 699 + tests/physics/gravity.cpp | 3763 +- tests/physics/gravity_monopole_accuracy.cpp | 1502 + tests/quadrature/policy.cpp | 785 +- tests/test_helpers.cppm | 266 +- tests/test_main.cpp | 511 +- tests/utils/blocks.cpp | 861 + 115 files changed, 260058 insertions(+), 163261 deletions(-) create mode 100644 clang-format-styles/style create mode 100644 experiments/README.md create mode 100644 experiments/experiment_main.cpp create mode 100644 experiments/experiment_results.cppm create mode 100644 experiments/gravity_accuracy_budget.cpp create mode 100755 format create mode 100644 libmeanfield/impl/mapping/compactification/kelvin.cpp create mode 100644 libmeanfield/impl/mapping/domain_mapper_new.cpp create mode 100644 libmeanfield/impl/mapping/transformations.cpp create mode 100644 libmeanfield/impl/operators/contexts/barotropic_closure_linearization_context.cpp create mode 100644 libmeanfield/impl/operators/contexts/gravity_field_context.cpp create mode 100644 libmeanfield/impl/operators/contexts/hydrostatic_equilibrium_context.cpp create mode 100644 libmeanfield/impl/operators/gravity_field.cpp create mode 100644 libmeanfield/impl/operators/gravity_field_jacobian.cpp create mode 100644 libmeanfield/impl/operators/kernels/barotropic_closure_kernels.cpp create mode 100644 libmeanfield/impl/operators/kernels/gravity_kernels.cpp create mode 100644 libmeanfield/impl/operators/kernels/hydrostatic_equilibrium_kernels.cpp create mode 100644 libmeanfield/impl/operators/kernels/pressure_force_kernels.cpp create mode 100644 libmeanfield/impl/operators/prepared_barotropic_closure.cpp create mode 100644 libmeanfield/impl/operators/prepared_gravity_source.cpp create mode 100644 libmeanfield/impl/operators/prepared_hdiv_mass.cpp create mode 100644 libmeanfield/impl/operators/prepared_hydrostatic_equilibrium.cpp create mode 100644 libmeanfield/include/profile.h create mode 100644 libmeanfield/interface/field/field_base.cppm create mode 100644 libmeanfield/interface/field/field_mfem.cppm create mode 100644 libmeanfield/interface/field/field_registry.cppm create mode 100644 libmeanfield/interface/mapping/compactification/compactification.cppm create mode 100644 libmeanfield/interface/mapping/compactification/kelvin.cppm create mode 100644 libmeanfield/interface/mapping/compactification/options.cppm create mode 100644 libmeanfield/interface/mapping/transformations.cppm create mode 100644 libmeanfield/interface/operators/contexts/barotropic_closure_linearization_context.cppm create mode 100644 libmeanfield/interface/operators/contexts/gravity_field_context.cppm create mode 100644 libmeanfield/interface/operators/contexts/hydrostatic_equilibrium_context.cppm create mode 100644 libmeanfield/interface/operators/gravity_field.cppm create mode 100644 libmeanfield/interface/operators/gravity_field_jacobian.cppm create mode 100644 libmeanfield/interface/operators/kernels/barotropic_closure_kernels.cppm create mode 100644 libmeanfield/interface/operators/kernels/gravity_kernels.cppm create mode 100644 libmeanfield/interface/operators/kernels/hydrostatic_equilibrium_kernels.cppm create mode 100644 libmeanfield/interface/operators/kernels/pressure_force_kernels.cppm create mode 100644 libmeanfield/interface/operators/prepared_barotropic_closure_operator.cppm create mode 100644 libmeanfield/interface/operators/prepared_gravity_source.cppm create mode 100644 libmeanfield/interface/operators/prepared_hdiv_mass.cppm create mode 100644 libmeanfield/interface/operators/prepared_hydrostatic_equilibrium_operator.cppm create mode 100644 libmeanfield/interface/physics/barotrope.cppm create mode 100644 libmeanfield/interface/physics/rigid_rotation.cppm create mode 100644 libmeanfield/interface/solver/fields.cppm create mode 100644 libmeanfield/interface/utils/blocks.cppm create mode 100644 tests/integrators/centrifugal.cpp create mode 100644 tests/integrators/gravity.cpp create mode 100644 tests/mapping/compactification/kelvin.cpp create mode 100644 tests/mapping/domain_mapper.cpp create mode 100644 tests/mapping/hdiv_mass_tensor.cpp create mode 100644 tests/operators/contexts/barotropic_closure_linearization_context.cpp create mode 100644 tests/operators/contexts/gravity_field_context.cpp create mode 100644 tests/operators/contexts/hydrostatic_equilibrium_context.cpp create mode 100644 tests/operators/gravity_field.cpp create mode 100644 tests/operators/kernels/barotropic_closure_kernels.cpp create mode 100644 tests/operators/kernels/gravity_kernels.cpp create mode 100644 tests/operators/kernels/hydrostatic_equilibrium_kernels.cpp create mode 100644 tests/operators/kernels/pressure_force_kernels.cpp create mode 100644 tests/operators/prepared_barotropic_closure.cpp create mode 100644 tests/operators/prepared_gravity_source.cpp create mode 100644 tests/operators/prepared_hdiv_mass.cpp create mode 100644 tests/operators/prepared_hydrostatic_equilibrium.cpp create mode 100644 tests/operators/prepared_hydrostatic_equilibrium_analytic_accuracy.cpp create mode 100644 tests/operators/prepared_hydrostatic_equilibrium_complete_jacobian.cpp create mode 100644 tests/operators/prepared_hydrostatic_equilibrium_displacement_jacobian.cpp create mode 100644 tests/operators/prepared_hydrostatic_equilibrium_jacobian.cpp create mode 100644 tests/physics/barotrope.cpp create mode 100644 tests/physics/barotrope_pressure.cpp create mode 100644 tests/physics/gravity_monopole_accuracy.cpp create mode 100644 tests/utils/blocks.cpp diff --git a/CMakeLists.txt b/CMakeLists.txt index 2cf77b0..b30c177 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -45,6 +45,7 @@ target_sources(mean_field libmeanfield/impl/fem.cpp libmeanfield/impl/mapping/coefficients.cpp libmeanfield/impl/mapping/domain_mapper.cpp + libmeanfield/impl/mapping/compactification/kelvin.cpp libmeanfield/impl/physics/gravity.cpp libmeanfield/impl/physics/solid.cpp libmeanfield/impl/utils/domain.cpp @@ -55,6 +56,21 @@ target_sources(mean_field libmeanfield/impl/integrators/gravity.cpp libmeanfield/impl/integrators/mass_continuity.cpp libmeanfield/impl/integrators/viscosity.cpp + libmeanfield/impl/mapping/domain_mapper_new.cpp + libmeanfield/impl/mapping/transformations.cpp + libmeanfield/impl/operators/gravity_field.cpp + libmeanfield/impl/operators/gravity_field_jacobian.cpp + libmeanfield/impl/operators/kernels/gravity_kernels.cpp + libmeanfield/impl/operators/prepared_hdiv_mass.cpp + libmeanfield/impl/operators/prepared_gravity_source.cpp + libmeanfield/impl/operators/contexts/gravity_field_context.cpp + libmeanfield/impl/operators/kernels/barotropic_closure_kernels.cpp + libmeanfield/impl/operators/prepared_barotropic_closure.cpp + libmeanfield/impl/operators/contexts/barotropic_closure_linearization_context.cpp + libmeanfield/impl/operators/kernels/hydrostatic_equilibrium_kernels.cpp + libmeanfield/impl/operators/contexts/hydrostatic_equilibrium_context.cpp + libmeanfield/impl/operators/prepared_hydrostatic_equilibrium.cpp + libmeanfield/impl/operators/kernels/pressure_force_kernels.cpp ) target_sources(mean_field @@ -67,6 +83,10 @@ target_sources(mean_field libmeanfield/interface/mapping/coefficients.cppm libmeanfield/interface/mapping/domain_mapper.cppm libmeanfield/interface/mapping/types.cppm + libmeanfield/interface/mapping/transformations.cppm + libmeanfield/interface/mapping/compactification/compactification.cppm + libmeanfield/interface/mapping/compactification/kelvin.cppm + libmeanfield/interface/mapping/compactification/options.cppm libmeanfield/interface/physics/context.cppm libmeanfield/interface/physics/gravity.cppm libmeanfield/interface/physics/solid.cppm @@ -82,6 +102,26 @@ target_sources(mean_field libmeanfield/interface/integrators/viscosity.cppm libmeanfield/interface/quadrature/policy.cppm libmeanfield/interface/quadrature/mfem.cppm + libmeanfield/interface/solver/fields.cppm + libmeanfield/interface/operators/gravity_field.cppm + libmeanfield/interface/operators/gravity_field_jacobian.cppm + libmeanfield/interface/operators/kernels/gravity_kernels.cppm + libmeanfield/interface/operators/kernels/barotropic_closure_kernels.cppm + libmeanfield/interface/utils/blocks.cppm + libmeanfield/interface/operators/contexts/gravity_field_context.cppm + libmeanfield/interface/operators/prepared_gravity_source.cppm + libmeanfield/interface/operators/prepared_hdiv_mass.cppm + libmeanfield/interface/operators/prepared_hydrostatic_equilibrium_operator.cppm + libmeanfield/interface/field/field_base.cppm + libmeanfield/interface/field/field_registry.cppm + libmeanfield/interface/field/field_mfem.cppm + libmeanfield/interface/physics/barotrope.cppm + libmeanfield/interface/operators/prepared_barotropic_closure_operator.cppm + libmeanfield/interface/operators/contexts/barotropic_closure_linearization_context.cppm + libmeanfield/interface/physics/rigid_rotation.cppm + libmeanfield/interface/operators/kernels/hydrostatic_equilibrium_kernels.cppm + libmeanfield/interface/operators/contexts/hydrostatic_equilibrium_context.cppm + libmeanfield/interface/operators/kernels/pressure_force_kernels.cppm ) @@ -116,10 +156,58 @@ add_executable(tests tests/physics/gravity.cpp tests/geometry/volume.cpp tests/quadrature/policy.cpp + tests/integrators/centrifugal.cpp + tests/integrators/gravity.cpp + tests/mapping/domain_mapper.cpp + tests/mapping/compactification/kelvin.cpp + tests/utils/blocks.cpp + tests/operators/gravity_field.cpp + tests/mapping/hdiv_mass_tensor.cpp + tests/operators/prepared_hdiv_mass.cpp + tests/operators/prepared_gravity_source.cpp + tests/operators/contexts/gravity_field_context.cpp + tests/physics/gravity_monopole_accuracy.cpp + tests/physics/barotrope.cpp + tests/operators/kernels/barotropic_closure_kernels.cpp + tests/operators/prepared_barotropic_closure.cpp + tests/operators/contexts/barotropic_closure_linearization_context.cpp + tests/operators/kernels/hydrostatic_equilibrium_kernels.cpp + tests/operators/contexts/hydrostatic_equilibrium_context.cpp + tests/operators/prepared_hydrostatic_equilibrium.cpp + tests/operators/prepared_hydrostatic_equilibrium_jacobian.cpp + tests/operators/prepared_hydrostatic_equilibrium_displacement_jacobian.cpp + tests/operators/prepared_hydrostatic_equilibrium_complete_jacobian.cpp + tests/operators/prepared_hydrostatic_equilibrium_analytic_accuracy.cpp + tests/physics/barotrope_pressure.cpp + tests/operators/kernels/pressure_force_kernels.cpp + ) target_link_libraries(tests PRIVATE mean_field test_mod Catch2::Catch2 Boost::boost) +add_library(experiment_mod) +target_sources(experiment_mod + PUBLIC + FILE_SET CXX_MODULES FILES + experiments/experiment_results.cppm +) +target_link_libraries(experiment_mod + PUBLIC + mean_field + test_mod +) + +add_executable(experiments + experiments/experiment_main.cpp + experiments/gravity_accuracy_budget.cpp +) + +target_link_libraries(experiments PRIVATE mean_field test_mod experiment_mod Catch2::Catch2 Boost::boost) + include (CTest) include (Catch) -catch_discover_tests(tests) \ No newline at end of file +catch_discover_tests( + tests + experiments + WORKING_DIRECTORY "${CMAKE_SOURCE_DIR}" +) \ No newline at end of file diff --git a/clang-format-styles/style b/clang-format-styles/style new file mode 100644 index 0000000..31980cb --- /dev/null +++ b/clang-format-styles/style @@ -0,0 +1,296 @@ +--- +BasedOnStyle: LLVM +AccessModifierOffset: -4 +AlignAfterOpenBracket: BlockIndent +AlignArrayOfStructures: None +AlignConsecutiveAssignments: + Enabled: true + AcrossEmptyLines: true + AcrossComments: true + AlignCompound: false + AlignFunctionDeclarations: false + AlignFunctionPointers: false + PadOperators: true +AlignConsecutiveBitFields: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionDeclarations: false + AlignFunctionPointers: false + PadOperators: false +AlignConsecutiveDeclarations: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionDeclarations: true + AlignFunctionPointers: false + PadOperators: false +AlignConsecutiveMacros: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionDeclarations: false + AlignFunctionPointers: false + PadOperators: false +AlignConsecutiveShortCaseStatements: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCaseArrows: false + AlignCaseColons: false +AlignConsecutiveTableGenBreakingDAGArgColons: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionDeclarations: false + AlignFunctionPointers: false + PadOperators: false +AlignConsecutiveTableGenCondOperatorColons: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionDeclarations: false + AlignFunctionPointers: false + PadOperators: false +AlignConsecutiveTableGenDefinitionColons: + Enabled: false + AcrossEmptyLines: false + AcrossComments: false + AlignCompound: false + AlignFunctionDeclarations: false + AlignFunctionPointers: false + PadOperators: false +AlignEscapedNewlines: Right +AlignOperands: Align +AlignTrailingComments: + Kind: Always + OverEmptyLines: 0 +AllowAllArgumentsOnNextLine: true +AllowAllParametersOfDeclarationOnNextLine: false +AllowBreakBeforeNoexceptSpecifier: Never +AllowShortBlocksOnASingleLine: Never +AllowShortCaseExpressionOnASingleLine: true +AllowShortCaseLabelsOnASingleLine: false +AllowShortCompoundRequirementOnASingleLine: true +AllowShortEnumsOnASingleLine: true +AllowShortFunctionsOnASingleLine: None +AllowShortIfStatementsOnASingleLine: Never +AllowShortLambdasOnASingleLine: All +AllowShortLoopsOnASingleLine: false +AllowShortNamespacesOnASingleLine: false +AlwaysBreakAfterDefinitionReturnType: None +AlwaysBreakBeforeMultilineStrings: false +AttributeMacros: + - __capability +BinPackArguments: true +BinPackLongBracedList: true +BinPackParameters: AlwaysOnePerLine +BitFieldColonSpacing: Both +BraceWrapping: + AfterCaseLabel: false + AfterClass: false + AfterControlStatement: Never + AfterEnum: false + AfterFunction: true + AfterNamespace: false + AfterObjCDeclaration: false + AfterStruct: false + AfterUnion: false + AfterExternBlock: false + BeforeCatch: false + BeforeElse: false + BeforeLambdaBody: false + BeforeWhile: false + IndentBraces: true + SplitEmptyFunction: true + SplitEmptyRecord: true + SplitEmptyNamespace: true +BracedInitializerIndentWidth: -1 +BreakAdjacentStringLiterals: true +BreakAfterAttributes: Leave +BreakAfterJavaFieldAnnotations: false +BreakAfterReturnType: None +BreakArrays: false +BreakBeforeBinaryOperators: None +BreakBeforeBraces: Attach +BreakBeforeConceptDeclarations: Always +BreakBeforeInlineASMColon: OnlyMultiline +BreakBeforeTemplateCloser: false +BreakBeforeTernaryOperators: true +BreakBinaryOperations: Never +BreakConstructorInitializers: BeforeColon +BreakFunctionDefinitionParameters: false +BreakInheritanceList: BeforeColon +BreakStringLiterals: true +BreakTemplateDeclarations: MultiLine +ColumnLimit: 80 +CommentPragmas: "^ IWYU pragma:" +CompactNamespaces: false +ConstructorInitializerIndentWidth: 4 +ContinuationIndentWidth: 4 +Cpp11BracedListStyle: true +DerivePointerAlignment: false +DisableFormat: false +EmptyLineAfterAccessModifier: Never +EmptyLineBeforeAccessModifier: Always +EnumTrailingComma: Leave +ExperimentalAutoDetectBinPacking: false +FixNamespaceComments: true +ForEachMacros: + - foreach + - Q_FOREACH + - BOOST_FOREACH +IfMacros: + - KJ_IF_MAYBE +IncludeBlocks: Preserve +IncludeCategories: + - Regex: ^"(llvm|llvm-c|clang|clang-c)/ + Priority: 2 + SortPriority: 0 + CaseSensitive: false + - Regex: ^(<|"(gtest|gmock|isl|json)/) + Priority: 3 + SortPriority: 0 + CaseSensitive: false + - Regex: .* + Priority: 1 + SortPriority: 0 + CaseSensitive: false +IncludeIsMainRegex: (Test)?$ +IncludeIsMainSourceRegex: "" +IndentAccessModifiers: false +IndentCaseBlocks: false +IndentCaseLabels: false +IndentExportBlock: true +IndentExternBlock: AfterExternBlock +IndentGotoLabels: true +IndentPPDirectives: None +IndentRequiresClause: true +IndentWidth: 4 +IndentWrappedFunctionNames: false +InsertBraces: false +InsertNewlineAtEOF: false +InsertTrailingCommas: None +IntegerLiteralSeparator: + Binary: 0 + BinaryMinDigits: 0 + Decimal: 0 + DecimalMinDigits: 0 + Hex: 0 + HexMinDigits: 0 +JavaScriptQuotes: Leave +JavaScriptWrapImports: true +KeepEmptyLines: + AtEndOfFile: false + AtStartOfBlock: true + AtStartOfFile: true +KeepFormFeed: false +LambdaBodyIndentation: Signature +LineEnding: DeriveLF +MacroBlockBegin: "" +MacroBlockEnd: "" +MainIncludeChar: Quote +MaxEmptyLinesToKeep: 1 +NamespaceIndentation: All +ObjCBinPackProtocolList: Auto +ObjCBlockIndentWidth: 2 +ObjCBreakBeforeNestedBlockParam: true +ObjCSpaceAfterProperty: false +ObjCSpaceBeforeProtocolList: true +OneLineFormatOffRegex: "" +PPIndentWidth: -1 +PackConstructorInitializers: BinPack +PenaltyBreakAssignment: 2 +PenaltyBreakBeforeFirstCallParameter: 19 +PenaltyBreakBeforeMemberAccess: 150 +PenaltyBreakComment: 300 +PenaltyBreakFirstLessLess: 120 +PenaltyBreakOpenParenthesis: 0 +PenaltyBreakScopeResolution: 500 +PenaltyBreakString: 1000 +PenaltyBreakTemplateDeclaration: 10 +PenaltyExcessCharacter: 1000000 +PenaltyIndentedWhitespace: 0 +PenaltyReturnTypeOnItsOwnLine: 60 +PointerAlignment: Right +QualifierAlignment: Leave +ReferenceAlignment: Pointer +ReflowComments: Always +RemoveBracesLLVM: false +RemoveEmptyLinesInUnwrappedLines: false +RemoveParentheses: Leave +RemoveSemicolon: false +RequiresClausePosition: OwnLine +RequiresExpressionIndentation: OuterScope +SeparateDefinitionBlocks: Leave +ShortNamespaceLines: 1 +SkipMacroDefinitionBody: false +SortIncludes: + Enabled: true + IgnoreCase: false +SortJavaStaticImport: Before +SortUsingDeclarations: LexicographicNumeric +SpaceAfterCStyleCast: false +SpaceAfterLogicalNot: false +SpaceAfterOperatorKeyword: false +SpaceAfterTemplateKeyword: true +SpaceAroundPointerQualifiers: Default +SpaceBeforeAssignmentOperators: true +SpaceBeforeCaseColon: false +SpaceBeforeCpp11BracedList: false +SpaceBeforeCtorInitializerColon: true +SpaceBeforeInheritanceColon: true +SpaceBeforeJsonColon: false +SpaceBeforeParens: ControlStatements +SpaceBeforeParensOptions: + AfterControlStatements: true + AfterForeachMacros: true + AfterFunctionDeclarationName: false + AfterFunctionDefinitionName: false + AfterIfMacros: true + AfterNot: false + AfterOverloadedOperator: false + AfterPlacementOperator: true + AfterRequiresInClause: false + AfterRequiresInExpression: false + BeforeNonEmptyParentheses: false +SpaceBeforeRangeBasedForLoopColon: true +SpaceBeforeSquareBrackets: false +SpaceInEmptyBlock: true +SpacesBeforeTrailingComments: 1 +SpacesInAngles: Never +SpacesInContainerLiterals: true +SpacesInLineCommentPrefix: + Minimum: 1 + Maximum: -1 +SpacesInParens: Never +SpacesInParensOptions: + ExceptDoubleParentheses: false + InConditionalStatements: false + InCStyleCasts: false + InEmptyParentheses: false + Other: false +SpacesInSquareBrackets: false +Standard: Latest +StatementAttributeLikeMacros: + - Q_EMIT +StatementMacros: + - Q_UNUSED + - QT_REQUIRE_VERSION +TabWidth: 8 +TableGenBreakInsideDAGArg: DontBreak +UseTab: Never +VerilogBreakBetweenInstancePorts: true +WhitespaceSensitiveMacros: + - BOOST_PP_STRINGIZE + - CF_SWIFT_NAME + - NS_SWIFT_NAME + - PP_STRINGIZE + - STRINGIZE +WrapNamespaceBodyWithEmptyLines: Leave +Language: Cpp diff --git a/experiments/README.md b/experiments/README.md new file mode 100644 index 0000000..af31656 --- /dev/null +++ b/experiments/README.md @@ -0,0 +1,30 @@ +# Accuracy experiments + +This directory is deliberately separate from `tests/`. It uses Catch2 only as +an MPI-aware runner, selector, configuration host, and failure reporter. A run +fails only when the calculation is invalid (for example, non-finite output or a +failed linear solve); measured accuracy is written as data, not as a regression +tolerance. + +`experiment_main.cpp` registers the `experiment` Catch2 reporter. It collects +rows recorded with `record_experiment_result` and writes one wide CSV table on +MPI rank zero. Each row carries sweep parameters and numerical metrics, so +results can be plotted or compared across commits. + +The initial budget has three sweeps at fixed mesh and polynomial orders: + +1. linear-solver tolerance: `1e-8`, `1e-10`, `1e-12`, `1e-14`; +2. production quadrature boost: `0`, `4`, `8`; +3. reference-space decomposition: numerical field/potential error, analytic + projection error, and numerical-to-projection gap. + +Run only the budget and choose its output path with: + +```text +./mean_field_experiments --experiment-output gravity_budget.csv --catch2 "[accuracy]" +``` + +The executable needs the same dependencies, generated module mapping, and +configuration registration as the existing Catch2 test executable. Add +`experiment_main.cpp` and `gravity_accuracy_budget.cpp` as a second executable +next to that target; do not add them to the ordinary test executable. diff --git a/experiments/experiment_main.cpp b/experiments/experiment_main.cpp new file mode 100644 index 0000000..d5e121d --- /dev/null +++ b/experiments/experiment_main.cpp @@ -0,0 +1,211 @@ +#include +#include +#include + +#include +#include +#include + +#include +#include +#include +#include +#include +#include +#include +#include +#include + + +import mean_field; +import test_helpers; +import experiment; + +using namespace experiment; + +static std::string escape_csv(const std::string& value) { + if (value.find_first_of(",\"\n") == std::string::npos) { + return value; + } + + std::string escaped{"\""}; + for (const char character : value) { + if (character == '\"') { + escaped += "\"\""; + } else { + escaped += character; + } + } + escaped += '\"'; + return escaped; +} + +static void write_experiment_csv() { + int rank = 0; + MPI_Comm_rank(MPI_COMM_WORLD, &rank); + if (rank != 0) { + return; + } + + const std::vector results = ExperimentRegistry::instance().results(); + std::set parameter_names; + std::set metric_names; + + for (const ExperimentResult& result : results) { + for (const auto& [name, value] : result.parameters) { + parameter_names.insert(name); + } + for (const auto& [name, value] : result.metrics) { + metric_names.insert(name); + } + } + + const std::string output_path = ExperimentRegistry::instance().output_path(); + std::ofstream output(output_path); + if (!output) { + std::cerr << "Unable to write experiment results to " << output_path << '\n'; + return; + } + + output << "experiment,case"; + for (const std::string& name : parameter_names) { + output << ',' << escape_csv(name); + } + for (const std::string& name : metric_names) { + output << ',' << escape_csv(name); + } + output << '\n'; + + output << std::setprecision(17); + for (const ExperimentResult& result : results) { + output << escape_csv(result.experiment_name) << ',' << escape_csv(result.case_name); + for (const std::string& name : parameter_names) { + const auto iterator = result.parameters.find(name); + output << ',' << (iterator == result.parameters.end() ? "" : escape_csv(iterator->second)); + } + for (const std::string& name : metric_names) { + const auto iterator = result.metrics.find(name); + output << ','; + if (iterator != result.metrics.end()) { + output << iterator->second; + } + } + output << '\n'; + } + + std::cout << "Wrote " << results.size() << " experiment rows to " << output_path << '\n'; +} + +class ExperimentReporter final : public Catch::StreamingReporterBase { +public: + using StreamingReporterBase::StreamingReporterBase; + + static std::string getDescription() { + return "Compact console reporter that writes structured experiment measurements to CSV."; + } + + void testCaseEnded(const Catch::TestCaseStats& statistics) override { + StreamingReporterBase::testCaseEnded(statistics); + const bool passed = statistics.totals.assertions.allPassed(); + std::cout << (passed ? "PASS " : "FAIL ") + << statistics.testInfo->name + << " (" << statistics.totals.assertions.passed + << " assertions)\n"; + } + + void testRunEnded(const Catch::TestRunStats& statistics) override { + StreamingReporterBase::testRunEnded(statistics); + write_experiment_csv(); + } +}; + +CATCH_REGISTER_REPORTER("experiment", ExperimentReporter) + +int main(int argc, char* argv[]) { + fourdst::config::Config config; + CLI::App app{"Mean Field accuracy experiments"}; + + app.allow_extras(); + app.set_help_flag("--config-help", "Show mean-field configuration options"); + fourdst::config::register_as_cli(config, app); + + std::string output_path{"accuracy_budget.csv"}; + app.add_option("--experiment-output", output_path, "CSV path for structured measurements"); + + std::vector configuration_arguments{argv[0]}; + std::vector catch_arguments_from_command_line; + bool parsing_catch_arguments = false; + + for (int index = 1; index < argc; ++index) { + if (std::string_view(argv[index]) == "--catch2") { + parsing_catch_arguments = true; + continue; + } + + if (parsing_catch_arguments) { + catch_arguments_from_command_line.emplace_back(argv[index]); + } else { + configuration_arguments.emplace_back(argv[index]); + } + } + + std::vector configuration_argv; + configuration_argv.reserve(configuration_arguments.size()); + for (const std::string& argument : configuration_arguments) { + configuration_argv.push_back(argument.c_str()); + } + + try { + app.parse(static_cast(configuration_argv.size()), configuration_argv.data()); + } catch (const CLI::ParseError& error) { + return app.exit(error); + } + + std::vector catch_arguments{argv[0]}; + for (const std::string& argument : app.remaining()) { + catch_arguments.push_back(argument); + } + for (const std::string& argument : catch_arguments_from_command_line) { + catch_arguments.push_back(argument); + } + + bool has_reporter = false; + for (const std::string& argument : catch_arguments) { + has_reporter = has_reporter || argument == "-r" || argument == "--reporter" || + argument.starts_with("-r=") || argument.starts_with("--reporter="); + } + if (!has_reporter) { + catch_arguments.emplace_back("--reporter"); + catch_arguments.emplace_back("experiment"); + } + + std::vector catch_argv; + catch_argv.reserve(catch_arguments.size()); + for (const std::string& argument : catch_arguments) { + catch_argv.push_back(argument.c_str()); + } + + Catch::Session session; + if (const int parse_result = session.applyCommandLine(static_cast(catch_argv.size()), catch_argv.data()); + parse_result != 0) { + return parse_result; + } + + mfem::Mpi::Init(argc, argv); + mfem::Device device("cpu"); + + mean_field::utils::Args args = config.main(); + if (app.count("--mesh_file") == 0) { + args.mesh_file = "sandbox.smesh"; + } + if (app.count("--p.rtol") == 0) { + args.p.rtol = 1.0e-12; + } + if (app.count("--p.atol") == 0) { + args.p.atol = 1.0e-12; + } + + ExperimentRegistry::instance().set_output_path(output_path); + test_utils::set_args(std::move(args)); + return session.run(); +} diff --git a/experiments/experiment_results.cppm b/experiments/experiment_results.cppm new file mode 100644 index 0000000..ca7c7a8 --- /dev/null +++ b/experiments/experiment_results.cppm @@ -0,0 +1,65 @@ +module; +#include +#include +#include +#include +#include +#include +#include +export module experiment; + +export namespace experiment { + struct ExperimentResult { + std::string experiment_name; + std::string case_name; + std::map parameters; + std::map metrics; + }; + + class ExperimentRegistry { + public: + static ExperimentRegistry& instance() { + static ExperimentRegistry registry; + return registry; + } + + void add_result(ExperimentResult result) { + std::scoped_lock lock(m_mutex); + m_results.push_back(std::move(result)); + } + + [[nodiscard]] std::vector results() const { + std::scoped_lock lock(m_mutex); + return m_results; + } + + void set_output_path(std::string output_path) { + std::scoped_lock lock(m_mutex); + m_output_path = std::move(output_path); + } + + [[nodiscard]] std::string output_path() const { + std::scoped_lock lock(m_mutex); + return m_output_path; + } + + private: + mutable std::mutex m_mutex; + std::vector m_results; + std::string m_output_path{"accuracy_budget.csv"}; + }; + + inline void record_experiment_result( + const std::string& experiment_name, + const std::string& case_name, + std::map parameters, + std::map metrics + ) { + ExperimentRegistry::instance().add_result({ + .experiment_name = experiment_name, + .case_name = case_name, + .parameters = std::move(parameters), + .metrics = std::move(metrics) + }); + } +} \ No newline at end of file diff --git a/experiments/gravity_accuracy_budget.cpp b/experiments/gravity_accuracy_budget.cpp new file mode 100644 index 0000000..462be98 --- /dev/null +++ b/experiments/gravity_accuracy_budget.cpp @@ -0,0 +1,616 @@ +#include + +#include +#include +#include +#include +#include +#include + +#include +#include + + +import mean_field; +import test_helpers; +import experiment; + +using namespace experiment; + +struct AccuracyBudgetEnergies { + double binding{0.0}; + double virial{0.0}; +}; + +struct AccuracyBudgetMetrics { + double direct_relative_residual{0.0}; + double gradient_relative_error{0.0}; + double gradient_projection_relative_error{0.0}; + double gradient_solution_projection_gap{0.0}; + double potential_relative_error{0.0}; + double potential_projection_relative_error{0.0}; + double potential_solution_projection_gap{0.0}; + double binding_relative_error{0.0}; + double virial_relative_error{0.0}; + double virial_consistency_error{0.0}; +}; + +static double global_norm(const mfem::Vector& vector, MPI_Comm communicator) { + const double local_norm_squared = vector * vector; + double global_norm_squared = 0.0; + MPI_Allreduce(&local_norm_squared, &global_norm_squared, 1, MPI_DOUBLE, MPI_SUM, communicator); + return std::sqrt(global_norm_squared); +} + +static double global_dot(const mfem::Vector& left, const mfem::Vector& right, MPI_Comm communicator) { + const double local_dot = left * right; + double global_dot_product = 0.0; + MPI_Allreduce(&local_dot, &global_dot_product, 1, MPI_DOUBLE, MPI_SUM, communicator); + return global_dot_product; +} + +static void zero_vacuum_density(const mean_field::fem::FEM& fem, mfem::GridFunction& density) { + for (int index = 0; index < fem.vacuum_tdof_rho.Size(); ++index) { + density(fem.vacuum_tdof_rho[index]) = 0.0; + } +} + +static int diagnostic_quadrature_order(const mean_field::fem::FEM& fem) { + return 2 * std::max(fem.L2_fes->GetMaxElementOrder(), fem.RT_fes->GetMaxElementOrder()) + 8; +} + +static mfem::Vector assemble_monopole_projection_rhs( + mean_field::fem::FEM& fem, + const mfem::GridFunction& displacement, + const double mass, + const double stellar_radius +) { + static_cast(displacement); + + mfem::Vector local_rhs(fem.RT_fes->GetVSize()); + local_rhs = 0.0; + + const int vacuum_attribute = fem.domain_mapper_stateless->GetVacuumElementAttribute(); + const int quadrature_order = diagnostic_quadrature_order(fem); + + for (int element_id = 0; element_id < fem.mesh->GetNE(); ++element_id) { + const mfem::FiniteElement& gravity_element = *fem.RT_fes->GetFE(element_id); + mfem::ElementTransformation* transformation = fem.mesh->GetElementTransformation(element_id); + + mfem::Array gravity_dofs; + mfem::DofTransformation* gravity_transform = fem.RT_fes->GetElementVDofs(element_id, gravity_dofs); + + const int dof_count = gravity_element.GetDof(); + const int dimension = transformation->GetSpaceDim(); + mfem::Vector element_rhs(dof_count); + mfem::Vector physical_position(dimension); + mfem::Vector analytic_field(dimension); + mfem::Vector pulled_field(dimension); + mfem::DenseMatrix mapping_jacobian(dimension); + mfem::DenseMatrix vector_shape(dof_count, dimension); + element_rhs = 0.0; + + const mfem::IntegrationRule& rule = mfem::IntRules.Get( + transformation->GetGeometryType(), + quadrature_order + ); + + for (int quadrature_point_id = 0; quadrature_point_id < rule.GetNPoints(); ++quadrature_point_id) { + const mfem::IntegrationPoint& point = rule.IntPoint(quadrature_point_id); + fem.mapping->GetPhysicalPoint(*transformation, point, physical_position); + + const double radius = physical_position.Norml2(); + MFEM_VERIFY(std::isfinite(radius) && radius > 0.0, "Invalid radius in monopole projection RHS."); + + analytic_field = physical_position; + if (transformation->Attribute == vacuum_attribute) { + analytic_field *= mean_field::utils::G * mass / (radius * radius * radius); + } else { + analytic_field *= mean_field::utils::G * mass / + (stellar_radius * stellar_radius * stellar_radius); + } + + fem.mapping->ComputeJacobian(*transformation, mapping_jacobian); + mapping_jacobian.MultTranspose(analytic_field, pulled_field); + + transformation->SetIntPoint(&point); + gravity_element.CalcVShape(*transformation, vector_shape); + const double reference_weight = point.weight * transformation->Weight(); + + for (int dof = 0; dof < dof_count; ++dof) { + for (int component = 0; component < dimension; ++component) { + element_rhs(dof) += reference_weight * vector_shape(dof, component) * pulled_field(component); + } + } + } + + if (gravity_transform != nullptr) { + gravity_transform->TransformDual(element_rhs); + } + local_rhs.AddElementVector(gravity_dofs, element_rhs); + } + + mfem::Vector true_rhs(fem.RT_fes->GetTrueVSize()); + true_rhs = 0.0; + const mfem::Operator* prolongation = fem.RT_fes->GetProlongationMatrix(); + if (prolongation != nullptr) { + prolongation->MultTranspose(local_rhs, true_rhs); + } else { + true_rhs = local_rhs; + } + + return true_rhs; +} + +static mfem::Vector project_monopole_gradient( + mean_field::fem::FEM& fem, + const mfem::GridFunction& displacement, + const double mass, + const double stellar_radius +) { + mfem::Vector displacement_true; + displacement.GetTrueDofs(displacement_true); + + const mfem::Vector projection_rhs = assemble_monopole_projection_rhs( + fem, + displacement, + mass, + stellar_radius + ); + + mean_field::operators::PreparedMappedHDivMassOperator mass_operator( + fem, + *fem.domain_mapper_stateless + ); + mass_operator.Prepare(displacement_true); + + mfem::CGSolver solver(fem.RT_fes->GetComm()); + solver.SetOperator(mass_operator); + solver.SetRelTol(1.0e-11); + solver.SetAbsTol(1.0e-13); + solver.SetMaxIter(4000); + solver.SetPrintLevel(0); + + mfem::Vector projected_gradient(fem.RT_fes->GetTrueVSize()); + projected_gradient = 0.0; + solver.Mult(projection_rhs, projected_gradient); + + mfem::Vector residual; + mass_operator.Mult(projected_gradient, residual); + residual -= projection_rhs; + + const double relative_residual = global_norm(residual, fem.RT_fes->GetComm()) / + std::max(global_norm(projection_rhs, fem.RT_fes->GetComm()), std::numeric_limits::epsilon()); + + REQUIRE(std::isfinite(relative_residual)); + REQUIRE(relative_residual < 1.0e-8); + return projected_gradient; +} + +static double mapped_hdiv_relative_gap( + mean_field::fem::FEM& fem, + const mfem::GridFunction& displacement, + const mfem::Vector& calculated, + const mfem::Vector& reference +) { + mfem::Vector displacement_true; + displacement.GetTrueDofs(displacement_true); + + mean_field::operators::PreparedMappedHDivMassOperator mass_operator( + fem, + *fem.domain_mapper_stateless + ); + mass_operator.Prepare(displacement_true); + + mfem::Vector difference(calculated); + difference -= reference; + mfem::Vector difference_action; + mfem::Vector reference_action; + mass_operator.Mult(difference, difference_action); + mass_operator.Mult(reference, reference_action); + + const double difference_energy = global_dot(difference, difference_action, fem.RT_fes->GetComm()); + const double reference_energy = global_dot(reference, reference_action, fem.RT_fes->GetComm()); + MFEM_VERIFY(reference_energy > 0.0, "Projected monopole field has zero mapped H(div) norm."); + + return std::sqrt(std::max(0.0, difference_energy) / reference_energy); +} + +static AccuracyBudgetEnergies measure_stellar_energies( + mean_field::fem::FEM& fem, + const mfem::GridFunction& density, + const mean_field::physics::GravitySolution& solution +) { + const int vacuum_attribute = fem.domain_mapper_stateless->GetVacuumElementAttribute(); + const int quadrature_order = diagnostic_quadrature_order(fem); + double local_binding = 0.0; + double local_virial = 0.0; + + mfem::Vector physical_position(3); + mfem::Vector reference_field(3); + mfem::Vector physical_field(3); + mfem::DenseMatrix mapping_jacobian(3); + + for (int element_id = 0; element_id < fem.mesh->GetNE(); ++element_id) { + mfem::ElementTransformation* transformation = fem.mesh->GetElementTransformation(element_id); + if (transformation->Attribute == vacuum_attribute) { + continue; + } + + const mfem::IntegrationRule& rule = mfem::IntRules.Get( + transformation->GetGeometryType(), + quadrature_order + ); + + for (int quadrature_point_id = 0; quadrature_point_id < rule.GetNPoints(); ++quadrature_point_id) { + const mfem::IntegrationPoint& point = rule.IntPoint(quadrature_point_id); + transformation->SetIntPoint(&point); + + fem.mapping->GetPhysicalPoint(*transformation, point, physical_position); + fem.mapping->ComputeJacobian(*transformation, mapping_jacobian); + const double mapping_determinant = mapping_jacobian.Det(); + MFEM_VERIFY(mapping_determinant > 0.0, "Non-positive mapping determinant in energy diagnostic."); + + solution.gradPhi.GetVectorValue(element_id, point, reference_field); + mapping_jacobian.Mult(reference_field, physical_field); + physical_field /= mapping_determinant; + + const double weight = point.weight * transformation->Weight() * mapping_determinant; + const double rho = density.GetValue(element_id, point); + const double phi = solution.phi.GetValue(element_id, point); + local_binding += 0.5 * rho * phi * weight; + local_virial -= rho * (physical_position * physical_field) * weight; + } + } + + AccuracyBudgetEnergies energies; + MPI_Allreduce(&local_binding, &energies.binding, 1, MPI_DOUBLE, MPI_SUM, fem.L2_fes->GetComm()); + MPI_Allreduce(&local_virial, &energies.virial, 1, MPI_DOUBLE, MPI_SUM, fem.L2_fes->GetComm()); + return energies; +} + +static double reduced_gravity_relative_residual( + mean_field::fem::FEM& fem, + const mfem::GridFunction& density, + const mfem::GridFunction& displacement, + const mean_field::physics::GravitySolution& solution +) { + using GravityFieldForm = mean_field::utils::blocks::gravity_field_form; + + constexpr auto gradient_block = mean_field::utils::blocks::get_residual_block( + mean_field::utils::blocks::gravity_field.gradient_term + ); + constexpr auto poisson_block = mean_field::utils::blocks::get_residual_block( + mean_field::utils::blocks::gravity_field.poisson_term + ); + + const std::array value_sizes{ + fem.L2_fes->GetTrueVSize(), fem.Vec_H1_fes->GetTrueVSize(), + fem.RT_fes->GetTrueVSize(), fem.L2_fes->GetTrueVSize() + }; + const std::array residual_sizes{ + fem.RT_fes->GetTrueVSize(), fem.L2_fes->GetTrueVSize() + }; + const mean_field::utils::blocks::form_layout layout(value_sizes, residual_sizes); + + mfem::Vector density_true; + mfem::Vector displacement_true; + mfem::Vector gradient_true; + mfem::Vector potential_true; + density.GetTrueDofs(density_true); + displacement.GetTrueDofs(displacement_true); + solution.gradPhi.GetTrueDofs(gradient_true); + solution.phi.GetTrueDofs(potential_true); + + mean_field::operators::context::gravity_field::GravityFieldLinearizationContext linearization_context( + fem, + *fem.domain_mapper_stateless + ); + mean_field::operators::GravityFieldJacobianOperator jacobian( + fem, + *fem.domain_mapper_stateless, + linearization_context, + layout.value_offsets(), + layout.residual_offsets() + ); + mean_field::operators::GravityFieldOperator field_operator( + fem, + *fem.domain_mapper_stateless, + linearization_context, + layout.value_offsets(), + jacobian + ); + mean_field::operators::context::gravity_field::GravityFieldGeometryContext geometry_context( + fem, + *fem.domain_mapper_stateless + ); + mean_field::operators::ReducedGravityFieldOperator reduced_operator( + field_operator, + geometry_context, + displacement_true + ); + + mfem::Vector right_hand_side; + reduced_operator.BuildRightHandSide(density_true, right_hand_side); + + mfem::BlockVector state(layout.residual_offsets()); + state = 0.0; + state.GetBlock(gradient_block) = gradient_true; + state.GetBlock(poisson_block) = potential_true; + + mfem::Vector residual; + reduced_operator.Mult(state, residual); + residual -= right_hand_side; + + return global_norm(residual, fem.L2_fes->GetComm()) / + std::max(global_norm(right_hand_side, fem.L2_fes->GetComm()), std::numeric_limits::epsilon()); +} + +static AccuracyBudgetMetrics measure_monopole_accuracy( + mean_field::fem::FEM& fem, + const mfem::GridFunction& density, + const mfem::GridFunction& displacement, + const mean_field::physics::GravitySolution& solution, + const mfem::ParGridFunction& projected_potential, + const mfem::Vector& projected_gradient, + const double mass, + const double stellar_radius +) { + mfem::Vector solution_gradient; + solution.gradPhi.GetTrueDofs(solution_gradient); + + mfem::Vector solution_potential; + mfem::Vector projection_potential; + solution.phi.GetTrueDofs(solution_potential); + projected_potential.GetTrueDofs(projection_potential); + + mfem::ParGridFunction projected_gradient_grid_function(fem.RT_fes.get()); + projected_gradient_grid_function.SetFromTrueDofs(projected_gradient); + + double local_solution_gradient_error = 0.0; + double local_projection_gradient_error = 0.0; + double local_gradient_norm = 0.0; + double local_solution_potential_error = 0.0; + double local_projection_potential_error = 0.0; + double local_potential_norm = 0.0; + + const int vacuum_attribute = fem.domain_mapper_stateless->GetVacuumElementAttribute(); + const int quadrature_order = diagnostic_quadrature_order(fem); + mfem::Vector physical_position(3); + mfem::Vector analytic_gradient(3); + mfem::Vector solution_reference_gradient(3); + mfem::Vector projection_reference_gradient(3); + mfem::Vector solution_physical_gradient(3); + mfem::Vector projection_physical_gradient(3); + mfem::DenseMatrix mapping_jacobian(3); + + for (int element_id = 0; element_id < fem.mesh->GetNE(); ++element_id) { + mfem::ElementTransformation* transformation = fem.mesh->GetElementTransformation(element_id); + const mfem::IntegrationRule& rule = mfem::IntRules.Get( + transformation->GetGeometryType(), + quadrature_order + ); + + for (int quadrature_point_id = 0; quadrature_point_id < rule.GetNPoints(); ++quadrature_point_id) { + const mfem::IntegrationPoint& point = rule.IntPoint(quadrature_point_id); + transformation->SetIntPoint(&point); + fem.mapping->GetPhysicalPoint(*transformation, point, physical_position); + fem.mapping->ComputeJacobian(*transformation, mapping_jacobian); + const double mapping_determinant = mapping_jacobian.Det(); + MFEM_VERIFY(mapping_determinant > 0.0, "Non-positive mapping determinant in accuracy diagnostic."); + + const double radius = physical_position.Norml2(); + MFEM_VERIFY(std::isfinite(radius) && radius > 0.0, "Invalid radius in monopole diagnostic."); + + analytic_gradient = physical_position; + double analytic_potential = 0.0; + if (transformation->Attribute == vacuum_attribute) { + analytic_gradient *= mean_field::utils::G * mass / (radius * radius * radius); + analytic_potential = -mean_field::utils::G * mass / radius; + } else { + analytic_gradient *= mean_field::utils::G * mass / + (stellar_radius * stellar_radius * stellar_radius); + analytic_potential = -mean_field::utils::G * mass * + (3.0 * stellar_radius * stellar_radius - radius * radius) / + (2.0 * stellar_radius * stellar_radius * stellar_radius); + } + + solution.gradPhi.GetVectorValue(element_id, point, solution_reference_gradient); + mapping_jacobian.Mult(solution_reference_gradient, solution_physical_gradient); + solution_physical_gradient /= mapping_determinant; + + projected_gradient_grid_function.GetVectorValue(element_id, point, projection_reference_gradient); + mapping_jacobian.Mult(projection_reference_gradient, projection_physical_gradient); + projection_physical_gradient /= mapping_determinant; + + const double solution_potential_value = solution.phi.GetValue(element_id, point); + const double projection_potential_value = projected_potential.GetValue(element_id, point); + const double weight = point.weight * transformation->Weight() * mapping_determinant; + + solution_physical_gradient -= analytic_gradient; + projection_physical_gradient -= analytic_gradient; + local_solution_gradient_error += weight * (solution_physical_gradient * solution_physical_gradient); + local_projection_gradient_error += weight * (projection_physical_gradient * projection_physical_gradient); + local_gradient_norm += weight * (analytic_gradient * analytic_gradient); + local_solution_potential_error += weight * + (solution_potential_value - analytic_potential) * (solution_potential_value - analytic_potential); + local_projection_potential_error += weight * + (projection_potential_value - analytic_potential) * (projection_potential_value - analytic_potential); + local_potential_norm += weight * analytic_potential * analytic_potential; + } + } + + const std::array local_values{ + local_solution_gradient_error, local_projection_gradient_error, local_gradient_norm, + local_solution_potential_error, local_projection_potential_error, local_potential_norm + }; + std::array global_values{}; + MPI_Allreduce( + local_values.data(), global_values.data(), static_cast(local_values.size()), + MPI_DOUBLE, MPI_SUM, fem.L2_fes->GetComm() + ); + + const AccuracyBudgetEnergies energies = measure_stellar_energies(fem, density, solution); + const double analytic_energy = -3.0 * mean_field::utils::G * mass * mass / (5.0 * stellar_radius); + + REQUIRE(global_values[2] > 0.0); + REQUIRE(global_values[5] > 0.0); + + AccuracyBudgetMetrics metrics; + metrics.direct_relative_residual = reduced_gravity_relative_residual(fem, density, displacement, solution); + metrics.gradient_relative_error = std::sqrt(global_values[0] / global_values[2]); + metrics.gradient_projection_relative_error = std::sqrt(global_values[1] / global_values[2]); + metrics.gradient_solution_projection_gap = mapped_hdiv_relative_gap( + fem, displacement, solution_gradient, projected_gradient + ); + metrics.potential_relative_error = std::sqrt(global_values[3] / global_values[5]); + metrics.potential_projection_relative_error = std::sqrt(global_values[4] / global_values[5]); + mfem::Vector potential_difference(solution_potential); + potential_difference -= projection_potential; + const double projection_potential_norm = global_norm(projection_potential, fem.L2_fes->GetComm()); + REQUIRE(projection_potential_norm > 0.0); + metrics.potential_solution_projection_gap = global_norm(potential_difference, fem.L2_fes->GetComm()) / + projection_potential_norm; + metrics.binding_relative_error = std::abs(energies.binding - analytic_energy) / std::abs(analytic_energy); + metrics.virial_relative_error = std::abs(energies.virial - analytic_energy) / std::abs(analytic_energy); + metrics.virial_consistency_error = std::abs(energies.binding - energies.virial) / + std::max(std::abs(energies.binding), std::numeric_limits::epsilon()); + return metrics; +} + +static void run_monopole_case( + const std::string& sweep_name, + const std::string& case_name, + mean_field::utils::Args args, + const double solver_tolerance, + const int quadrature_boost +) { + args.p.rtol = solver_tolerance; + args.p.atol = std::min(args.p.atol, solver_tolerance * 1.0e-2); + args.p.max_iters = std::max(args.p.max_iters, 2000); + args.quadrature.global_boost = quadrature_boost; + + mean_field::fem::FEM fem = mean_field::fem::setup_fem(args.mesh_file, args, 0); + REQUIRE(fem.mapping != nullptr); + REQUIRE(fem.domain_mapper_stateless != nullptr); + + const double stellar_radius = mean_field::utils::RADIUS; + const double mass = mean_field::utils::MASS; + const double density_value = mass / ((4.0 / 3.0) * M_PI * stellar_radius * stellar_radius * stellar_radius); + + mfem::ParGridFunction displacement(fem.Vec_H1_fes.get()); + displacement = 0.0; + fem.mapping->ResetDisplacement(); + mean_field::physics::update_stiffness_matrix(fem); + + mfem::GridFunction density(fem.L2_fes.get()); + density = density_value; + zero_vacuum_density(fem, density); + mean_field::analysis::conserve_mass(fem, density, mass); + fem.com = mean_field::analysis::get_com(fem, density); + fem.Q = mean_field::physics::compute_quadrupole_moment_tensor(fem, density, fem.com); + + const mean_field::physics::GravitySolution solution = + mean_field::physics::grav_potential_new(fem, args, density, displacement); + + auto analytic_potential = [mass, stellar_radius](const mfem::Vector& position) { + const double radius = position.Norml2(); + if (radius >= stellar_radius) { + return -mean_field::utils::G * mass / radius; + } + return -mean_field::utils::G * mass * + (3.0 * stellar_radius * stellar_radius - radius * radius) / + (2.0 * stellar_radius * stellar_radius * stellar_radius); + }; + mean_field::mapping::PhysicalPositionFunctionCoefficient potential_coefficient( + *fem.mapping, + analytic_potential + ); + mfem::ParGridFunction projected_potential(fem.L2_fes.get()); + projected_potential.ProjectCoefficient(potential_coefficient); + + const mfem::Vector projected_gradient = project_monopole_gradient( + fem, + displacement, + mass, + stellar_radius + ); + + const AccuracyBudgetMetrics metrics = measure_monopole_accuracy( + fem, + density, + displacement, + solution, + projected_potential, + projected_gradient, + mass, + stellar_radius + ); + + REQUIRE(std::isfinite(metrics.direct_relative_residual)); + REQUIRE(std::isfinite(metrics.gradient_relative_error)); + REQUIRE(std::isfinite(metrics.potential_relative_error)); + REQUIRE(std::isfinite(metrics.virial_consistency_error)); + + record_experiment_result( + sweep_name, + case_name, + { + {"solver_rtol", std::to_string(solver_tolerance)}, + {"quadrature_global_boost", std::to_string(quadrature_boost)}, + {"mesh_file", args.mesh_file} + }, + { + {"direct_relative_residual", metrics.direct_relative_residual}, + {"gradient_relative_error", metrics.gradient_relative_error}, + {"gradient_projection_relative_error", metrics.gradient_projection_relative_error}, + {"gradient_solution_projection_gap", metrics.gradient_solution_projection_gap}, + {"potential_relative_error", metrics.potential_relative_error}, + {"potential_projection_relative_error", metrics.potential_projection_relative_error}, + {"potential_solution_projection_gap", metrics.potential_solution_projection_gap}, + {"binding_relative_error", metrics.binding_relative_error}, + {"virial_relative_error", metrics.virial_relative_error}, + {"virial_consistency_error", metrics.virial_consistency_error} + } + ); +} + +TEST_CASE("Uniform Monopole Accuracy Budget: Solver Tolerance", tags::gravity & tags::accuracy & tags::integration) { + const mean_field::utils::Args args = test_utils::setup_args(); + constexpr std::array solver_tolerances{1.0e-8, 1.0e-10, 1.0e-12, 1.0e-14}; + + for (const double solver_tolerance : solver_tolerances) { + run_monopole_case( + "solver_tolerance", + "uniform_monopole", + args, + solver_tolerance, + 0 + ); + } +} + +TEST_CASE("Uniform Monopole Accuracy Budget: Quadrature", tags::gravity & tags::accuracy & tags::integration) { + const mean_field::utils::Args args = test_utils::setup_args(); + constexpr std::array quadrature_boosts{0, 4, 8}; + + for (const int quadrature_boost : quadrature_boosts) { + run_monopole_case( + "quadrature", + "uniform_monopole", + args, + 1.0e-13, + quadrature_boost + ); + } +} + +TEST_CASE("Uniform Monopole Accuracy Budget: Projection Decomposition", tags::gravity & tags::accuracy & tags::integration) { + run_monopole_case( + "projection_decomposition", + "uniform_monopole", + test_utils::setup_args(), + 1.0e-13, + 0 + ); +} diff --git a/format b/format new file mode 100755 index 0000000..f6e8e75 --- /dev/null +++ b/format @@ -0,0 +1,3 @@ +#!/bin/bash +find libmeanfield tests -type f \( -name '*.cpp' \) | xargs -I{} clang-format -style=file:clang-format-styles/style -i {} +find libmeanfield tests -type f \( -name '*.cppm' \) | xargs -I{} clang-format -style=file:clang-format-styles/style -i {} diff --git a/libmeanfield/impl/analysis/integral.cpp b/libmeanfield/impl/analysis/integral.cpp index dd86852..5dcfdf7 100644 --- a/libmeanfield/impl/analysis/integral.cpp +++ b/libmeanfield/impl/analysis/integral.cpp @@ -1,53 +1,110 @@ module; +#include #include module mean_field; import :mapping.coefficients; +namespace { + template + const mfem::IntegrationRule &get_density_rule( + const mean_field::fem::FEM &fem, + const mfem::ElementTransformation &transformation, + const std::array< + int, + FormT::dynamicOrderCount> &dynamic_orders = {}, + const mean_field::utils::DOMAINS domain = + mean_field::utils::DOMAINS::ALL + ) { + using DensityField = + mean_field::field::Field; + + const mean_field::quadrature::Query query = + DensityField::make_query( + mean_field::quadrature::QuadratureRole::diagnostic, + transformation.OrderW(), dynamic_orders, domain, + fem.has_mapping() ? mean_field::quadrature::MappingKind::general + : mean_field::quadrature::MappingKind::none + ); + + return *fem.quadratureFactory + ->get(query, transformation.GetGeometryType()) + .integration_rule; + } +} // namespace + namespace mean_field::analysis { - double domain_integrate_grid_function(const fem::FEM &fem, const mfem::GridFunction &gf, utils::DOMAINS domain, mapping::COORDINATE_SPACE coord_space) { - mfem::LinearForm lf(fem.H1_fes.get()); + double domain_integrate_grid_function( + const fem::FEM &fem, + const mfem::GridFunction &gf, + utils::DOMAINS domain, + mapping::COORDINATE_SPACE coord_space + ) { + mfem::LinearForm lf(fem.densityFes.get()); mfem::GridFunctionCoefficient gf_c(&gf); double local_integral; mfem::Array elem_markers; populate_element_mask(fem.mesh.get(), domain, elem_markers); + const mfem::ElementTransformation &representative_transformation = + *fem.mesh->GetElementTransformation(0); + const mfem::IntegrationRule &integration_rule = + get_density_rule( + fem, representative_transformation, {}, domain + ); - if (fem.has_mapping() && coord_space == mapping::COORDINATE_SPACE::PHYSICAL) { + if (fem.has_mapping() && + coord_space == mapping::COORDINATE_SPACE::PHYSICAL) { mapping::MappedScalarCoefficient mapped_gf_c(*fem.mapping, gf_c); - // ReSharper disable once CppDFAMemoryLeak // Disabled because MFEM takes ownership so memory is not leaked + // ReSharper disable once CppDFAMemoryLeak // Disabled because MFEM + // takes ownership so memory is not leaked auto *lf_integrator = new mfem::DomainLFIntegrator(mapped_gf_c); - lf_integrator->SetIntRule(fem.int_rule.get()); + lf_integrator->SetIntRule(&integration_rule); lf.AddDomainIntegrator(lf_integrator, elem_markers); lf.Assemble(); - local_integral = lf.Sum(); } else { if (coord_space == mapping::COORDINATE_SPACE::PHYSICAL) { MFEM_ABORT( - "Physical evaluation mode requested but no mapping provided. Check domain bounds and mapping setup."); + "Physical evaluation mode requested but no mapping " + "provided. Check " + "domain bounds and mapping setup." + ); } - lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(gf_c), elem_markers); + auto *lf_integrator = new mfem::DomainLFIntegrator(gf_c); + lf_integrator->SetIntRule(&integration_rule); + lf.AddDomainIntegrator(lf_integrator, elem_markers); lf.Assemble(); local_integral = lf.Sum(); } double global_integral = 0.0; - MPI_Allreduce(&local_integral, &global_integral, 1, MPI_DOUBLE, MPI_SUM, fem.H1_fes->GetComm()); + MPI_Allreduce( + &local_integral, &global_integral, 1, MPI_DOUBLE, MPI_SUM, + fem.mesh->GetComm() + ); return global_integral; } - mfem::Vector get_com(const fem::FEM &fem, const mfem::GridFunction &rho) { + mfem::Vector get_com( + const fem::FEM &fem, + const mfem::GridFunction &rho + ) { const int dim = fem.mesh->Dimension(); mfem::Vector local_com(dim); - local_com = 0.0; + local_com = 0.0; double local_mass = 0.0; - for (int i = 0; i < fem.H1_fes->GetNE(); ++i) { - if (fem.mesh->GetAttribute(i) == 3) continue; - mfem::ElementTransformation *trans = fem.H1_fes->GetElementTransformation(i); - const mfem::IntegrationRule &ir = *fem.int_rule; + for (int i = 0; i < fem.mesh->GetNE(); ++i) { + if (fem.mesh->GetAttribute(i) == 3) + continue; + mfem::ElementTransformation *trans = + fem.mesh->GetElementTransformation(i); + const mfem::IntegrationRule &ir = + get_density_rule( + fem, *trans, std::array{1}, utils::DOMAINS::STELLAR + ); for (int j = 0; j < ir.GetNPoints(); ++j) { const mfem::IntegrationPoint &ip = ir.IntPoint(j); @@ -77,11 +134,14 @@ namespace mean_field::analysis { double global_mass = 0.0; mfem::Vector global_com(dim); - MPI_Comm comm = fem.H1_fes->GetComm(); + MPI_Comm comm = fem.mesh->GetComm(); MPI_Allreduce(&local_mass, &global_mass, 1, MPI_DOUBLE, MPI_SUM, comm); - MPI_Allreduce(local_com.GetData(), global_com.GetData(), dim, MPI_DOUBLE, MPI_SUM, comm); + MPI_Allreduce( + local_com.GetData(), global_com.GetData(), dim, MPI_DOUBLE, MPI_SUM, + comm + ); if (global_mass > 1e-18) { global_com /= global_mass; @@ -92,19 +152,32 @@ namespace mean_field::analysis { return global_com; } - void conserve_mass(const fem::FEM &fem, mfem::GridFunction &rho, const double target_mass) { - if (const double current_mass = domain_integrate_grid_function(fem, rho, utils::DOMAINS::STELLAR); current_mass > 1e-15) + void conserve_mass( + const fem::FEM &fem, + mfem::GridFunction &rho, + const double target_mass + ) { + if (const double current_mass = domain_integrate_grid_function( + fem, rho, utils::DOMAINS::STELLAR + ); + current_mass > 1e-15) rho *= (target_mass / current_mass); } - double get_moment_of_inertia(const fem::FEM &fem, const mfem::GridFunction &rho) { + double get_moment_of_inertia( + const fem::FEM &fem, + const mfem::GridFunction &rho + ) { auto s2_func = [](const mfem::Vector &x) { return std::pow(x(0), 2) + std::pow(x(1), 2); }; std::unique_ptr s2_coeff; if (fem.has_mapping()) { - s2_coeff = std::make_unique(*fem.mapping, s2_func); + s2_coeff = + std::make_unique( + *fem.mapping, s2_func + ); } else { s2_coeff = std::make_unique(s2_func); } @@ -112,53 +185,82 @@ namespace mean_field::analysis { mfem::GridFunctionCoefficient rho_coeff(&rho); mfem::ProductCoefficient I_integrand(rho_coeff, *s2_coeff); - mfem::LinearForm I_lf(fem.H1_fes.get()); + mfem::LinearForm I_lf(fem.densityFes.get()); + const mfem::ElementTransformation &representative_transformation = + *fem.mesh->GetElementTransformation(0); + const mfem::IntegrationRule &integration_rule = + get_density_rule( + fem, representative_transformation, std::array{2}, + utils::DOMAINS::STELLAR + ); + mfem::Array stellar_markers; + populate_element_mask( + fem.mesh.get(), utils::DOMAINS::STELLAR, stellar_markers + ); - double I = 0.0; - // TODO: Need to filter here to just the stellar domain and also update the IntRule + double local_I = 0.0; if (fem.has_mapping()) { - mapping::MappedScalarCoefficient mapped_integrand(*fem.mapping, I_integrand); - I_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(mapped_integrand)); + mapping::MappedScalarCoefficient mapped_integrand( + *fem.mapping, I_integrand + ); + auto *integrator = new mfem::DomainLFIntegrator(mapped_integrand); + integrator->SetIntRule(&integration_rule); + I_lf.AddDomainIntegrator(integrator, stellar_markers); I_lf.Assemble(); - I = I_lf.Sum(); + local_I = I_lf.Sum(); } else { - I_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(I_integrand)); + auto *integrator = new mfem::DomainLFIntegrator(I_integrand); + integrator->SetIntRule(&integration_rule); + I_lf.AddDomainIntegrator(integrator, stellar_markers); I_lf.Assemble(); - I = I_lf.Sum(); + local_I = I_lf.Sum(); } - return I; + double global_I = 0.0; + MPI_Allreduce( + &local_I, &global_I, 1, MPI_DOUBLE, MPI_SUM, fem.mesh->GetComm() + ); + return global_I; } double get_mesh_volume( - const fem::FEM& fem, + const fem::FEM &fem, const mapping::COORDINATE_SPACE coordinate_space, const utils::DOMAINS domain ) { mfem::ParMesh &mesh = *fem.mesh; - const mapping::DomainMapper &map = *fem.mapping; - const mfem::IntegrationRule &ir = *fem.int_rule; - const bool physical = (coordinate_space == mapping::COORDINATE_SPACE::PHYSICAL); + if (physical && !fem.has_mapping()) { + MFEM_ABORT( + "Physical volume requested but no domain mapping is available." + ); + } + double local_volume = 0.0; for (int e = 0; e < mesh.GetNE(); ++e) { const int attr = mesh.GetAttribute(e); switch (domain) { - case utils::DOMAINS::ALL: - break; - case utils::DOMAINS::STELLAR: - if (attr == 3) continue; - break; - case utils::DOMAINS::VACUUM: - if (attr != 3) continue; - break; - default: - MFEM_ABORT("Unsupported domain type for volume computation."); + case utils::DOMAINS::ALL: + break; + case utils::DOMAINS::STELLAR: + if (attr == 3) + continue; + break; + case utils::DOMAINS::VACUUM: + if (attr != 3) + continue; + break; + default: + MFEM_ABORT("Unsupported domain type for volume computation."); } mfem::ElementTransformation *T = mesh.GetElementTransformation(e); + const mfem::IntegrationRule &ir = + get_density_rule( + fem, *T, {}, domain + ); for (int q = 0; q < ir.GetNPoints(); ++q) { const mfem::IntegrationPoint &ip = ir.IntPoint(q); @@ -167,7 +269,7 @@ namespace mean_field::analysis { double dV = ip.weight * T->Weight(); if (physical) { - dV *= std::fabs(map.ComputeDetJ(*T, ip)); + dV *= std::fabs(fem.mapping->ComputeDetJ(*T, ip)); } local_volume += dV; @@ -175,8 +277,10 @@ namespace mean_field::analysis { } double global_volume = 0.0; - MPI_Allreduce(&local_volume, &global_volume, 1, MPI_DOUBLE, MPI_SUM, - mesh.GetComm()); + MPI_Allreduce( + &local_volume, &global_volume, 1, MPI_DOUBLE, MPI_SUM, + mesh.GetComm() + ); return global_volume; } -} \ No newline at end of file +} // namespace mean_field::analysis diff --git a/libmeanfield/impl/fem.cpp b/libmeanfield/impl/fem.cpp index a02bffd..dbcd146 100644 --- a/libmeanfield/impl/fem.cpp +++ b/libmeanfield/impl/fem.cpp @@ -1,190 +1,560 @@ module; -#include + +#include +#include +#include +#include #include +#include +#include +#include #include #include module mean_field; + import :boundary.contexts; +import :field.mfem; import :mapping.coefficients; import :utils.misc; import :utils.user; - namespace mean_field::fem { - FEM setup_fem(const std::string &filename, const utils::Args &args, const int extra_refine) { + FEM setup_fem( + const std::string &filename, + const utils::Args &args, + const int extraRefine + ) { FEM fem; - //================================================================== - // Section 1: Mesh and FE Space Setup - //================================================================== - fem.smesh = stroid::IO::LoadStroidMesh(filename).value(); - if (extra_refine > 0) { - stroid::refinement::UniformRefinement(fem.smesh, extra_refine); + using GravityPotential = field::Gravity::Potential; + using GravityFlux = field::Gravity::Flux; + using DisplacementVector = field::Displacement::Vector; + using DensityScalar = field::Density::Scalar; + using EnthalpyScalar = field::Enthalpy::Scalar; + + // ===================================================================== + // Section 1: Mesh construction + // ===================================================================== + + fem.smesh = stroid::IO::LoadStroidMesh(filename).value(); + + if (extraRefine > 0) { + stroid::refinement::UniformRefinement(fem.smesh, extraRefine); } - fem.mesh = std::make_unique(MPI_COMM_WORLD, *fem.smesh.mesh); + int mpiSize = 1; + MPI_Comm_size(MPI_COMM_WORLD, &mpiSize); + + const std::unique_ptr meshPartitioning( + fem.smesh.mesh->GeneratePartitioning(mpiSize, 1) + ); + + fem.mesh = std::make_unique( + MPI_COMM_WORLD, *fem.smesh.mesh, meshPartitioning.get(), 1 + ); + fem.mesh->EnsureNodes(); - const int geom_order = utils::get_mesh_order(*fem.mesh); - const int dim = fem.mesh->Dimension(); + // ===================================================================== + // Section 2: Exterior compactification coordinate + // ===================================================================== - const int v_order = 2; - const int rho_order = 2; - const int p = rho_order ; + if (fem.smesh.exterior_coordinate == nullptr) { + throw std::runtime_error("Exterior coordinate not set."); + } - const int cb_type = mfem::BasisType::GaussLobatto; - const int ob_type = mfem::BasisType::IntegratedGLL; + if (fem.smesh.exterior_coordinate->space == nullptr) { + throw std::runtime_error("Space for exterior coordinate not set."); + } - fem.RT_fec = std::make_unique(p, dim, cb_type, ob_type); - fem.RT_fes = std::make_unique(fem.mesh.get(), fem.RT_fec.get()); + if (fem.smesh.exterior_coordinate->values == nullptr) { + throw std::runtime_error("Values for exterior coordinate not set."); + } - fem.H1_fec = std::make_unique(v_order, dim); - fem.L2_fec = std::make_unique(rho_order, dim); + const mfem::FiniteElementSpace &serialCoordinateSpace = + *fem.smesh.exterior_coordinate->space; - // Gravity (Scalar H1) and Velocity (Vector H1) - fem.H1_fes = std::make_unique(fem.mesh.get(), fem.H1_fec.get()); - fem.Vec_H1_fes = std::make_unique(fem.mesh.get(), fem.H1_fec.get(), dim, - mfem::Ordering::byNODES); + const mfem::GridFunction &serialCoordinate = + *fem.smesh.exterior_coordinate->values; - // Density & Pressure (Scalar Discontinuous L2) - fem.L2_fes = std::make_unique(fem.mesh.get(), fem.L2_fec.get()); + if (serialCoordinate.FESpace() != &serialCoordinateSpace) { + throw std::runtime_error( + "Exterior coordinate values are not associated with the " + "supplied finite-element space." + ); + } - //================================================================== - // Section 2: Domain Mapping - //================================================================== - auto [r_star_ref, r_inf_ref] = utils::discover_bounds(fem.mesh.get(), 3) - .or_else([](const boundary::BoundsError &err)-> std::expected { - throw std::runtime_error("Unable to determine vacuum domain reference boundary..."); - }).value(); + if (serialCoordinateSpace.GetMesh() != fem.smesh.mesh.get()) { + throw std::runtime_error( + "Exterior coordinate space is not associated with the " + "loaded STROID mesh." + ); + } - fem.mapping = std::make_unique(r_star_ref, r_inf_ref); + if (serialCoordinateSpace.GetVDim() != 1) { + throw std::runtime_error( + "Exterior coordinate must be a scalar field." + ); + } - //================================================================== - // Section 3: Multi-physics Block-offsets - //================================================================== - fem.block_true_offsets.SetSize(3); - fem.block_true_offsets[0] = 0; - fem.block_true_offsets[1] = fem.Vec_H1_fes->GetTrueVSize(); - fem.block_true_offsets[2] = fem.block_true_offsets[1] + fem.L2_fes->GetTrueVSize(); + if (serialCoordinate.Size() != serialCoordinateSpace.GetVSize()) { + throw std::runtime_error( + "Exterior coordinate value count does not match its " + "finite-element space." + ); + } - fem.gravity_block_true_offsets.SetSize(3); - fem.gravity_block_true_offsets[0] = 0; - fem.gravity_block_true_offsets[1] = fem.RT_fes->GetTrueVSize(); - fem.gravity_block_true_offsets[2] = fem.gravity_block_true_offsets[1] + fem.L2_fes->GetTrueVSize(); + const int compactificationOrder = + serialCoordinateSpace.GetMaxElementOrder(); - //================================================================== - // Section 4: Multipole BC setup. - //================================================================== - fem.com.SetSize(dim); + const int dimension = fem.mesh->Dimension(); + + fem.compactificationFec = std::make_unique( + compactificationOrder, dimension + ); + + fem.compactificationFes = std::make_unique( + fem.mesh.get(), fem.compactificationFec.get() + ); + + mfem::ParGridFunction distributedCoordinate( + fem.mesh.get(), &serialCoordinate, meshPartitioning.get() + ); + + if (distributedCoordinate.Size() != + fem.compactificationFes->GetVSize()) { + throw std::runtime_error( + "Distributed exterior coordinate does not match the " + "constructed parallel finite-element space." + ); + } + + fem.compactificationCoordinate = + std::make_unique( + fem.compactificationFes.get() + ); + + *fem.compactificationCoordinate = distributedCoordinate; + + double localMinimum = std::numeric_limits::infinity(); + + double localMaximum = -std::numeric_limits::infinity(); + + for (int index = 0; index < fem.compactificationCoordinate->Size(); + ++index) { + const double value = (*fem.compactificationCoordinate)(index); + + if (!std::isfinite(value)) { + throw std::runtime_error( + "Exterior coordinate contains a non-finite value." + ); + } + + localMinimum = std::min(localMinimum, value); + + localMaximum = std::max(localMaximum, value); + } + + double globalMinimum = 0.0; + double globalMaximum = 0.0; + + MPI_Allreduce( + &localMinimum, &globalMinimum, 1, MPI_DOUBLE, MPI_MIN, + MPI_COMM_WORLD + ); + + MPI_Allreduce( + &localMaximum, &globalMaximum, 1, MPI_DOUBLE, MPI_MAX, + MPI_COMM_WORLD + ); + + constexpr double coordinateTolerance = 1.0e-12; + + if (globalMinimum < -coordinateTolerance || + globalMaximum > 1.0 + coordinateTolerance) { + throw std::runtime_error( + "Exterior coordinate lies outside the expected " + "interval [0, 1]." + ); + } + + // ===================================================================== + // Section 3: Compile-time field realization + // ===================================================================== + + // --------------------------------------------------------------------- + // Gravity potential: scalar L2 + // --------------------------------------------------------------------- + + fem.gravityPotentialFec = + GravityField::make_fec(dimension); + + fem.gravityPotentialFes = GravityField::make_fespace( + *fem.mesh, *fem.gravityPotentialFec + ); + + // --------------------------------------------------------------------- + // Gravity flux: H(div)/RT. Basis choices are encoded by field.mfem. + // --------------------------------------------------------------------- + + fem.gravityFluxFec = GravityField::make_fec(dimension); + + fem.gravityFluxFes = GravityField::make_fespace( + *fem.mesh, *fem.gravityFluxFec + ); + + // --------------------------------------------------------------------- + // Displacement: vector H1. Ordering is encoded by field.mfem. + // --------------------------------------------------------------------- + + fem.displacementFec = + DisplacementField::make_fec(dimension); + + fem.displacementFes = + DisplacementField::make_fespace( + *fem.mesh, *fem.displacementFec + ); + + fem.displacement = + std::make_unique(fem.displacementFes.get()); + + *fem.displacement = 0.0; + + // --------------------------------------------------------------------- + // Density: scalar discontinuous L2 + // --------------------------------------------------------------------- + + fem.densityFec = DensityField::make_fec(dimension); + + fem.densityFes = DensityField::make_fespace( + *fem.mesh, *fem.densityFec + ); + + // --------------------------------------------------------------------- + // Specific enthalpy: scalar continuous H1 + // --------------------------------------------------------------------- + + fem.enthalpyFec = EnthalpyField::make_fec(dimension); + + fem.enthalpyFes = EnthalpyField::make_fespace( + *fem.mesh, *fem.enthalpyFec + ); + + // ===================================================================== + // Section 4: Domain mapping + // ===================================================================== + + auto [stellarRadiusReference, infinityRadiusReference] = + utils::discover_bounds(fem.mesh.get(), 3) + .or_else( + [](const boundary::BoundsError &) + -> std::expected< + boundary::Bounds, boundary::BoundsError> { + throw std::runtime_error( + "Unable to determine vacuum-domain reference " + "boundaries." + ); + } + ) + .value(); + + fem.mapping = std::make_unique( + *fem.displacement, stellarRadiusReference, infinityRadiusReference + ); + + // ===================================================================== + // Section 5: Block offsets + // + // Legacy layouts only. New coupled operators use :utils.blocks forms. + // + // Main system: [Displacement | Density] + // Gravity system: [Flux | Potential] + // ===================================================================== + + fem.blockTrueOffsets.SetSize(3); + fem.blockTrueOffsets[0] = 0; + + fem.blockTrueOffsets[1] = fem.displacementFes->GetTrueVSize(); + + fem.blockTrueOffsets[2] = + fem.blockTrueOffsets[1] + fem.densityFes->GetTrueVSize(); + + fem.gravityBlockTrueOffsets.SetSize(3); + fem.gravityBlockTrueOffsets[0] = 0; + + fem.gravityBlockTrueOffsets[1] = fem.gravityFluxFes->GetTrueVSize(); + + fem.gravityBlockTrueOffsets[2] = + fem.gravityBlockTrueOffsets[1] + + fem.gravityPotentialFes->GetTrueVSize(); + + // ===================================================================== + // Section 6: Multipole data + // ===================================================================== + + fem.com.SetSize(dimension); fem.com = 0.0; - fem.Q.SetSize(dim, dim); + + fem.Q.SetSize(dimension, dimension); fem.Q = 0.0; - //================================================================== - // Section 5: Integration Rules - //================================================================== - MFEM_ASSERT(fem.mesh->GetElementGeometry(0) == mfem::Geometry::CUBE, - "Currently only hexahedral meshes are supported"); - const int element_order = fem.H1_fes->GetMaxElementOrder(); - fem.int_order = 2 * element_order + geom_order - 2 + args.quad_boost; + // ===================================================================== + // Section 7: Essential boundaries and domain masks + // ===================================================================== - fem.int_rule = std::make_unique(mfem::IntRules.Get(mfem::Geometry::CUBE, fem.int_order)); + fem.essentialDisplacementTdofs.SetSize(0); - //================================================================== - // Section 6: Essential Boundaries & Domain Masks - //================================================================== - fem.ess_v_tdofs.SetSize(0); + populate_element_mask( + fem.mesh.get(), utils::DOMAINS::STELLAR, + fem.gravityContext.stellar_mask + ); - populate_element_mask(fem.mesh.get(), utils::DOMAINS::STELLAR, fem.gravity_context.stellar_mask); + const int boundaryAttributeCount = fem.mesh->bdr_attributes.Max(); - const int n_bdr_attrs = fem.mesh->bdr_attributes.Max(); - fem.boundary_context.inf_bounds.SetSize(n_bdr_attrs); - fem.boundary_context.stellar_bounds.SetSize(n_bdr_attrs); + fem.boundaryContext.inf_bounds.SetSize(boundaryAttributeCount); - fem.boundary_context.inf_bounds = 0; - fem.boundary_context.stellar_bounds = 0; + fem.boundaryContext.stellar_bounds.SetSize(boundaryAttributeCount); - fem.boundary_context.inf_bounds[static_cast(boundary::Boundaries::INF_SURFACE) - 1] = 1; - fem.boundary_context.stellar_bounds[static_cast(boundary::Boundaries::STELLAR_SURFACE) - 1] = 1; + fem.boundaryContext.inf_bounds = 0; + fem.boundaryContext.stellar_bounds = 0; - //================================================================== - // Section 7: Gravity Context Setup - //================================================================== - fem.gravity_context.minres = std::make_unique(fem.mesh->GetComm()); - fem.gravity_context.minres->SetRelTol(1e-12); - fem.gravity_context.minres->SetAbsTol(1e-12); - fem.gravity_context.minres->SetMaxIter(1000); - fem.gravity_context.minres->SetPrintLevel(0); + fem.boundaryContext.inf_bounds + [static_cast(boundary::Boundaries::INF_SURFACE) - 1] = 1; - fem.gravity_context.prec_Phi = std::make_unique(); - fem.gravity_context.prec_Phi->SetPrintLevel(0); + fem.boundaryContext.stellar_bounds + [static_cast(boundary::Boundaries::STELLAR_SURFACE) - 1] = 1; - fem.gravity_context.block_prec = std::make_unique(fem.gravity_block_true_offsets); + // ===================================================================== + // Section 8: Gravity solver context + // ===================================================================== + + fem.gravityContext.minres = + std::make_unique(fem.mesh->GetComm()); + + fem.gravityContext.minres->SetRelTol(1.0e-12); + fem.gravityContext.minres->SetAbsTol(1.0e-12); + fem.gravityContext.minres->SetMaxIter(1000); + fem.gravityContext.minres->SetPrintLevel(0); + + fem.gravityContext.prec_Phi = std::make_unique(); + + fem.gravityContext.prec_Phi->SetPrintLevel(0); + + fem.gravityContext.block_prec = + std::make_unique( + fem.gravityBlockTrueOffsets + ); + + fem.gravityContext.minres->SetPreconditioner( + *fem.gravityContext.block_prec + ); + + // ===================================================================== + // Section 9: Vacuum true-DOF masks + // ===================================================================== - fem.gravity_context.minres->SetPreconditioner(*fem.gravity_context.block_prec); - //========================================================= - // Section 10: Set All vacuum elements true degrees of freedom - //========================================================= { - mfem::Array vacuum_mask; - utils::populate_element_mask(fem.mesh.get(), utils::DOMAINS::VACUUM, vacuum_mask); + mfem::Array vacuumMask; - utils::populate_domain_tdofs(fem.Vec_H1_fes.get(), vacuum_mask, fem.vacuum_tdof_v); - utils::populate_domain_tdofs(fem.L2_fes.get(), vacuum_mask, fem.vacuum_tdof_rho); + utils::populate_element_mask( + fem.mesh.get(), utils::DOMAINS::VACUUM, vacuumMask + ); + + utils::populate_domain_tdofs( + fem.displacementFes.get(), vacuumMask, + fem.vacuumDisplacementTdofs + ); + + utils::populate_domain_tdofs( + fem.densityFes.get(), vacuumMask, fem.vacuumDensityTdofs + ); + + utils::populate_domain_tdofs( + fem.enthalpyFes.get(), vacuumMask, fem.vacuumEnthalpyTdofs + ); } - const quadrature::QuadratureOptions& quadrature_options = args.quadrature; + // ===================================================================== + // Section 10: Quadrature policy + // ===================================================================== - if (quadrature_options.validation.reject_negative_boosts && quadrature_options.global_boost < 0) { - throw std::invalid_argument("Global quadrature boost cannot be negative."); + const quadrature::QuadratureOptions &quadratureOptions = + args.quadrature; + + if (quadratureOptions.validation.reject_negative_boosts && + quadratureOptions.global_boost < 0) { + throw std::invalid_argument( + "Global quadrature boost cannot be negative." + ); } - quadrature::RuleSet quadrature_rule_set = quadrature::make_rule_set(quadrature_options.mode, quadrature_options.global_boost); + quadrature::RuleSet quadratureRuleSet = quadrature::make_rule_set( + quadratureOptions.mode, quadratureOptions.global_boost + ); - if (quadrature_options.fallback_fixed_order.has_value()) { - if (*quadrature_options.fallback_fixed_order < 0) { - throw std::invalid_argument("Fallback quadrature order cannot be negative."); + if (quadratureOptions.fallback_fixed_order.has_value()) { + if (*quadratureOptions.fallback_fixed_order < 0) { + throw std::invalid_argument( + "Fallback quadrature order cannot be negative." + ); } - quadrature_rule_set.fallback.fixed_order = quadrature_options.fallback_fixed_order; + + quadratureRuleSet.fallback.fixed_order = + quadratureOptions.fallback_fixed_order; } - auto apply_quadrature_options = [&quadrature_options](quadrature::RuleControl& rule_control, const quadrature::QuadratureTermOptions& term_options) { - if (term_options.fixed_order.has_value() && *term_options.fixed_order < 0) { - throw std::invalid_argument("Fixed quadrature order cannot be negative."); - } + auto apply_quadrature_options = + [&quadratureOptions]( + quadrature::RuleControl &ruleControl, + const quadrature::QuadratureTermOptions &termOptions + ) { + if (termOptions.fixed_order.has_value() && + *termOptions.fixed_order < 0) { + throw std::invalid_argument( + "Fixed quadrature order cannot be negative." + ); + } - if (quadrature_options.validation.reject_negative_boosts && term_options.additional_boost < 0) { - throw std::invalid_argument("Term quadrature boost cannot be negative."); - } + if (quadratureOptions.validation.reject_negative_boosts && + termOptions.additional_boost < 0) { + throw std::invalid_argument( + "Term quadrature boost cannot be negative." + ); + } - rule_control.boost += term_options.additional_boost; + ruleControl.boost += termOptions.additional_boost; - if (term_options.fixed_order.has_value()) { - rule_control.fixed_order = term_options.fixed_order; - } - }; + if (termOptions.fixed_order.has_value()) { + ruleControl.fixed_order = termOptions.fixed_order; + } + }; - apply_quadrature_options(quadrature_rule_set.gravity_hdiv_mass, quadrature_options.gravity_hdiv_mass); - apply_quadrature_options(quadrature_rule_set.gravity_divergence, quadrature_options.gravity_divergence); - apply_quadrature_options(quadrature_rule_set.gravity_source, quadrature_options.gravity_source); - apply_quadrature_options(quadrature_rule_set.gravity_boundary, quadrature_options.gravity_boundary); - apply_quadrature_options(quadrature_rule_set.density_projection, quadrature_options.density_projection); - apply_quadrature_options(quadrature_rule_set.mass_conservation, quadrature_options.mass_conservation); - apply_quadrature_options(quadrature_rule_set.center_of_mass, quadrature_options.center_of_mass); - apply_quadrature_options(quadrature_rule_set.quadrupole, quadrature_options.quadrupole); - apply_quadrature_options(quadrature_rule_set.gravitational_energy, quadrature_options.gravitational_energy); - apply_quadrature_options(quadrature_rule_set.virial, quadrature_options.virial); - apply_quadrature_options(quadrature_rule_set.error_norm, quadrature_options.error_norm); + apply_quadrature_options( + quadratureRuleSet.gravity_hdiv_mass, + quadratureOptions.gravity_hdiv_mass + ); - apply_quadrature_options(quadrature_rule_set.roles.discretization, quadrature_options.roles.discretization); - apply_quadrature_options(quadrature_rule_set.roles.preconditioner, quadrature_options.roles.preconditioner); - apply_quadrature_options(quadrature_rule_set.roles.diagnostic, quadrature_options.roles.diagnostic); - apply_quadrature_options(quadrature_rule_set.roles.projection, quadrature_options.roles.projection); + apply_quadrature_options( + quadratureRuleSet.gravity_divergence, + quadratureOptions.gravity_divergence + ); + + apply_quadrature_options( + quadratureRuleSet.gravity_source, quadratureOptions.gravity_source + ); + + apply_quadrature_options( + quadratureRuleSet.gravity_boundary, + quadratureOptions.gravity_boundary + ); + + apply_quadrature_options( + quadratureRuleSet.centrifugal, quadratureOptions.centrifugal + ); + + apply_quadrature_options( + quadratureRuleSet.density_projection, + quadratureOptions.density_projection + ); + + apply_quadrature_options( + quadratureRuleSet.eos_closure, quadratureOptions.eos_closure + ); + + apply_quadrature_options( + quadratureRuleSet.hydrostatic_equilibrium, + quadratureOptions.hydrostatic_equilibrium + ); + + apply_quadrature_options( + quadratureRuleSet.isobaric_surface, + quadratureOptions.isobaric_surface + ); + + apply_quadrature_options( + quadratureRuleSet.mesh_extension, quadratureOptions.mesh_extension + ); + + apply_quadrature_options( + quadratureRuleSet.mass_conservation, + quadratureOptions.mass_conservation + ); + + apply_quadrature_options( + quadratureRuleSet.mass_normalization, + quadratureOptions.mass_normalization + ); + + apply_quadrature_options( + quadratureRuleSet.center_of_mass, quadratureOptions.center_of_mass + ); + + apply_quadrature_options( + quadratureRuleSet.quadrupole, quadratureOptions.quadrupole + ); + + apply_quadrature_options( + quadratureRuleSet.gravitational_energy, + quadratureOptions.gravitational_energy + ); + + apply_quadrature_options( + quadratureRuleSet.pressure_integral, + quadratureOptions.pressure_integral + ); + + apply_quadrature_options( + quadratureRuleSet.pressure_force, quadratureOptions.pressure_force + ); + + apply_quadrature_options( + quadratureRuleSet.virial, quadratureOptions.virial + ); + + apply_quadrature_options( + quadratureRuleSet.error_norm, quadratureOptions.error_norm + ); + + apply_quadrature_options( + quadratureRuleSet.roles.discretization, + quadratureOptions.roles.discretization + ); + + apply_quadrature_options( + quadratureRuleSet.roles.preconditioner, + quadratureOptions.roles.preconditioner + ); + + apply_quadrature_options( + quadratureRuleSet.roles.diagnostic, + quadratureOptions.roles.diagnostic + ); + + apply_quadrature_options( + quadratureRuleSet.roles.projection, + quadratureOptions.roles.projection + ); + + fem.quadratureFactory = std::make_unique( + quadrature::Policy(std::move(quadratureRuleSet)) + ); + + // ===================================================================== + // Section 11: Stateless domain mapper + // ===================================================================== + + auto exteriorDomain = std::make_unique< + const mapping::compactification::KelvinCompactification>( + args.kelvin_options + ); + + fem.domainMapperStateless = + std::make_unique( + args.domain_mapper_options, std::move(exteriorDomain) + ); - fem.quadrature_factory = std::make_unique(quadrature::Policy(std::move(quadrature_rule_set))); return fem; } -} - +} // namespace mean_field::fem \ No newline at end of file diff --git a/libmeanfield/impl/integrators/advection.cpp b/libmeanfield/impl/integrators/advection.cpp index dac2bf1..4aee392 100644 --- a/libmeanfield/impl/integrators/advection.cpp +++ b/libmeanfield/impl/integrators/advection.cpp @@ -4,7 +4,9 @@ module; module mean_field; namespace mean_field::integrators { - AdvectionIntegrator::AdvectionIntegrator(const mapping::DomainMapper &map) : m_map(map) {} + AdvectionIntegrator::AdvectionIntegrator(const mapping::DomainMapper &map) + : m_map(map) { + } void AdvectionIntegrator::AssembleElementVector( const mfem::Array &el, @@ -16,17 +18,17 @@ namespace mean_field::integrators { return; } - const mfem::FiniteElement *fe_v = el[0]; + const mfem::FiniteElement *fe_v = el[0]; const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - const mfem::Vector &v_dofs = *elfun[0]; - const mfem::Vector &rho_dofs = *elfun[1]; + const mfem::Vector &v_dofs = *elfun[0]; + const mfem::Vector &rho_dofs = *elfun[1]; - mfem::Vector &r_v = *elvec[0]; + mfem::Vector &r_v = *elvec[0]; r_v.SetSize(dof_v * dim); r_v = 0.0; if (elvec[1]) { @@ -37,7 +39,8 @@ namespace mean_field::integrators { mfem::Vector shape_v(dof_v), shape_rho(dof_rho); mfem::DenseMatrix dshape_v_ref(dof_v, dim), dshape_v_phys(dof_v, dim); - const mfem::IntegrationRule *ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder() + 1); + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder() + 1); for (int q = 0; q < ir->GetNPoints(); q++) { const mfem::IntegrationPoint &ip = ir->IntPoint(q); @@ -80,7 +83,8 @@ namespace mean_field::integrators { for (int i = 0; i < dof_v; ++i) { for (int c = 0; c < dim; ++c) { - r_v(i + c * dof_v) += shape_v(i) * rho_val * adv_val(c) * weight; + r_v(i + c * dof_v) += + shape_v(i) * rho_val * adv_val(c) * weight; } } } @@ -91,27 +95,30 @@ namespace mean_field::integrators { mfem::ElementTransformation &Tr, const mfem::Array &elfun, const mfem::Array2D &elmats - ) { - const mfem::FiniteElement *fe_v = el[0]; + ) { + const mfem::FiniteElement *fe_v = el[0]; const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - const mfem::Vector &v_dofs = *elfun[0]; - const mfem::Vector &rho_dofs = *elfun[1]; + const mfem::Vector &v_dofs = *elfun[0]; + const mfem::Vector &rho_dofs = *elfun[1]; - mfem::DenseMatrix *dv_dv = elmats(0, 0); - mfem::DenseMatrix *dv_drho = elmats(0, 1); + mfem::DenseMatrix *dv_dv = elmats(0, 0); + mfem::DenseMatrix *dv_drho = elmats(0, 1); - if (dv_dv) *dv_dv = 0.0; - if (dv_drho) *dv_drho = 0.0; + if (dv_dv) + *dv_dv = 0.0; + if (dv_drho) + *dv_drho = 0.0; mfem::Vector shape_v(dof_v), shape_rho(dof_rho); mfem::DenseMatrix dshape_v_ref(dof_v, dim), dshape_v_phys(dof_v, dim); - const mfem::IntegrationRule *ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder() + 1); + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder() + 1); for (int q = 0; q < ir->GetNPoints(); q++) { const mfem::IntegrationPoint &ip = ir->IntPoint(q); @@ -164,22 +171,27 @@ namespace mean_field::integrators { double v_dot_grad_phi_j = 0.0; for (int k = 0; k < dim; ++k) { - v_dot_grad_phi_j += v_val(k) * dshape_v_phys(j, k); + v_dot_grad_phi_j += + v_val(k) * dshape_v_phys(j, k); } for (int d = 0; d < dim; ++d) { // Trial function component - int col = j + d * dof_v; + int col = j + d * dof_v; // \rho (\delta \vec{v} \cdot \nabla \vec{v}) - // \delta v is along direction 'd' for the cth component of advection + // \delta v is along direction 'd' for the cth + // component of advection double termA = shape_v(j) * grad_v(c, d); // \rho(\vec{v} \cdot \nabla \delta \vec{v}) - // Only non-zero when the advected component matches the test component - double termB = (c == d) ? v_dot_grad_phi_j : 0.0; + // Only non-zero when the advected component + // matches the test component + double termB = + (c == d) ? v_dot_grad_phi_j : 0.0; - (*dv_dv)(row, col) += shape_v(i) * rho_val * (termA + termB) * weight; + (*dv_dv)(row, col) += shape_v(i) * rho_val * + (termA + termB) * weight; } } } @@ -192,7 +204,7 @@ namespace mean_field::integrators { for (int c = 0; c < dim; ++c) { int row = i + c * dof_v; for (int j = 0; j < dof_rho; ++j) { - int col = j; + int col = j; // \delta \rho * (\vec{v} \cdot \nabla \vec{v}) double term = shape_rho(j) * adv_val(c); @@ -203,4 +215,4 @@ namespace mean_field::integrators { } } } -} \ No newline at end of file +} // namespace mean_field::integrators \ No newline at end of file diff --git a/libmeanfield/impl/integrators/centrifugal.cpp b/libmeanfield/impl/integrators/centrifugal.cpp index 9837529..f7de9fe 100644 --- a/libmeanfield/impl/integrators/centrifugal.cpp +++ b/libmeanfield/impl/integrators/centrifugal.cpp @@ -3,41 +3,49 @@ module; module mean_field; namespace mean_field::integrators { - CentrifugalForceIntegrator::CentrifugalForceIntegrator( - const mapping::DomainMapper& map, - const mfem::Vector& omega - ) : m_map(map), m_omega(3) { - MFEM_ASSERT(omega.Size() == 3, "Omega vector must be 3D"); - m_omega = omega; - } - - void CentrifugalForceIntegrator::SetOmega(const mfem::Vector& omega) { + CentrifugalForceIntegrator::CentrifugalForceIntegrator( + const mapping::DomainMapper &map, + const mfem::Vector &omega + ) + : m_map(map), + m_omega(3) { MFEM_ASSERT(omega.Size() == 3, "Omega vector must be 3D"); m_omega = omega; } + void CentrifugalForceIntegrator::SetOmega(const mfem::Vector &omega) { + MFEM_ASSERT(omega.Size() == 3, "Omega vector must be 3D"); + m_omega = omega; + } + + void CentrifugalForceIntegrator::SetIntegrationRule( + const mfem::IntegrationRule &ir + ) { + m_ir = &ir; + } + void CentrifugalForceIntegrator::AssembleElementVector( const mfem::Array &el, mfem::ElementTransformation &Tr, const mfem::Array &elfun, const mfem::Array &elvec ) { - if (utils::is_vacuum(Tr, elvec)) { - return; - } + if (utils::is_vacuum(Tr, elvec)) { + return; + } - const mfem::FiniteElement* fe_v = el[0]; - const mfem::FiniteElement* fe_rho = el[1]; + const mfem::FiniteElement *fe_v = el[0]; + const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - const mfem::Vector& rho_dofs = *elfun[1]; + const mfem::Vector &rho_dofs = *elfun[1]; - mfem::Vector& r_v = *elvec[0]; - r_v = 0.0; + mfem::Vector &r_v = *elvec[0]; r_v.SetSize(dof_v * dim); + r_v = 0.0; if (elvec[1]) { elvec[1]->SetSize(dof_rho); *elvec[1] = 0.0; @@ -47,10 +55,15 @@ namespace mean_field::integrators { mfem::Vector x_phys(dim); mfem::Vector a(dim), b(dim); - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); + MFEM_VERIFY( + m_ir, "CentrifugalForceIntegrator must be configured with an " + "integration rule before assembly. Call " + "SetIntegrationRule first." + ); + const mfem::IntegrationRule *ir = m_ir; for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& ip = ir->IntPoint(q); + const mfem::IntegrationPoint &ip = ir->IntPoint(q); Tr.SetIntPoint(&ip); auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); @@ -61,14 +74,14 @@ namespace mean_field::integrators { m_map.GetPhysicalPoint(Tr, ip, x_phys); // ω x r - a(0) = m_omega(1) * x_phys(2) - m_omega(2) * x_phys(1); - a(1) = m_omega(2) * x_phys(0) - m_omega(0) * x_phys(2); - a(2) = m_omega(0) * x_phys(1) - m_omega(1) * x_phys(0); + a(0) = m_omega(1) * x_phys(2) - m_omega(2) * x_phys(1); + a(1) = m_omega(2) * x_phys(0) - m_omega(0) * x_phys(2); + a(2) = m_omega(0) * x_phys(1) - m_omega(1) * x_phys(0); // ω x (ω x r) [centrifugal acceleration] - b(0) = m_omega(1) * a(2) - m_omega(2) * a(1); - b(1) = m_omega(2) * a(0) - m_omega(0) * a(2); - b(2) = m_omega(0) * a(1) - m_omega(1) * a(0); + b(0) = m_omega(1) * a(2) - m_omega(2) * a(1); + b(1) = m_omega(2) * a(0) - m_omega(0) * a(2); + b(2) = m_omega(0) * a(1) - m_omega(1) * a(0); double rho_val = 0.0; for (int i = 0; i < dof_rho; ++i) { @@ -89,30 +102,39 @@ namespace mean_field::integrators { const mfem::Array &elfun, const mfem::Array2D &elmats ) { - const mfem::FiniteElement* fe_v = el[0]; - const mfem::FiniteElement* fe_rho = el[1]; + if (utils::is_vacuum(Tr, elmats)) { + return; + } + const mfem::FiniteElement *fe_v = el[0]; + const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - mfem::DenseMatrix* dv_dv = elmats(0,0); - mfem::DenseMatrix* dv_drho = elmats(0,1); + mfem::DenseMatrix *dv_dv = elmats(0, 0); + mfem::DenseMatrix *dv_drho = elmats(0, 1); - if (dv_dv) *dv_dv = 0.0; - if (elmats(1, 0)) *elmats(1, 0) = 0.0; - if (elmats(1, 1)) *elmats(1, 1) = 0.0; - if (dv_drho) *dv_drho = 0.0; - if (!dv_drho) return; + if (dv_dv) + *dv_dv = 0.0; + if (elmats(1, 0)) + *elmats(1, 0) = 0.0; + if (elmats(1, 1)) + *elmats(1, 1) = 0.0; + if (dv_drho) + *dv_drho = 0.0; + if (!dv_drho) + return; mfem::Vector shape_v(dof_v), shape_rho(dof_rho); mfem::Vector x_phys(dim); mfem::Vector a(dim), b(dim); - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& ip = ir->IntPoint(q); + const mfem::IntegrationPoint &ip = ir->IntPoint(q); Tr.SetIntPoint(&ip); auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); @@ -137,10 +159,11 @@ namespace mean_field::integrators { for (int c = 0; c < dim; ++c) { const int row = i + c * dof_v; for (int j = 0; j < dof_rho; ++j) { - (*dv_drho)(row, j) += shape_v(i) * shape_rho(j) * b(c) * weight; + (*dv_drho)(row, j) += + shape_v(i) * shape_rho(j) * b(c) * weight; } } } } } -} \ No newline at end of file +} // namespace mean_field::integrators \ No newline at end of file diff --git a/libmeanfield/impl/integrators/coriolis.cpp b/libmeanfield/impl/integrators/coriolis.cpp index f6a9c78..a1e9f94 100644 --- a/libmeanfield/impl/integrators/coriolis.cpp +++ b/libmeanfield/impl/integrators/coriolis.cpp @@ -4,38 +4,43 @@ module; module mean_field; namespace mean_field::integrators { - CoriolisIntegrator::CoriolisIntegrator(const mapping::DomainMapper& map, const mfem::Vector& omega) - : m_map(map), m_omega(omega) { + CoriolisIntegrator::CoriolisIntegrator( + const mapping::DomainMapper &map, + const mfem::Vector &omega + ) + : m_map(map), + m_omega(omega) { m_omega_mat.SetSize(3, 3); - m_omega_mat = 0.0; + m_omega_mat = 0.0; m_omega_mat(0, 1) = -m_omega(2); - m_omega_mat(0, 2) = m_omega(1); - m_omega_mat(1, 0) = m_omega(2); + m_omega_mat(0, 2) = m_omega(1); + m_omega_mat(1, 0) = m_omega(2); m_omega_mat(1, 2) = -m_omega(0); m_omega_mat(2, 0) = -m_omega(1); - m_omega_mat(2, 1) = m_omega(0); + m_omega_mat(2, 1) = m_omega(0); } - void CoriolisIntegrator::AssembleElementVector(const mfem::Array &el, - mfem::ElementTransformation &Tr, - const mfem::Array &elfun, - const mfem::Array &elvec + void CoriolisIntegrator::AssembleElementVector( + const mfem::Array &el, + mfem::ElementTransformation &Tr, + const mfem::Array &elfun, + const mfem::Array &elvec ) { if (utils::is_vacuum(Tr, elvec)) { return; } - const mfem::FiniteElement* fe_v = el[0]; - const mfem::FiniteElement* fe_rho = el[1]; + const mfem::FiniteElement *fe_v = el[0]; + const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - const mfem::Vector& v_dofs = *elfun[0]; - const mfem::Vector& rho_dofs = *elfun[1]; + const mfem::Vector &v_dofs = *elfun[0]; + const mfem::Vector &rho_dofs = *elfun[1]; - mfem::Vector& r_v = *elvec[0]; + mfem::Vector &r_v = *elvec[0]; r_v.SetSize(dof_v * dim); r_v = 0.0; if (elvec[1]) { @@ -44,10 +49,11 @@ namespace mean_field::integrators { } mfem::Vector shape_v(dof_v), shape_rho(dof_rho); - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& ip = ir->IntPoint(q); + const mfem::IntegrationPoint &ip = ir->IntPoint(q); Tr.SetIntPoint(&ip); auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); @@ -56,11 +62,14 @@ namespace mean_field::integrators { fe_rho->CalcShape(ip, shape_rho); double rho_val = 0.0; - for (int i = 0; i < dof_rho; ++i) rho_val += rho_dofs(i) * shape_rho(i); + for (int i = 0; i < dof_rho; ++i) + rho_val += rho_dofs(i) * shape_rho(i); - mfem::Vector v_val(dim); v_val = 0.0; + mfem::Vector v_val(dim); + v_val = 0.0; for (int i = 0; i < dof_v; ++i) { - for (int c = 0; c < dim; ++c) v_val(c) += v_dofs(i + c * dof_v) * shape_v(i); + for (int c = 0; c < dim; ++c) + v_val(c) += v_dofs(i + c * dof_v) * shape_v(i); } mfem::Vector F_coriolis(dim); @@ -69,39 +78,44 @@ namespace mean_field::integrators { for (int i = 0; i < dof_v; ++i) { for (int c = 0; c < dim; ++c) { - r_v(i + c * dof_v) += shape_v(i) * rho_val * F_coriolis(c) * weight; + r_v(i + c * dof_v) += + shape_v(i) * rho_val * F_coriolis(c) * weight; } } } } - void CoriolisIntegrator::AssembleElementGrad(const mfem::Array &el, - mfem::ElementTransformation &Tr, - const mfem::Array &elfun, - const mfem::Array2D &elmats + void CoriolisIntegrator::AssembleElementGrad( + const mfem::Array &el, + mfem::ElementTransformation &Tr, + const mfem::Array &elfun, + const mfem::Array2D &elmats ) { - const mfem::FiniteElement* fe_v = el[0]; - const mfem::FiniteElement* fe_rho = el[1]; + const mfem::FiniteElement *fe_v = el[0]; + const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - const mfem::Vector& v_dofs = *elfun[0]; - const mfem::Vector& rho_dofs = *elfun[1]; + const mfem::Vector &v_dofs = *elfun[0]; + const mfem::Vector &rho_dofs = *elfun[1]; - mfem::DenseMatrix* dv_dv = elmats(0, 0); - mfem::DenseMatrix* dv_drho = elmats(0, 1); + mfem::DenseMatrix *dv_dv = elmats(0, 0); + mfem::DenseMatrix *dv_drho = elmats(0, 1); - if (dv_dv) *dv_dv = 0.0; - if (dv_drho) *dv_drho = 0.0; + if (dv_dv) + *dv_dv = 0.0; + if (dv_drho) + *dv_drho = 0.0; mfem::Vector shape_v(dof_v), shape_rho(dof_rho); - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& ip = ir->IntPoint(q); + const mfem::IntegrationPoint &ip = ir->IntPoint(q); Tr.SetIntPoint(&ip); auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); @@ -110,11 +124,14 @@ namespace mean_field::integrators { fe_rho->CalcShape(ip, shape_rho); double rho_val = 0.0; - for (int i = 0; i < dof_rho; ++i) rho_val += rho_dofs(i) * shape_rho(i); + for (int i = 0; i < dof_rho; ++i) + rho_val += rho_dofs(i) * shape_rho(i); - mfem::Vector v_val(dim); v_val = 0.0; + mfem::Vector v_val(dim); + v_val = 0.0; for (int i = 0; i < dof_v; ++i) { - for (int c = 0; c < dim; ++c) v_val(c) += v_dofs(i + c * dof_v) * shape_v(i); + for (int c = 0; c < dim; ++c) + v_val(c) += v_dofs(i + c * dof_v) * shape_v(i); } mfem::Vector F_coriolis(dim); @@ -124,12 +141,14 @@ namespace mean_field::integrators { if (dv_dv) { for (int i = 0; i < dof_v; ++i) { for (int c = 0; c < dim; ++c) { - int row = i + c * dof_v; + const int row = i + c * dof_v; for (int j = 0; j < dof_v; ++j) { for (int d = 0; d < dim; ++d) { - int col = j + d * dof_v; + int col = j + d * dof_v; double coupling = m_omega_mat(c, d); - (*dv_dv)(row, col) += shape_v(i) * shape_v(j) * 2.0 * rho_val * coupling * weight; + (*dv_dv)(row, col) += shape_v(i) * shape_v(j) * + 2.0 * rho_val * coupling * + weight; } } } @@ -142,11 +161,12 @@ namespace mean_field::integrators { int row = i + c * dof_v; for (int j = 0; j < dof_rho; ++j) { int col = j; - (*dv_drho)(row, col) += shape_v(i) * shape_rho(j) * F_coriolis(c) * weight; + (*dv_drho)(row, col) += shape_v(i) * shape_rho(j) * + F_coriolis(c) * weight; } } } } } } -} \ No newline at end of file +} // namespace mean_field::integrators \ No newline at end of file diff --git a/libmeanfield/impl/integrators/gravity.cpp b/libmeanfield/impl/integrators/gravity.cpp index b04abad..e3b2783 100644 --- a/libmeanfield/impl/integrators/gravity.cpp +++ b/libmeanfield/impl/integrators/gravity.cpp @@ -1,124 +1,341 @@ module; #include module mean_field; +import :solver.fields; + +namespace { + using namespace mean_field; + + constexpr int velocity_block = + solver::block_index(solver::FieldBlock::velocity); + constexpr int density_block = + solver::block_index(solver::FieldBlock::density); + constexpr int gravity_gradient_block = + solver::block_index(solver::FieldBlock::gravity_gradient); + constexpr int displacement_block = + solver::block_index(solver::FieldBlock::displacement); +} // namespace namespace mean_field::integrators { - GravityForceIntegrator::GravityForceIntegrator( - const mapping::DomainMapper& map, - const mfem::GridFunction& phi - ): m_map(map), m_phi(&phi) {} + GravityMomentumIntegrator::GravityMomentumIntegrator( + const mapping::DomainMapper &map, + const GravityForceJacobianMode jacobian_mode + ) + : m_map(map), + m_jacobian_mode(jacobian_mode) { + } - void GravityForceIntegrator::SetPotential(const mfem::GridFunction& phi) { m_phi = φ }; + void GravityMomentumIntegrator::SetJacobianMode( + const GravityForceJacobianMode jacobian_mode + ) { + m_jacobian_mode = jacobian_mode; + } - void GravityForceIntegrator::AssembleElementVector( + void GravityMomentumIntegrator::SetIntegrationRule( + const mfem::IntegrationRule &integration_rule + ) { + m_integration_rule = &integration_rule; + } + + GravityForceJacobianMode + GravityMomentumIntegrator::GetJacobianMode() const { + return m_jacobian_mode; + } + + void GravityMomentumIntegrator::AssembleElementVector( const mfem::Array &el, mfem::ElementTransformation &Tr, const mfem::Array &elfun, const mfem::Array &elvec ) { - if (utils::is_vacuum(Tr, elvec)) { return; } - const mfem::FiniteElement* fe_v = el[0]; - const mfem::FiniteElement* fe_rho = el[1]; + MFEM_VERIFY( + m_integration_rule, + "GravityForceIntegrator must be configured with an " + "integration rule before assembly." + ); + MFEM_VERIFY( + el.Size() > gravity_gradient_block, + "GravityForceIntegrator requires velocity, density, and " + "gravity-gradient finite elements." + ); + MFEM_VERIFY( + elfun.Size() > gravity_gradient_block, + "GravityForceIntegrator requires velocity, density, and " + "gravity-gradient element states." + ); + MFEM_VERIFY( + elvec.Size() > velocity_block && elvec[velocity_block], + "GravityForceIntegrator requires a velocity residual block." + ); + MFEM_VERIFY( + el[velocity_block] && el[density_block] && + el[gravity_gradient_block], + "GravityForceIntegrator received a null finite element." + ); + MFEM_VERIFY( + elfun[density_block] && elfun[gravity_gradient_block], + "GravityForceIntegrator received a null element state." + ); - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const mfem::FiniteElement *velocity_element = el[velocity_block]; + const mfem::FiniteElement *density_element = el[density_block]; + const mfem::FiniteElement *gravity_gradient_element = + el[gravity_gradient_block]; - const mfem::Vector& rho_dofs = *elfun[1]; + const int velocity_dofs_count = velocity_element->GetDof(); + const int density_dofs_count = density_element->GetDof(); + const int gravity_gradient_dofs_count = + gravity_gradient_element->GetDof(); + const int dim = Tr.GetSpaceDim(); - mfem::Vector& r_v = *elvec[0]; - r_v.SetSize(dof_v * dim); - r_v = 0.0; - if (elvec[1]) { - elvec[1]->SetSize(dof_rho); - *elvec[1] = 0.0; + const mfem::Vector &density_dofs = *elfun[density_block]; + const mfem::Vector &gravity_gradient_dofs = + *elfun[gravity_gradient_block]; + + MFEM_VERIFY( + density_dofs.Size() == density_dofs_count, + "GravityForceIntegrator received an incorrectly sized density " + "state." + ); + MFEM_VERIFY( + gravity_gradient_dofs.Size() == gravity_gradient_dofs_count, + "GravityForceIntegrator received an incorrectly sized " + "gravity-gradient " + "state." + ); + + for (int block = 0; block < elvec.Size(); ++block) { + if (elvec[block]) { + *elvec[block] = 0.0; + } } - mfem::Vector shape_v(dof_v), shape_rho(dof_rho); - mfem::Vector grad_phi_ref(dim), grad_phi_phys(dim), grad_phi_elem(dim); + mfem::Vector &velocity_residual = *elvec[velocity_block]; + velocity_residual.SetSize(dim * velocity_dofs_count); + velocity_residual = 0.0; - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); + if (elvec.Size() > density_block && elvec[density_block]) { + elvec[density_block]->SetSize(density_dofs_count); + *elvec[density_block] = 0.0; + } - for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& ip = ir->IntPoint(q); - Tr.SetIntPoint(&ip); + if (elvec.Size() > gravity_gradient_block && + elvec[gravity_gradient_block]) { + elvec[gravity_gradient_block]->SetSize(gravity_gradient_dofs_count); + *elvec[gravity_gradient_block] = 0.0; + } - auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); - m_phi->GetGradient(Tr, grad_phi_elem); - mfem::DenseMatrix J_map(dim, dim), J_map_inv(dim, dim); - m_map.ComputeJacobian(Tr, J_map); - mfem::CalcInverse(J_map, J_map_inv); - J_map_inv.MultTranspose(grad_phi_elem, grad_phi_phys); + mfem::Vector velocity_shape(velocity_dofs_count); + mfem::Vector density_shape(density_dofs_count); + mfem::DenseMatrix gravity_gradient_shape( + gravity_gradient_dofs_count, dim + ); + mfem::Vector gravity_gradient_element_value(dim); + mfem::Vector gravity_gradient_physical_value(dim); - fe_v->CalcShape(ip, shape_v); - fe_rho->CalcShape(ip, shape_rho); + const mfem::IntegrationRule &integration_rule = *m_integration_rule; - double rho_val = 0.0; - for (int i = 0; i < dof_rho; ++i) { - rho_val += rho_dofs(i) * shape_rho(i); + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + Tr.SetIntPoint(&integration_point); + + const mapping::VolumeQuadratureContext context = + m_map.GetQuadratureContext(Tr, integration_point); + + velocity_element->CalcShape(integration_point, velocity_shape); + density_element->CalcShape(integration_point, density_shape); + gravity_gradient_element->CalcVShape(Tr, gravity_gradient_shape); + + gravity_gradient_shape.MultTranspose( + gravity_gradient_dofs, gravity_gradient_element_value + ); + context.J_inv.MultTranspose( + gravity_gradient_element_value, gravity_gradient_physical_value + ); + + double density_value = 0.0; + for (int i = 0; i < density_dofs_count; ++i) { + density_value += density_dofs(i) * density_shape(i); } - for (int i = 0; i < dof_v; ++i) { - for (int c = 0; c < dim; ++c) { - r_v(i + c * dof_v) += shape_v(i) * rho_val * grad_phi_phys(c) * weight; + for (int i = 0; i < velocity_dofs_count; ++i) { + for (int component = 0; component < dim; ++component) { + velocity_residual(i + component * velocity_dofs_count) += + velocity_shape(i) * density_value * + gravity_gradient_physical_value(component) * + context.weight; } } } } - void GravityForceIntegrator::AssembleElementGrad( + void GravityMomentumIntegrator::AssembleElementGrad( const mfem::Array &el, mfem::ElementTransformation &Tr, const mfem::Array &elfun, const mfem::Array2D &elmats ) { - const mfem::FiniteElement* fe_v = el[0]; - const mfem::FiniteElement* fe_rho = el[1]; + if (utils::is_vacuum(Tr, elmats)) { + return; + } - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + MFEM_VERIFY( + m_integration_rule, + "GravityForceIntegrator must be configured with an " + "integration rule before assembly." + ); + MFEM_VERIFY( + el.Size() > gravity_gradient_block, + "GravityForceIntegrator requires velocity, density, and " + "gravity-gradient finite elements." + ); + MFEM_VERIFY( + elfun.Size() > gravity_gradient_block, + "GravityForceIntegrator requires velocity, density, and " + "gravity-gradient element states." + ); + MFEM_VERIFY( + el[velocity_block] && el[density_block] && + el[gravity_gradient_block], + "GravityForceIntegrator received a null finite element." + ); + MFEM_VERIFY( + elfun[density_block] && elfun[gravity_gradient_block], + "GravityForceIntegrator received a null element state." + ); - mfem::DenseMatrix* dv_dv = elmats(0, 0); - mfem::DenseMatrix* dv_drho = elmats(0, 1); + for (int row = 0; row < elmats.NumRows(); ++row) { + for (int column = 0; column < elmats.NumCols(); ++column) { + if (elmats(row, column)) { + *elmats(row, column) = 0.0; + } + } + } - if (dv_dv) *dv_dv = 0.0; - if (dv_drho) *dv_drho = 0.0; + if (m_jacobian_mode == GravityForceJacobianMode::exact) { + MFEM_ABORT( + "Exact GravityForceIntegrator geometry Jacobian is unavailable " + "until " + "DomainMapper linearization is " + "implemented." + ); + } - if (!dv_drho) return; + const mfem::FiniteElement *velocity_element = el[velocity_block]; + const mfem::FiniteElement *density_element = el[density_block]; + const mfem::FiniteElement *gravity_gradient_element = + el[gravity_gradient_block]; - mfem::Vector shape_v(dof_v), shape_rho(dof_rho); - mfem::Vector grad_phi_ref(dim), grad_phi_phys(dim), grad_phi_elem(dim); + const int velocity_dofs_count = velocity_element->GetDof(); + const int density_dofs_count = density_element->GetDof(); + const int gravity_gradient_dofs_count = + gravity_gradient_element->GetDof(); + const int dim = Tr.GetSpaceDim(); - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); + const mfem::Vector &density_dofs = *elfun[density_block]; + const mfem::Vector &gravity_gradient_dofs = + *elfun[gravity_gradient_block]; - for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& ip = ir->IntPoint(q); - Tr.SetIntPoint(&ip); + MFEM_VERIFY( + density_dofs.Size() == density_dofs_count, + "GravityForceIntegrator received an incorrectly sized density " + "state." + ); + MFEM_VERIFY( + gravity_gradient_dofs.Size() == gravity_gradient_dofs_count, + "GravityForceIntegrator received an incorrectly sized " + "gravity-gradient " + "state." + ); - auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); - m_phi->GetGradient(Tr, grad_phi_elem); - mfem::DenseMatrix J_map(dim, dim), J_map_inv(dim, dim); - m_map.ComputeJacobian(Tr, J_map); - mfem::CalcInverse(J_map, J_map_inv); - J_map_inv.MultTranspose(grad_phi_elem, grad_phi_phys); + mfem::DenseMatrix *dv_drho = elmats(velocity_block, density_block); + mfem::DenseMatrix *dv_dgrad_phi = + m_jacobian_mode == GravityForceJacobianMode::field_coupled + ? elmats(velocity_block, gravity_gradient_block) + : nullptr; - fe_v->CalcShape(ip, shape_v); - fe_rho->CalcShape(ip, shape_rho); + if (!dv_drho && !dv_dgrad_phi) { + return; + } + mfem::Vector velocity_shape(velocity_dofs_count); + mfem::Vector density_shape(density_dofs_count); + mfem::DenseMatrix gravity_gradient_shape( + gravity_gradient_dofs_count, dim + ); + mfem::Vector gravity_gradient_element_value(dim); + mfem::Vector gravity_gradient_physical_value(dim); + mfem::Vector gravity_basis_element(dim); + mfem::Vector gravity_basis_physical(dim); - for (int i = 0; i < dof_v; ++i) { - for (int c = 0; c < dim; ++c) { - const int row = i + c * dof_v; - for (int j = 0; j < dof_rho; ++j) { - (*dv_drho)(row, j) += shape_v(i) * shape_rho(j) * grad_phi_phys(c) * weight; + const mfem::IntegrationRule &integration_rule = *m_integration_rule; + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + Tr.SetIntPoint(&integration_point); + + const mapping::VolumeQuadratureContext context = + m_map.GetQuadratureContext(Tr, integration_point); + + velocity_element->CalcShape(integration_point, velocity_shape); + density_element->CalcShape(integration_point, density_shape); + gravity_gradient_element->CalcVShape(Tr, gravity_gradient_shape); + + gravity_gradient_shape.MultTranspose( + gravity_gradient_dofs, gravity_gradient_element_value + ); + context.J_inv.MultTranspose( + gravity_gradient_element_value, gravity_gradient_physical_value + ); + + double density_value = 0.0; + for (int i = 0; i < density_dofs_count; ++i) { + density_value += density_dofs(i) * density_shape(i); + } + + if (dv_drho) { + for (int i = 0; i < velocity_dofs_count; ++i) { + for (int component = 0; component < dim; ++component) { + const int row = i + component * velocity_dofs_count; + + for (int j = 0; j < density_dofs_count; ++j) { + (*dv_drho)(row, j) += + velocity_shape(i) * density_shape(j) * + gravity_gradient_physical_value(component) * + context.weight; + } + } + } + } + + if (dv_dgrad_phi) { + for (int j = 0; j < gravity_gradient_dofs_count; ++j) { + for (int component = 0; component < dim; ++component) { + gravity_basis_element(component) = + gravity_gradient_shape(j, component); + } + + context.J_inv.MultTranspose( + gravity_basis_element, gravity_basis_physical + ); + + for (int i = 0; i < velocity_dofs_count; ++i) { + for (int component = 0; component < dim; ++component) { + const int row = i + component * velocity_dofs_count; + (*dv_dgrad_phi)(row, j) += + velocity_shape(i) * density_value * + gravity_basis_physical(component) * + context.weight; + } } } } } } -} \ No newline at end of file +} // namespace mean_field::integrators \ No newline at end of file diff --git a/libmeanfield/impl/integrators/mass_continuity.cpp b/libmeanfield/impl/integrators/mass_continuity.cpp index b10d6ee..cf79f39 100644 --- a/libmeanfield/impl/integrators/mass_continuity.cpp +++ b/libmeanfield/impl/integrators/mass_continuity.cpp @@ -4,7 +4,10 @@ module; module mean_field; namespace mean_field::integrators { - ContinuityVolumeIntegrator::ContinuityVolumeIntegrator(const mapping::DomainMapper& map) : m_map(map) {}; + ContinuityVolumeIntegrator::ContinuityVolumeIntegrator( + const mapping::DomainMapper &map + ) + : m_map(map) { }; void ContinuityVolumeIntegrator::AssembleElementVector( const mfem::Array &el, @@ -16,35 +19,37 @@ namespace mean_field::integrators { return; } - const mfem::FiniteElement *fe_v = el[0]; + const mfem::FiniteElement *fe_v = el[0]; const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - const mfem::Vector v_dofs = *elfun[0]; - const mfem::Vector rho_dofs = *elfun[1]; + const mfem::Vector v_dofs = *elfun[0]; + const mfem::Vector rho_dofs = *elfun[1]; - void* data_rho_before = elvec[1] ? (void*)elvec[1]->GetData() : nullptr; + void *data_rho_before = + elvec[1] ? (void *)elvec[1]->GetData() : nullptr; int size_rho_before = elvec[1] ? elvec[1]->Size() : -1; if (elvec[0]) { elvec[0]->SetSize(dof_v * dim); *elvec[0] = 0.0; } - mfem::Vector& r_rho = *elvec[1]; + mfem::Vector &r_rho = *elvec[1]; r_rho.SetSize(dof_rho); r_rho = 0.0; - mfem::Vector shape_v(dof_v), shape_rho(dof_rho); - mfem::DenseMatrix dshape_rho_ref(dof_rho, dim), dshape_rho_phys(dof_rho, dim); + mfem::DenseMatrix dshape_rho_ref(dof_rho, dim), + dshape_rho_phys(dof_rho, dim); - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& ip = ir->IntPoint(q); + const mfem::IntegrationPoint &ip = ir->IntPoint(q); Tr.SetIntPoint(&ip); auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); @@ -54,7 +59,8 @@ namespace mean_field::integrators { fe_rho->CalcDShape(ip, dshape_rho_ref); mfem::Mult(dshape_rho_ref, J_inv, dshape_rho_phys); - mfem::Vector v_val(dim); v_val = 0.0; + mfem::Vector v_val(dim); + v_val = 0.0; for (int i = 0; i < dof_v; ++i) { for (int c = 0; c < dim; ++c) { const int row = i + c * dof_v; @@ -83,32 +89,38 @@ namespace mean_field::integrators { const mfem::Array2D &elmats ) { - const mfem::FiniteElement *fe_v = el[0]; + const mfem::FiniteElement *fe_v = el[0]; const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - const mfem::Vector& v_dofs = *elfun[0]; - const mfem::Vector& rho_dofs = *elfun[1]; + const mfem::Vector &v_dofs = *elfun[0]; + const mfem::Vector &rho_dofs = *elfun[1]; - mfem::DenseMatrix* drho_dv = elmats(1, 0); - mfem::DenseMatrix* drho_drho = elmats(1, 1); + mfem::DenseMatrix *drho_dv = elmats(1, 0); + mfem::DenseMatrix *drho_drho = elmats(1, 1); - if (elmats(0, 0)) *elmats(0, 0) = 0.0; - if (elmats(0, 1)) *elmats(0, 1) = 0.0; + if (elmats(0, 0)) + *elmats(0, 0) = 0.0; + if (elmats(0, 1)) + *elmats(0, 1) = 0.0; - if (drho_dv) *drho_dv = 0.0; - if (drho_drho) *drho_drho = 0.0; + if (drho_dv) + *drho_dv = 0.0; + if (drho_drho) + *drho_drho = 0.0; mfem::Vector shape_v(dof_v), shape_rho(dof_rho); - mfem::DenseMatrix dshape_rho_ref(dof_rho, dim), dshape_rho_phys(dof_rho, dim); + mfem::DenseMatrix dshape_rho_ref(dof_rho, dim), + dshape_rho_phys(dof_rho, dim); - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& ip = ir->IntPoint(q); + const mfem::IntegrationPoint &ip = ir->IntPoint(q); Tr.SetIntPoint(&ip); auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); @@ -118,7 +130,8 @@ namespace mean_field::integrators { fe_rho->CalcDShape(ip, dshape_rho_ref); mfem::Mult(dshape_rho_ref, J_inv, dshape_rho_phys); - mfem::Vector v_val(dim); v_val = 0.0; + mfem::Vector v_val(dim); + v_val = 0.0; for (int i = 0; i < dof_v; ++i) { for (int c = 0; c < dim; ++c) { const int row = i + c * dof_v; @@ -136,7 +149,8 @@ namespace mean_field::integrators { for (int j = 0; j < dof_v; ++j) { for (int d = 0; d < dim; ++d) { const int col = j + d * dof_v; - (*drho_dv)(i, col) -= dshape_rho_phys(i, d) * rho_val * shape_v(j) * weight; + (*drho_dv)(i, col) -= dshape_rho_phys(i, d) * + rho_val * shape_v(j) * weight; } } } @@ -149,15 +163,19 @@ namespace mean_field::integrators { grad_psi_dot_v += dshape_rho_phys(i, c) * v_val(c); } for (int j = 0; j < dof_rho; ++j) { - (*drho_drho)(i, j) -= grad_psi_dot_v * shape_rho(j) * weight; - + (*drho_drho)(i, j) -= + grad_psi_dot_v * shape_rho(j) * weight; } } } } } - ContinuityFaceIntegrator::ContinuityFaceIntegrator(const mapping::DomainMapper& map): m_map(map) {} + ContinuityFaceIntegrator::ContinuityFaceIntegrator( + const mapping::DomainMapper &map + ) + : m_map(map) { + } void ContinuityFaceIntegrator::AssembleFaceVector( const mfem::Array &el1, @@ -166,19 +184,19 @@ namespace mean_field::integrators { const mfem::Array &elfun, const mfem::Array &elvect ) { - const mfem::FiniteElement *fe_v_minus = el1[0]; - const mfem::FiniteElement *fe_v_plus = el2[0]; + const mfem::FiniteElement *fe_v_minus = el1[0]; + const mfem::FiniteElement *fe_v_plus = el2[0]; const mfem::FiniteElement *fe_rho_minus = el1[1]; - const mfem::FiniteElement *fe_rho_plus = el2[1]; + const mfem::FiniteElement *fe_rho_plus = el2[1]; - const int dof_v_minus = fe_v_minus->GetDof(); - const int dof_v_plus = fe_v_plus->GetDof(); + const int dof_v_minus = fe_v_minus->GetDof(); + const int dof_v_plus = fe_v_plus->GetDof(); - const int dof_rho_minus = fe_rho_minus->GetDof(); - const int dof_rho_plus = fe_rho_plus->GetDof(); + const int dof_rho_minus = fe_rho_minus->GetDof(); + const int dof_rho_plus = fe_rho_plus->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dim = Tr.GetSpaceDim(); if (elvect[0]) { elvect[0]->SetSize(dim * dof_v_minus + dim * dof_v_plus); @@ -186,10 +204,10 @@ namespace mean_field::integrators { } mfem::Vector &r_rho = *elvect[1]; r_rho.SetSize(dof_rho_minus + dof_rho_plus); - r_rho = 0.0; + r_rho = 0.0; const int attr_minus = Tr.Elem1->Attribute; - const int attr_plus = (Tr.Elem2 != nullptr) ? Tr.Elem2->Attribute : -1; + const int attr_plus = (Tr.Elem2 != nullptr) ? Tr.Elem2->Attribute : -1; constexpr int VACUUM_ATTR = 3; if (attr_minus == VACUUM_ATTR || attr_plus == VACUUM_ATTR) { @@ -200,30 +218,39 @@ namespace mean_field::integrators { return; // Boundary face, } - const mfem::Vector &v_dofs = *elfun[0]; // Size: dim * dof_v_minus + dim*dof_v_plus - const mfem::Vector &rho_dofs = *elfun[1]; // Size: dof_rho_minus + dof_rho_plus + const mfem::Vector &v_dofs = + *elfun[0]; // Size: dim * dof_v_minus + dim*dof_v_plus + const mfem::Vector &rho_dofs = + *elfun[1]; // Size: dof_rho_minus + dof_rho_plus // Helpers to auto offset to the correct point in the dof array - auto rho_minus_dof = [&](const int i) {return rho_dofs(i);}; - auto rho_plus_dof = [&](const int i) {return rho_dofs(i + dof_rho_minus);}; - auto v_minus_dof = [&](const int k, const int c) {return v_dofs(k + c * dof_v_minus);}; + auto rho_minus_dof = [&](const int i) { return rho_dofs(i); }; + auto rho_plus_dof = [&](const int i) { + return rho_dofs(i + dof_rho_minus); + }; + auto v_minus_dof = [&](const int k, const int c) { + return v_dofs(k + c * dof_v_minus); + }; - const int p_v = fe_v_minus->GetOrder(); - const int p_rho = fe_rho_minus->GetOrder(); + const int p_v = fe_v_minus->GetOrder(); + const int p_rho = fe_rho_minus->GetOrder(); const int int_order = 2 * std::max(p_v, p_rho) + 1; - const mfem::IntegrationRule *ir = &mfem::IntRules.Get(Tr.GetGeometryType(), int_order); + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(Tr.GetGeometryType(), int_order); - mfem::Vector shape_v_minus(dof_v_minus), shape_rho_minus(dof_rho_minus), shape_rho_plus(dof_rho_plus); + mfem::Vector shape_v_minus(dof_v_minus), shape_rho_minus(dof_rho_minus), + shape_rho_plus(dof_rho_plus); for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& face_ip = ir->IntPoint(q); + const mfem::IntegrationPoint &face_ip = ir->IntPoint(q); Tr.SetAllIntPoints(&face_ip); const mfem::IntegrationPoint &ip_minus = Tr.GetElement1IntPoint(); - const mfem::IntegrationPoint &ip_plus = Tr.GetElement2IntPoint(); + const mfem::IntegrationPoint &ip_plus = Tr.GetElement2IntPoint(); - auto [n_unit, ds, v_dot_n_scale] = m_map.GetFaceQuadratureContext(Tr, face_ip); + auto [n_unit, ds, v_dot_n_scale] = + m_map.GetFaceQuadratureContext(Tr, face_ip); fe_v_minus->CalcShape(ip_minus, shape_v_minus); fe_rho_minus->CalcShape(ip_minus, shape_rho_minus); @@ -251,12 +278,14 @@ namespace mean_field::integrators { } // Upwind density - // I use the convention that the flow is positive when moving from minus to plus + // I use the convention that the flow is positive when moving from + // minus to plus const double rho_up = (u_n >= 0) ? rho_minus_val : rho_plus_val; const double flux_weighted = u_n * rho_up * ds; - // Note the normals need to be in opposite directions for these two fluxes + // Note the normals need to be in opposite directions for these two + // fluxes for (int i = 0; i < dof_rho_minus; ++i) { r_rho(i) += shape_rho_minus(i) * flux_weighted; } @@ -274,25 +303,26 @@ namespace mean_field::integrators { const mfem::Array &elfun, const mfem::Array2D &elmats ) { - const mfem::FiniteElement *fe_v_minus = el1[0]; - const mfem::FiniteElement *fe_v_plus = el2[0]; + const mfem::FiniteElement *fe_v_minus = el1[0]; + const mfem::FiniteElement *fe_v_plus = el2[0]; const mfem::FiniteElement *fe_rho_minus = el1[1]; - const mfem::FiniteElement *fe_rho_plus = el2[1]; + const mfem::FiniteElement *fe_rho_plus = el2[1]; - const int dof_v_minus = fe_v_minus->GetDof(); - const int dof_v_plus = fe_v_plus->GetDof(); - const int dof_rho_minus = fe_rho_minus->GetDof(); - const int dof_rho_plus = fe_rho_plus->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v_minus = fe_v_minus->GetDof(); + const int dof_v_plus = fe_v_plus->GetDof(); + const int dof_rho_minus = fe_rho_minus->GetDof(); + const int dof_rho_plus = fe_rho_plus->GetDof(); + const int dim = Tr.GetSpaceDim(); - const int N_v_total = dim * (dof_v_minus + dof_v_plus); - const int N_rho_total = dof_rho_minus + dof_rho_plus; + const int N_v_total = dim * (dof_v_minus + dof_v_plus); + const int N_rho_total = dof_rho_minus + dof_rho_plus; - auto size_and_zero_mat = [&](mfem::DenseMatrix* mat, const int r_size, const int c_size) { - if (mat) { - mat->SetSize(r_size, c_size); - *mat = 0.0; - } + auto size_and_zero_mat = [&](mfem::DenseMatrix *mat, const int r_size, + const int c_size) { + if (mat) { + mat->SetSize(r_size, c_size); + *mat = 0.0; + } }; size_and_zero_mat(elmats(0, 0), N_v_total, N_v_total); @@ -300,34 +330,41 @@ namespace mean_field::integrators { size_and_zero_mat(elmats(1, 0), N_rho_total, N_v_total); size_and_zero_mat(elmats(1, 1), N_rho_total, N_rho_total); - if (skip_face(Tr)) return; + if (skip_face(Tr)) + return; - mfem::DenseMatrix *drho_dv = elmats(1, 0); + mfem::DenseMatrix *drho_dv = elmats(1, 0); mfem::DenseMatrix *drho_drho = elmats(1, 1); - if (!drho_dv && !drho_drho) return; + if (!drho_dv && !drho_drho) + return; - const mfem::Vector &v_dofs = *elfun[0]; + const mfem::Vector &v_dofs = *elfun[0]; const mfem::Vector &rho_dofs = *elfun[1]; - const int int_order = 2 * std::max(fe_v_minus->GetOrder(), fe_rho_minus->GetOrder()) + 1; - const mfem::IntegrationRule *ir = &mfem::IntRules.Get(Tr.GetGeometryType(), int_order); + const int int_order = + 2 * std::max(fe_v_minus->GetOrder(), fe_rho_minus->GetOrder()) + 1; + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(Tr.GetGeometryType(), int_order); - mfem::Vector shape_v_minus(dof_v_minus), shape_rho_minus(dof_rho_minus), shape_rho_plus(dof_rho_plus); + mfem::Vector shape_v_minus(dof_v_minus), shape_rho_minus(dof_rho_minus), + shape_rho_plus(dof_rho_plus); for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& face_ip = ir->IntPoint(q); + const mfem::IntegrationPoint &face_ip = ir->IntPoint(q); Tr.SetAllIntPoints(&face_ip); const mfem::IntegrationPoint &ip_minus = Tr.GetElement1IntPoint(); - const mfem::IntegrationPoint &ip_plus = Tr.GetElement2IntPoint(); + const mfem::IntegrationPoint &ip_plus = Tr.GetElement2IntPoint(); - auto [n_unit, ds, v_dot_n_scale] = m_map.GetFaceQuadratureContext(Tr, face_ip); + auto [n_unit, ds, v_dot_n_scale] = + m_map.GetFaceQuadratureContext(Tr, face_ip); fe_v_minus->CalcShape(ip_minus, shape_v_minus); fe_rho_minus->CalcShape(ip_minus, shape_rho_minus); fe_rho_plus->CalcShape(ip_plus, shape_rho_plus); - const double u_n = compute_u_n(v_dofs, shape_v_minus, n_unit, dof_v_minus, dim); + const double u_n = + compute_u_n(v_dofs, shape_v_minus, n_unit, dof_v_minus, dim); double rho_minus_val = 0.0; for (int i = 0; i < dof_rho_minus; ++i) { @@ -353,18 +390,21 @@ namespace mean_field::integrators { (*drho_drho)(i, ip) += shape_rho_minus(i) * col_w; } for (int j = 0; j < dof_rho_plus; ++j) { - (*drho_drho)(dof_rho_minus + j, ip) -= shape_rho_plus(j) * col_w; + (*drho_drho)(dof_rho_minus + j, ip) -= + shape_rho_plus(j) * col_w; } } } else { for (int jp = 0; jp < dof_rho_plus; ++jp) { const double col_w = u_w * shape_rho_plus(jp); - const int col_idx = dof_rho_minus + jp; + const int col_idx = dof_rho_minus + jp; for (int i = 0; i < dof_rho_minus; ++i) { - (*drho_drho)(i, col_idx) += shape_rho_minus(i) * col_w; + (*drho_drho)(i, col_idx) += + shape_rho_minus(i) * col_w; } for (int j = 0; j < dof_rho_plus; ++j) { - (*drho_drho)(dof_rho_minus + j, col_idx) -= shape_rho_plus(j) * col_w; + (*drho_drho)(dof_rho_minus + j, col_idx) -= + shape_rho_plus(j) * col_w; } } } @@ -375,13 +415,15 @@ namespace mean_field::integrators { for (int c = 0; c < dim; ++c) { const double n_c_rho_w = n_unit(c) * rho_w; for (int k = 0; k < dof_v_minus; ++k) { - const int col_idx = k + c * dof_v_minus; + const int col_idx = k + c * dof_v_minus; const double col_w = n_c_rho_w * shape_v_minus(k); for (int i = 0; i < dof_rho_minus; ++i) { - (*drho_dv)(i, col_idx) += shape_rho_minus(i) * col_w; + (*drho_dv)(i, col_idx) += + shape_rho_minus(i) * col_w; } for (int j = 0; j < dof_rho_plus; ++j) { - (*drho_dv)(dof_rho_minus + j, col_idx) -= shape_rho_plus(j) * col_w; + (*drho_dv)(dof_rho_minus + j, col_idx) -= + shape_rho_plus(j) * col_w; } } } @@ -389,9 +431,11 @@ namespace mean_field::integrators { } } - bool ContinuityFaceIntegrator::skip_face(const mfem::FaceElementTransformations& Tr) { + bool ContinuityFaceIntegrator::skip_face( + const mfem::FaceElementTransformations &Tr + ) { constexpr int VACUUM_ATTR = 3; - const int attr_minus = Tr.Elem1->Attribute; + const int attr_minus = Tr.Elem1->Attribute; const int attr_plus = (Tr.Elem2 != nullptr) ? Tr.Elem2->Attribute : -1; if (attr_minus == VACUUM_ATTR || attr_plus == VACUUM_ATTR) { return true; // No flux contribution for vacuum faces @@ -402,7 +446,13 @@ namespace mean_field::integrators { return false; } - double ContinuityFaceIntegrator::compute_u_n(const mfem::Vector& v_dofs, const mfem::Vector& shape_v_minus, const mfem::Vector& n_unit, int dof_v_minus, int dim) { + double ContinuityFaceIntegrator::compute_u_n( + const mfem::Vector &v_dofs, + const mfem::Vector &shape_v_minus, + const mfem::Vector &n_unit, + int dof_v_minus, + int dim + ) { double u_n = 0.0; for (int c = 0; c < dim; ++c) { double v_c = 0.0; @@ -413,5 +463,4 @@ namespace mean_field::integrators { } return u_n; } -} - +} // namespace mean_field::integrators diff --git a/libmeanfield/impl/integrators/viscosity.cpp b/libmeanfield/impl/integrators/viscosity.cpp index bbf6d4b..0014a2f 100644 --- a/libmeanfield/impl/integrators/viscosity.cpp +++ b/libmeanfield/impl/integrators/viscosity.cpp @@ -4,12 +4,18 @@ module mean_field; namespace mean_field::integrators { ViscosityIntegrator::ViscosityIntegrator( - const mapping::DomainMapper& map, + const mapping::DomainMapper &map, const double mu, const int quad_boost - ) : m_map(map), m_mu(mu), m_quad_boost(quad_boost) {} + ) + : m_map(map), + m_mu(mu), + m_quad_boost(quad_boost) { + } - void ViscosityIntegrator::SetMu(const double mu) { m_mu = mu; } + void ViscosityIntegrator::SetMu(const double mu) { + m_mu = mu; + } void ViscosityIntegrator::AssembleElementVector( const mfem::Array &el, @@ -21,19 +27,19 @@ namespace mean_field::integrators { return; } - void* data_before = (void*)elvec[0]->GetData(); - int size_before = elvec[0]->Size(); + void *data_before = (void *)elvec[0]->GetData(); + int size_before = elvec[0]->Size(); - const mfem::FiniteElement* fe_v = el[0]; - const mfem::FiniteElement* fe_rho = el[1]; + const mfem::FiniteElement *fe_v = el[0]; + const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - const mfem::Vector& v_dofs = *elfun[0]; + const mfem::Vector &v_dofs = *elfun[0]; - mfem::Vector& r_v = *elvec[0]; + mfem::Vector &r_v = *elvec[0]; r_v.SetSize(dof_v * dim); r_v = 0.0; if (elvec[1]) { @@ -43,12 +49,13 @@ namespace mean_field::integrators { mfem::DenseMatrix dshape_v_ref(dof_v, dim), dshape_v_phys(dof_v, dim); - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder() + m_quad_boost); + const mfem::IntegrationRule *ir = &mfem::IntRules.Get( + fe_v->GetGeomType(), 2 * fe_v->GetOrder() + m_quad_boost + ); for (int q = 0; q < ir->GetNPoints(); ++q) { - - const mfem::IntegrationPoint& ip = ir->IntPoint(q); + const mfem::IntegrationPoint &ip = ir->IntPoint(q); Tr.SetIntPoint(&ip); auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); @@ -57,12 +64,13 @@ namespace mean_field::integrators { mfem::Mult(dshape_v_ref, J_inv, dshape_v_phys); // ∇v(c,j) = δj v_c - mfem::DenseMatrix grad_v(dim, dim); grad_v = 0.0; + mfem::DenseMatrix grad_v(dim, dim); + grad_v = 0.0; for (int n = 0; n < dof_v; ++n) { for (int c = 0; c < dim; ++c) { const double vn_c = v_dofs(n + c * dof_v); for (int j = 0; j < dim; ++j) { - grad_v( c, j) += vn_c * dshape_v_phys(n, j); + grad_v(c, j) += vn_c * dshape_v_phys(n, j); } } } @@ -80,7 +88,8 @@ namespace mean_field::integrators { double acc = 0.0; for (int j = 0; j < dim; ++j) { double D_cj = grad_v(c, j) + grad_v(j, c); - if (c == j) D_cj -= (2.0 / 3.0) * div_v; + if (c == j) + D_cj -= (2.0 / 3.0) * div_v; acc += dshape_v_phys(i, j) * D_cj; } r_v(i + c * dof_v) += mu_w * acc; @@ -95,27 +104,33 @@ namespace mean_field::integrators { const mfem::Array &elfun, const mfem::Array2D &elmats ) { - const mfem::FiniteElement* fe_v = el[0]; - const mfem::FiniteElement* fe_rho = el[1]; + const mfem::FiniteElement *fe_v = el[0]; + const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - mfem::DenseMatrix* dv_dv = elmats(0, 0); - mfem::DenseMatrix* dv_drho = elmats(0, 1); + mfem::DenseMatrix *dv_dv = elmats(0, 0); + mfem::DenseMatrix *dv_drho = elmats(0, 1); - if (dv_drho) *dv_drho =0.0; - if (dv_dv) *dv_dv = 0.0; - if (elmats(1, 0)) *elmats(1, 0) = 0.0; - if (elmats(1, 1)) *elmats(1, 1) = 0.0; - if (!dv_dv) return; + if (dv_drho) + *dv_drho = 0.0; + if (dv_dv) + *dv_dv = 0.0; + if (elmats(1, 0)) + *elmats(1, 0) = 0.0; + if (elmats(1, 1)) + *elmats(1, 1) = 0.0; + if (!dv_dv) + return; mfem::DenseMatrix dshape_v_ref(dof_v, dim), dshape_v_phys(dof_v, dim); - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& ip = ir->IntPoint(q); + const mfem::IntegrationPoint &ip = ir->IntPoint(q); Tr.SetIntPoint(&ip); auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); @@ -137,20 +152,20 @@ namespace mean_field::integrators { for (int d = 0; d < dim; ++d) { const int col = n + d * dof_v; - double val = 0.0; - if (c == d) val += dot_grad; + double val = 0.0; + if (c == d) + val += dot_grad; val += dshape_v_phys(i, d) * dshape_v_phys(n, c); - val -= (2.0 / 3.0) * dshape_v_phys(i, c) * dshape_v_phys(n, d); + val -= (2.0 / 3.0) * dshape_v_phys(i, c) * + dshape_v_phys(n, d); (*dv_dv)(row, col) += mu_w * val; } } } } } - } - -} \ No newline at end of file +} // namespace mean_field::integrators \ No newline at end of file diff --git a/libmeanfield/impl/mapping/coefficients.cpp b/libmeanfield/impl/mapping/coefficients.cpp index 2b226a4..ab5cc0c 100644 --- a/libmeanfield/impl/mapping/coefficients.cpp +++ b/libmeanfield/impl/mapping/coefficients.cpp @@ -10,30 +10,38 @@ namespace mean_field::mapping { ////////////////////////////// MappedScalarCoefficient::MappedScalarCoefficient( const DomainMapper &map, - mfem::Coefficient &coeff, + Coefficient &coeff, const COORDINATE_SPACE coord_space - ) : m_map(map), - m_coeff(coeff), - m_coord_space(coord_space) {}; + ) + : m_map(map), + m_coeff(coeff), + m_coord_space(coord_space) { }; - double MappedScalarCoefficient::Eval(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) { + double MappedScalarCoefficient::Eval( + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) { T.SetIntPoint(&ip); double f_val = 0.0; switch (m_coord_space) { - case COORDINATE_SPACE::PHYSICAL: { - f_val = eval_at_point(m_coeff, T, ip); - const double detJ = m_map.ComputeDetJ(T, ip); - return f_val * fabs(detJ); - } - case COORDINATE_SPACE::REFERENCE: { - f_val = m_coeff.Eval(T, ip); - return f_val; - } + case COORDINATE_SPACE::PHYSICAL: { + f_val = eval_at_point(m_coeff, T, ip); + const double detJ = m_map.ComputeDetJ(T, ip); + return f_val * fabs(detJ); + } + case COORDINATE_SPACE::REFERENCE: { + f_val = m_coeff.Eval(T, ip); + return f_val; + } } } - double MappedScalarCoefficient::eval_at_point(mfem::Coefficient &c, mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) { + double MappedScalarCoefficient::eval_at_point( + Coefficient &c, + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) { return c.Eval(T, ip); } @@ -45,22 +53,26 @@ namespace mean_field::mapping { const DomainMapper &map, mfem::Coefficient &sigma, const int dim - ) : mfem::MatrixCoefficient(dim), - m_map(map), - m_scalar(&sigma), - m_tensor(nullptr) { - }; + ) + : MatrixCoefficient(dim), + m_map(map), + m_scalar(&sigma), + m_tensor(nullptr) { }; MappedDiffusionCoefficient::MappedDiffusionCoefficient( const DomainMapper &map, - mfem::MatrixCoefficient &sigma - ) : mfem::MatrixCoefficient(sigma.GetHeight()), - m_map(map), - m_scalar(nullptr), - m_tensor(&sigma) { - }; + MatrixCoefficient &sigma + ) + : MatrixCoefficient(sigma.GetHeight()), + m_map(map), + m_scalar(nullptr), + m_tensor(&sigma) { }; - void MappedDiffusionCoefficient::Eval(mfem::DenseMatrix &K, mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) { + void MappedDiffusionCoefficient::Eval( + mfem::DenseMatrix &K, + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) { const int dim = height; T.SetIntPoint(&ip); @@ -90,13 +102,17 @@ namespace mean_field::mapping { /////////////////////////////// MappedVectorCoefficient::MappedVectorCoefficient( const DomainMapper &map, - mfem::VectorCoefficient &coeff - ) : mfem::VectorCoefficient(coeff.GetVDim()), - m_map(map), - m_coeff(coeff) { - }; + VectorCoefficient &coeff + ) + : VectorCoefficient(coeff.GetVDim()), + m_map(map), + m_coeff(coeff) { }; - void MappedVectorCoefficient::Eval(mfem::Vector &V, mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) { + void MappedVectorCoefficient::Eval( + mfem::Vector &V, + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) { const int dim = vdim; T.SetIntPoint(&ip); @@ -118,24 +134,32 @@ namespace mean_field::mapping { PhysicalPositionFunctionCoefficient::PhysicalPositionFunctionCoefficient( const DomainMapper &map, Func f // std::function - ) : m_f(std::move(f)), - m_map(map) {}; + ) + : m_f(std::move(f)), + m_map(map) { }; - double PhysicalPositionFunctionCoefficient::Eval(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) { + double PhysicalPositionFunctionCoefficient::Eval( + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) { T.SetIntPoint(&ip); mfem::Vector x; m_map.GetPhysicalPoint(T, ip, x); return m_f(x); } - MappedHDivMassCoefficient::MappedHDivMassCoefficient(const DomainMapper& map, const int dim) - : mfem::MatrixCoefficient(dim), - m_map(map) {} + MappedHDivMassCoefficient::MappedHDivMassCoefficient( + const DomainMapper &map, + const int dim + ) + : MatrixCoefficient(dim), + m_map(map) { + } void MappedHDivMassCoefficient::Eval( - mfem::DenseMatrix& matrix, - mfem::ElementTransformation& transformation, - const mfem::IntegrationPoint& integration_point + mfem::DenseMatrix &matrix, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point ) { transformation.SetIntPoint(&integration_point); @@ -144,9 +168,12 @@ namespace mean_field::mapping { const double map_determinant = map_jacobian.Det(); - MFEM_VERIFY(map_determinant > 0.0, "Domain mapping has a non-positive Jacobian determinant."); + MFEM_VERIFY( + map_determinant > 0.0, + "Domain mapping has a non-positive Jacobian determinant." + ); mfem::MultAtB(map_jacobian, map_jacobian, matrix); matrix *= 1.0 / std::abs(map_determinant); } -} +} // namespace mean_field::mapping diff --git a/libmeanfield/impl/mapping/compactification/kelvin.cpp b/libmeanfield/impl/mapping/compactification/kelvin.cpp new file mode 100644 index 0000000..822ea6c --- /dev/null +++ b/libmeanfield/impl/mapping/compactification/kelvin.cpp @@ -0,0 +1,266 @@ +module; + +#include +#include +#include + +module mean_field; + +namespace { + bool vector_is_finite(const mfem::Vector &vector) { + for (int i = 0; i < vector.Size(); ++i) { + if (!std::isfinite(vector(i))) + return false; + } + return true; + } + + bool matrix_is_finite(const mfem::DenseMatrix &matrix) { + for (int i = 0; i < matrix.Height(); ++i) { + for (int j = 0; j < matrix.Width(); ++j) { + if (!std::isfinite(matrix(i, j))) + return false; + } + } + return true; + } +} // namespace + +namespace mean_field::mapping::compactification { + KelvinCompactification::KelvinCompactification( + options::KelvinCompactificationOptions options + ) + : m_options(options) { + if (!std::isfinite(m_options.r_star_ref) || + !std::isfinite(m_options.r_inf_ref)) { + throw std::invalid_argument( + "Kelvin compactification radii must be finite." + ); + } + + if (m_options.r_star_ref <= 0.0 || + m_options.r_inf_ref <= m_options.r_star_ref) { + throw std::invalid_argument( + "Kelvin compactification requires 0 < r_star_ref < r_inf_ref." + ); + } + + if (!std::isfinite(m_options.coordinate_tolerance) || + m_options.coordinate_tolerance < 0.0 || + m_options.coordinate_tolerance >= 1.0) { + throw std::invalid_argument( + "Kelvin compactification coordinate tolerance must be finite " + "and lie " + "in [0, 1)." + ); + } + } + + MappingStatus KelvinCompactification::ComputeRadialFactors( + const double compactification_coordinate, + RadialFactors &factors + ) const { + if (!std::isfinite(compactification_coordinate)) + return MappingStatus::non_finite_input; + + const double tolerance = m_options.coordinate_tolerance; + + if (compactification_coordinate < -tolerance || + compactification_coordinate > 1.0 + tolerance) { + return MappingStatus::outside_reference_domain; + } + + double coordinate = compactification_coordinate; + if (coordinate < 0.0) + coordinate = 0.0; + + if (coordinate >= 1.0 - tolerance) { + return MappingStatus::at_compactified_infinity; + } + + const double radial_extent = m_options.r_inf_ref - m_options.r_star_ref; + const double computational_radius = + m_options.r_star_ref + coordinate * radial_extent; + + if (!std::isfinite(computational_radius) || + computational_radius <= 0.0) { + return MappingStatus::invalid_reference_radius; + } + + const double one_minus_coordinate = 1.0 - coordinate; + const double denominator = computational_radius * one_minus_coordinate; + + if (!std::isfinite(denominator) || denominator <= 0.0) { + return MappingStatus::non_finite_result; + } + + const double scale = m_options.r_star_ref / denominator; + const double scale_derivative = + scale * + (1.0 / one_minus_coordinate - radial_extent / computational_radius); + + if (!std::isfinite(scale) || !std::isfinite(scale_derivative)) { + return MappingStatus::non_finite_result; + } + + factors.coordinate = coordinate; + factors.computational_radius = computational_radius; + factors.scale = scale; + factors.scale_derivative = scale_derivative; + + return MappingStatus::valid; + } + + MappingStatus KelvinCompactification::Evaluate( + const ExteriorMapInput &input, + ExteriorMapResult &result + ) const { + const int dimension = input.reference_position.Size(); + + if (dimension <= 0 || input.displaced_position.Size() != dimension || + input.compactification_coordinate_gradient.Size() != dimension) { + return MappingStatus::invalid_dimension; + } + + if (input.displacement_jacobian.Height() != dimension || + input.displacement_jacobian.Width() != dimension) { + return MappingStatus::invalid_dimension; + } + + if (!vector_is_finite(input.reference_position) || + !vector_is_finite(input.displaced_position) || + !vector_is_finite(input.compactification_coordinate_gradient) || + !matrix_is_finite(input.displacement_jacobian)) { + return MappingStatus::non_finite_input; + } + + RadialFactors factors; + const MappingStatus factor_status = + ComputeRadialFactors(input.compactification_coordinate, factors); + if (factor_status != MappingStatus::valid) + return factor_status; + + result.physical_position.SetSize(dimension); + result.mapping_jacobian.SetSize(dimension, dimension); + + for (int i = 0; i < dimension; ++i) { + result.physical_position(i) = + factors.scale * input.displaced_position(i); + + for (int j = 0; j < dimension; ++j) { + const double scale_gradient = + factors.scale_derivative * + input.compactification_coordinate_gradient(j); + result.mapping_jacobian(i, j) = + factors.scale * input.displacement_jacobian(i, j) + + input.displaced_position(i) * scale_gradient; + } + } + + if (!vector_is_finite(result.physical_position) || + !matrix_is_finite(result.mapping_jacobian)) { + return MappingStatus::non_finite_result; + } + + const double mapping_determinant = result.mapping_jacobian.Det(); + + if (!std::isfinite(mapping_determinant)) + return MappingStatus::non_finite_result; + if (mapping_determinant <= 0.0) + return MappingStatus::non_positive_determinant; + + return MappingStatus::valid; + } + + MappingStatus KelvinCompactification::EvaluateVariation( + const ExteriorMapInput &input, + const ExteriorMapResult &result, + const ExteriorMapDirection &direction, + ExteriorMapVariation &variation + ) const { + const int dimension = input.reference_position.Size(); + + if (dimension <= 0 || input.displaced_position.Size() != dimension || + input.compactification_coordinate_gradient.Size() != dimension) { + return MappingStatus::invalid_dimension; + } + + if (input.displacement_jacobian.Height() != dimension || + input.displacement_jacobian.Width() != dimension) { + return MappingStatus::invalid_dimension; + } + + if (result.physical_position.Size() != dimension || + result.mapping_jacobian.Height() != dimension || + result.mapping_jacobian.Width() != dimension) { + return MappingStatus::invalid_dimension; + } + + if (direction.displaced_position_variation.Size() != dimension || + direction.displacement_jacobian_variation.Height() != dimension || + direction.displacement_jacobian_variation.Width() != dimension) { + return MappingStatus::invalid_dimension; + } + + if (!vector_is_finite(input.reference_position) || + !vector_is_finite(input.displaced_position) || + !vector_is_finite(input.compactification_coordinate_gradient) || + !matrix_is_finite(input.displacement_jacobian)) { + return MappingStatus::non_finite_input; + } + + if (!vector_is_finite(result.physical_position) || + !matrix_is_finite(result.mapping_jacobian) || + !vector_is_finite(direction.displaced_position_variation) || + !matrix_is_finite(direction.displacement_jacobian_variation)) { + return MappingStatus::non_finite_input; + } + + RadialFactors factors; + const MappingStatus factor_status = + ComputeRadialFactors(input.compactification_coordinate, factors); + if (factor_status != MappingStatus::valid) + return factor_status; + + variation.physical_position_variation.SetSize(dimension); + variation.mapping_jacobian_variation.SetSize(dimension, dimension); + + for (int i = 0; i < dimension; ++i) { + variation.physical_position_variation(i) = + factors.scale * direction.displaced_position_variation(i); + + for (int j = 0; j < dimension; ++j) { + const double scale_gradient = + factors.scale_derivative * + input.compactification_coordinate_gradient(j); + variation.mapping_jacobian_variation(i, j) = + factors.scale * + direction.displacement_jacobian_variation(i, j) + + direction.displaced_position_variation(i) * scale_gradient; + } + } + + if (!vector_is_finite(variation.physical_position_variation) || + !matrix_is_finite(variation.mapping_jacobian_variation)) { + return MappingStatus::non_finite_result; + } + + return MappingStatus::valid; + } + + std::string_view KelvinCompactification::GetName() const noexcept { + return "KelvinCompactification"; + } + + double KelvinCompactification::GetReferenceStellarRadius() const noexcept { + return m_options.r_star_ref; + } + + double KelvinCompactification::GetReferenceInfinityRadius() const noexcept { + return m_options.r_inf_ref; + } + + double KelvinCompactification::GetCoordinateTolerance() const noexcept { + return m_options.coordinate_tolerance; + } +} // namespace mean_field::mapping::compactification \ No newline at end of file diff --git a/libmeanfield/impl/mapping/domain_mapper.cpp b/libmeanfield/impl/mapping/domain_mapper.cpp index 6ec90ba..7fb44f6 100644 --- a/libmeanfield/impl/mapping/domain_mapper.cpp +++ b/libmeanfield/impl/mapping/domain_mapper.cpp @@ -2,26 +2,52 @@ module; #include module mean_field; +import :mapping.types; + +namespace { + double get_positive_map_jacobian( + const mean_field::mapping::DomainMapper &domain_mapper, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + mfem::DenseMatrix &map_jacobian + ) { + transformation.SetIntPoint(&integration_point); + domain_mapper.ComputeJacobian(transformation, map_jacobian); + + const double map_determinant = map_jacobian.Det(); + MFEM_VERIFY( + map_determinant > 0.0, + "Domain mapping has a non-positive Jacobian determinant." + ); + return map_determinant; + } +} // namespace namespace mean_field::mapping { DomainMapper::DomainMapper( const double r_star_ref, const double r_inf_ref - ) : m_d(nullptr), - m_r_star_ref(r_star_ref), - m_r_inf_ref(r_inf_ref) { + ) + : m_d(nullptr), + m_r_star_ref(r_star_ref), + m_r_inf_ref(r_inf_ref) { InitAllScratchSpaces(); + CalcIsIdentity() ? m_displacement_is_identity = true + : m_displacement_is_identity = false; } DomainMapper::DomainMapper( const mfem::GridFunction &d, const double r_star_ref, const double r_inf_ref - ) : m_d(&d), - m_dim(d.FESpace()->GetMesh()->Dimension()), - m_r_star_ref(r_star_ref), - m_r_inf_ref(r_inf_ref) { + ) + : m_d(&d), + m_dim(d.FESpace()->GetMesh()->Dimension()), + m_r_star_ref(r_star_ref), + m_r_inf_ref(r_inf_ref) { InitAllScratchSpaces(); + CalcIsIdentity() ? m_displacement_is_identity = true + : m_displacement_is_identity = false; } bool DomainMapper::is_vacuum(const mfem::ElementTransformation &T) const { @@ -29,7 +55,9 @@ namespace mean_field::mapping { return T.Attribute == m_vacuum_attr; } else if (T.ElementType == mfem::ElementTransformation::BDR_ELEMENT) { return T.Attribute == m_vacuum_attr - 1; - // TODO: In a more robust code this should really be read from the stroid API to ensure that the vacuum boundary is really 1 - the vacuum material attribute + // TODO: In a more robust code this should really be read from the + // stroid API to ensure that the vacuum boundary is really 1 - the + // vacuum material attribute } return false; } @@ -37,28 +65,69 @@ namespace mean_field::mapping { void DomainMapper::SetDisplacement(const mfem::GridFunction &d) { if (m_dim != d.FESpace()->GetMesh()->Dimension()) { const std::string err_msg = std::format( - "Dimension mismatch: DomainMapper is initialized for dimension {}, but provided displacement field has dimension {}.", - m_dim, d.FESpace()->GetMesh()->Dimension()); + "Dimension mismatch: DomainMapper is initialized for dimension " + "{}, " + "but provided displacement field has " + "dimension {}.", + m_dim, d.FESpace()->GetMesh()->Dimension() + ); throw std::invalid_argument(err_msg); } m_d = &d; InvalidateCache(); + + CalcIsIdentity() ? m_displacement_is_identity = true + : m_displacement_is_identity = false; } - bool DomainMapper::IsIdentity() const { - return (m_d == nullptr); + bool DomainMapper::HasCompactification() const noexcept { + return std::isfinite(m_r_star_ref) && std::isfinite(m_r_inf_ref) && + m_r_star_ref > 0.0 && m_r_inf_ref > m_r_star_ref && + m_xi_clamp > 0.0 && m_xi_clamp < 1.0; + } + + bool DomainMapper::HasDisplacementField() const noexcept { + return m_d != nullptr; + } + + bool DomainMapper::CalcIsIdentity() const { + if (m_d == nullptr) { + return true; + } + + const int local_identity = m_d->Normlinf() == 0.0 ? 1 : 0; + + const auto *parallel_displacement = + dynamic_cast(m_d); + + if (parallel_displacement == nullptr) { + return local_identity == 1; + } + + int global_identity = 0; + MPI_Allreduce( + &local_identity, &global_identity, 1, MPI_INT, MPI_MIN, + parallel_displacement->ParFESpace()->GetComm() + ); + + return global_identity == 1; } void DomainMapper::ResetDisplacement() { m_d = nullptr; InvalidateCache(); + CalcIsIdentity() ? m_displacement_is_identity = true + : m_displacement_is_identity = false; } - void DomainMapper::ComputeJacobian(mfem::ElementTransformation &T, mfem::DenseMatrix &J) const { + void DomainMapper::ComputeJacobian( + mfem::ElementTransformation &T, + mfem::DenseMatrix &J + ) const { J.SetSize(m_dim, m_dim); - J = 0.0; + J = 0.0; m_J_D = 0.0; - if (IsIdentity()) { + if (!HasDisplacementField()) { for (int i = 0; i < m_dim; ++i) { m_J_D(i, i) = 1.0; // Identity mapping } @@ -76,7 +145,7 @@ namespace mean_field::mapping { if (is_vacuum(T)) { T.Transform(T.GetIntPoint(), m_x_ref); - if (IsIdentity()) { + if (!HasDisplacementField()) { m_x_disp = m_x_ref; } else { m_shape.SetSize(m_fe->GetDof()); @@ -91,15 +160,22 @@ namespace mean_field::mapping { } } - double DomainMapper::ComputeDetJ(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) const { - if (IsIdentity() && !is_vacuum(T)) return 1.0; // If no mapping, the determinant of the Jacobian is 1 + double DomainMapper::ComputeDetJ( + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) const { + if (!HasDisplacementField() && !is_vacuum(T)) + return 1.0; // If no mapping, the determinant of the Jacobian is 1 T.SetIntPoint(&ip); mfem::DenseMatrix J; ComputeJacobian(T, J); return J.Det(); } - void DomainMapper::ComputeMappedDiffusionTensor(mfem::ElementTransformation &T, mfem::DenseMatrix &D) const { + void DomainMapper::ComputeMappedDiffusionTensor( + mfem::ElementTransformation &T, + mfem::DenseMatrix &D + ) const { ComputeJacobian(T, m_J_temp); const double detJ = m_J_temp.Det(); mfem::CalcInverse(m_J_temp, m_JInv_temp); @@ -108,41 +184,56 @@ namespace mean_field::mapping { D *= fabs(detJ); } - void DomainMapper::ComputeInverseJacobian(mfem::ElementTransformation &T, mfem::DenseMatrix &JInv) const { + void DomainMapper::ComputeInverseJacobian( + mfem::ElementTransformation &T, + mfem::DenseMatrix &JInv + ) const { ComputeJacobian(T, m_J_temp); JInv.SetSize(m_dim, m_dim); mfem::CalcInverse(m_J_temp, JInv); } - DomainMapper::VolumeQuadratureContext DomainMapper::GetQuadratureContext(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) const { + VolumeQuadratureContext DomainMapper::GetQuadratureContext( + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) const { const int dim = T.GetSpaceDim(); mfem::DenseMatrix J_map(dim, dim), J_inv(dim, dim); ComputeJacobian(T, J_map); mfem::DenseMatrix J_full(dim, dim); mfem::Mult(J_map, T.Jacobian(), J_full); mfem::CalcInverse(J_full, J_inv); - const double detJ = std::fabs(ComputeDetJ(T, ip)); + const double detJ = std::fabs(ComputeDetJ(T, ip)); const double weight = ip.weight * T.Weight() * detJ; return {.J_inv = J_inv, .detJ = detJ, .weight = weight}; } - DomainMapper::FaceQuadratureContext DomainMapper::GetFaceQuadratureContext(mfem::FaceElementTransformations &T, const mfem::IntegrationPoint &ip) const { + FaceQuadratureContext DomainMapper::GetFaceQuadratureContext( + mfem::FaceElementTransformations &T, + const mfem::IntegrationPoint &ip + ) const { const int dim = T.GetSpaceDim(); T.SetAllIntPoints(&ip); mfem::Vector n_raw(dim); mfem::CalcOrtho(T.Jacobian(), n_raw); - if (IsIdentity()) { + if (!HasDisplacementField() && !is_vacuum(T)) { const double n_raw_mag = n_raw.Norml2(); mfem::Vector n_unit(dim); n_unit = n_raw; n_unit /= n_raw_mag; - return FaceQuadratureContext{.normal=n_unit, .ds=ip.weight * n_raw_mag, .v_dot_n_scale = 1.0}; + return FaceQuadratureContext{ + .normal = n_unit, + .ds = ip.weight * n_raw_mag, + .v_dot_n_scale = 1.0 + }; } - // Nanson's Formula (https://en.wikiversity.org/wiki/Continuum_mechanics/Volume_change_and_area_change) - // Since the displacement field lives in H1 it should be irrelevant if we pick Elem1 or Elem2 + // Nanson's Formula + // (https://en.wikiversity.org/wiki/Continuum_mechanics/Volume_change_and_area_change) + // Since the displacement field lives in H1 it should be irrelevant if + // we pick Elem1 or Elem2 mfem::DenseMatrix J_map(dim, dim); ComputeJacobian(*T.Elem1, J_map); const double detJ_map = J_map.Det(); @@ -162,18 +253,21 @@ namespace mean_field::mapping { const double n_raw_mag = n_raw.Norml2(); return FaceQuadratureContext{ - .normal = n_unit, - .ds = ip.weight * n_raw_mag, + .normal = n_unit, + .ds = ip.weight * n_raw_mag, .v_dot_n_scale = n_phys_mag / n_raw_mag }; - } - void DomainMapper::GetPhysicalPoint(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip, mfem::Vector &x_phys) const { + void DomainMapper::GetPhysicalPoint( + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip, + mfem::Vector &x_phys + ) const { x_phys.SetSize(m_dim); T.Transform(ip, m_x_ref); - if (IsIdentity()) { + if (!HasDisplacementField()) { x_phys = m_x_ref; } else { UpdateElementCache(T); @@ -189,11 +283,91 @@ namespace mean_field::mapping { } } - void DomainMapper::GetVectorValue(const int i, const mfem::IntegrationPoint &ip, mfem::Vector &val) const { + void DomainMapper::GetVectorValue( + const int i, + const mfem::IntegrationPoint &ip, + mfem::Vector &val + ) const { m_d->GetVectorValue(i, ip, val); } - const mfem::GridFunction *DomainMapper::GetDisplacement() const { return m_d; } + void DomainMapper::MapHDivFluxToPhysical( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + const mfem::Vector &reference_flux, + mfem::Vector &physical_flux + ) const { + MFEM_VERIFY( + reference_flux.Size() == m_dim, + "The reference H(div) flux has the wrong dimension." + ); + + mfem::DenseMatrix map_jacobian(m_dim, m_dim); + const double map_determinant = get_positive_map_jacobian( + *this, transformation, integration_point, map_jacobian + ); + + mfem::Vector mapped_flux(m_dim); + map_jacobian.Mult(reference_flux, mapped_flux); + mapped_flux /= map_determinant; + + physical_flux = mapped_flux; + } + + void DomainMapper::MapPhysicalFluxToHDivReference( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + const mfem::Vector &physical_flux, + mfem::Vector &reference_flux + ) const { + MFEM_VERIFY( + physical_flux.Size() == m_dim, + "The physical flux has the wrong dimension." + ); + + mfem::DenseMatrix map_jacobian(m_dim, m_dim); + const double map_determinant = get_positive_map_jacobian( + *this, transformation, integration_point, map_jacobian + ); + + mfem::DenseMatrix inverse_map_jacobian(m_dim, m_dim); + mfem::CalcInverse(map_jacobian, inverse_map_jacobian); + + mfem::Vector mapped_flux(m_dim); + inverse_map_jacobian.Mult(physical_flux, mapped_flux); + mapped_flux *= map_determinant; + + reference_flux = mapped_flux; + } + + void DomainMapper::MapReferenceGradientToPhysical( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + const mfem::Vector &reference_gradient, + mfem::Vector &physical_gradient + ) const { + MFEM_VERIFY( + reference_gradient.Size() == m_dim, + "The reference gradient has the wrong dimension." + ); + + mfem::DenseMatrix map_jacobian(m_dim, m_dim); + get_positive_map_jacobian( + *this, transformation, integration_point, map_jacobian + ); + + mfem::DenseMatrix inverse_map_jacobian(m_dim, m_dim); + mfem::CalcInverse(map_jacobian, inverse_map_jacobian); + + mfem::Vector mapped_gradient(m_dim); + inverse_map_jacobian.MultTranspose(reference_gradient, mapped_gradient); + + physical_gradient = mapped_gradient; + } + + const mfem::GridFunction *DomainMapper::GetDisplacement() const { + return m_d; + } double DomainMapper::GetPhysInfRadius() const { return 1.0 - m_xi_clamp; @@ -208,11 +382,12 @@ namespace mean_field::mapping { } double DomainMapper::GetCacheHitRate() const { - return (static_cast(m_cache_hits)) / static_cast(m_cache_misses + m_cache_hits); + return (static_cast(m_cache_hits)) / + static_cast(m_cache_misses + m_cache_hits); } void DomainMapper::ResetCacheStats() const { - m_cache_hits = 0; + m_cache_hits = 0; m_cache_misses = 0; } @@ -225,28 +400,36 @@ namespace mean_field::mapping { m_d_val.SetSize(m_dim); } - void DomainMapper::ApplyKelvinMapping(const mfem::Vector &x_ref, mfem::Vector &x_phys) const { + void DomainMapper::ApplyKelvinMapping( + const mfem::Vector &x_ref, + mfem::Vector &x_phys + ) const { const double r_ref = x_ref.Norml2(); double xi = (r_ref - m_r_star_ref) / (m_r_inf_ref - m_r_star_ref); - xi = std::clamp(xi, 0.0, m_xi_clamp); + xi = std::clamp(xi, 0.0, m_xi_clamp); const double factor = m_r_star_ref / (r_ref * (1 - xi)); x_phys *= factor; } - void DomainMapper::ComputeKelvinJacobian(const mfem::Vector &x_ref, const mfem::Vector &x_disp, const mfem::DenseMatrix &J_D, - mfem::DenseMatrix &J) const { - const double r_ref = x_ref.Norml2(); + void DomainMapper::ComputeKelvinJacobian( + const mfem::Vector &x_ref, + const mfem::Vector &x_disp, + const mfem::DenseMatrix &J_D, + mfem::DenseMatrix &J + ) const { + const double r_ref = x_ref.Norml2(); const double delta_R = m_r_inf_ref - m_r_star_ref; - double xi = (r_ref - m_r_star_ref) / delta_R; - xi = std::clamp(xi, 0.0, m_xi_clamp); + double xi = (r_ref - m_r_star_ref) / delta_R; + xi = std::clamp(xi, 0.0, m_xi_clamp); - const double denom = 1.0 - xi; + const double denom = 1.0 - xi; - const double k = m_r_star_ref / (r_ref * denom); + const double k = m_r_star_ref / (r_ref * denom); - const double dk_dr = m_r_star_ref * ((1.0 / (delta_R * r_ref * denom * denom)) - ( - 1.0 / (r_ref * r_ref * denom))); + const double dk_dr = + m_r_star_ref * ((1.0 / (delta_R * r_ref * denom * denom)) - + (1.0 / (r_ref * r_ref * denom))); J.SetSize(m_dim, m_dim); const double outer_factor = dk_dr / r_ref; @@ -262,13 +445,17 @@ namespace mean_field::mapping { m_cached_elem_id = -1; } - void DomainMapper::UpdateElementCache(const mfem::ElementTransformation &T) const { - if (IsIdentity()) return; + void DomainMapper::UpdateElementCache( + const mfem::ElementTransformation &T + ) const { + if (!HasDisplacementField()) + return; - if (T.ElementNo != m_cached_elem_id || T.ElementType != m_cached_elem_type) { + if (T.ElementNo != m_cached_elem_id || + T.ElementType != m_cached_elem_type) { m_cache_misses++; - m_cached_elem_id = T.ElementNo; - m_cached_elem_type = T.ElementType; + m_cached_elem_id = T.ElementNo; + m_cached_elem_type = T.ElementType; const mfem::FiniteElementSpace *fes = m_d->FESpace(); mfem::Array vdofs; @@ -291,4 +478,4 @@ namespace mean_field::mapping { m_cache_hits++; } } -} +} // namespace mean_field::mapping diff --git a/libmeanfield/impl/mapping/domain_mapper_new.cpp b/libmeanfield/impl/mapping/domain_mapper_new.cpp new file mode 100644 index 0000000..c639ed7 --- /dev/null +++ b/libmeanfield/impl/mapping/domain_mapper_new.cpp @@ -0,0 +1,916 @@ +module; + +#include +#include +#include +#include +#include + +module mean_field; +import :mapping.types; +import :mapping.compactification; +import :utils.user; + +namespace { + bool vector_is_finite(const mfem::Vector &vector) { + for (int i = 0; i < vector.Size(); ++i) { + if (!std::isfinite(vector(i))) + return false; + } + return true; + } + + bool matrix_is_finite(const mfem::DenseMatrix &matrix) { + for (int i = 0; i < matrix.Height(); ++i) { + for (int j = 0; j < matrix.Width(); ++j) { + if (!std::isfinite(matrix(i, j))) + return false; + } + } + return true; + } +} // namespace + +namespace mean_field::mapping { + ElementCompactificationData::ElementCompactificationData( + const mfem::FiniteElement &element, + const mfem::Vector &dofs + ) + : m_element(&element), + m_dofs(dofs) { + if (element.GetRangeType() != mfem::FiniteElement::SCALAR) { + throw std::invalid_argument( + "Compactification coordinate requires a scalar finite element." + ); + } + + if (element.GetMapType() != mfem::FiniteElement::VALUE) { + throw std::invalid_argument( + "Compactification coordinate requires a value-mapped scalar " + "finite " + "element." + ); + } + + if (element.GetDerivType() != mfem::FiniteElement::GRAD) { + throw std::invalid_argument( + "Compactification coordinate finite element must provide a " + "gradient." + ); + } + + if (element.GetDof() <= 0) { + throw std::invalid_argument( + "Compactification coordinate finite element has no degrees of " + "freedom." + ); + } + + if (dofs.Size() != element.GetDof()) { + throw std::invalid_argument( + "Compactification coordinate DOF count does not match its " + "finite " + "element." + ); + } + } + + const mfem::FiniteElement & + ElementCompactificationData::GetElement() const noexcept { + return *m_element; + } + + const mfem::Vector &ElementCompactificationData::GetDofs() const noexcept { + return m_dofs; + } + + int ElementCompactificationData::GetDofCount() const noexcept { + return m_dofs.Size(); + } + + ElementDisplacementData::ElementDisplacementData( + const mfem::FiniteElement &element, + const mfem::Vector &displacement_dofs, + const mfem::Ordering::Type ordering + ) + : m_element(&element), + m_dimension(0), + m_ordering(ordering) { + const int dof_count = element.GetDof(); + if (dof_count <= 0) + throw std::invalid_argument( + "The displacement element must have at least one degree of " + "freedom." + ); + if (displacement_dofs.Size() <= 0 || + displacement_dofs.Size() % dof_count != 0) { + throw std::invalid_argument( + "The displacement vector size must be a positive multiple of " + "the " + "element degree-of-freedom count." + ); + } + + m_dimension = displacement_dofs.Size() / dof_count; + m_dof_matrix.SetSize(dof_count, m_dimension); + + if (ordering == mfem::Ordering::byNODES) { + for (int component = 0; component < m_dimension; ++component) { + for (int i = 0; i < dof_count; ++i) { + m_dof_matrix(i, component) = + displacement_dofs(i + component * dof_count); + } + } + } else if (ordering == mfem::Ordering::byVDIM) { + for (int i = 0; i < dof_count; ++i) { + for (int component = 0; component < m_dimension; ++component) { + m_dof_matrix(i, component) = + displacement_dofs(component + i * m_dimension); + } + } + } else { + throw std::invalid_argument( + "Unsupported MFEM displacement ordering." + ); + } + } + + const mfem::FiniteElement & + ElementDisplacementData::GetElement() const noexcept { + return *m_element; + } + + const mfem::DenseMatrix & + ElementDisplacementData::GetDofMatrix() const noexcept { + return m_dof_matrix; + } + + int ElementDisplacementData::GetDimension() const noexcept { + return m_dimension; + } + + int ElementDisplacementData::GetDofCount() const noexcept { + return m_element->GetDof(); + } + + mfem::Ordering::Type ElementDisplacementData::GetOrdering() const noexcept { + return m_ordering; + } + + ElementDisplacementData ElementDisplacementDataFromElementVDofs( + const mfem::FiniteElement &element, + const mfem::Vector &displacement_dofs + ) { + return ElementDisplacementData( + element, displacement_dofs, mfem::Ordering::byNODES + ); + } + + DomainMapperStateless::Workspace::Workspace(const int dimension) { + SetDimension(dimension); + } + + void DomainMapperStateless::Workspace::SetDimension(const int dimension) { + if (dimension <= 0) { + throw std::invalid_argument( + "Domain mapping workspace dimension must be positive." + ); + } + + m_dimension = dimension; + + m_field_value.SetSize(dimension); + m_field_jacobian.SetSize(dimension, dimension); + + m_compactification_point.coordinate = 0.0; + m_compactification_point.coordinate_gradient.SetSize(dimension); + + m_reference_normal.SetSize(dimension); + m_mapped_normal.SetSize(dimension); + m_full_element_jacobian.SetSize(dimension, dimension); + + m_vector_temp.SetSize(dimension); + m_matrix_temp_1.SetSize(dimension, dimension); + m_matrix_temp_2.SetSize(dimension, dimension); + + m_exterior_result.physical_position.SetSize(dimension); + m_exterior_result.mapping_jacobian.SetSize(dimension, dimension); + + m_exterior_variation.physical_position_variation.SetSize(dimension); + m_exterior_variation.mapping_jacobian_variation.SetSize( + dimension, dimension + ); + } + + int DomainMapperStateless::Workspace::GetDimension() const noexcept { + return m_dimension; + } + + DomainMapperStateless::DomainMapperStateless( + const utils::DomainMapperStatelessOptions options, + std::unique_ptr exterior_map + ) + : m_options(options), + m_exterior_map(std::move(exterior_map)) { + if (m_options.dimension <= 0) + throw std::invalid_argument( + "The domain-mapping dimension must be positive." + ); + if (m_options.vacuum_element_attribute <= 0) + throw std::invalid_argument( + "The vacuum element attribute must be positive." + ); + if (!m_exterior_map) + throw std::invalid_argument( + "DomainMapperStateless requires an exterior-domain mapping." + ); + } + + bool DomainMapperStateless::IsCompactifiedElement( + const mfem::ElementTransformation &transformation + ) const noexcept { + return transformation.Attribute == m_options.vacuum_element_attribute; + } + + int DomainMapperStateless::GetDimension() const noexcept { + return m_options.dimension; + } + + int DomainMapperStateless::GetVacuumElementAttribute() const noexcept { + return m_options.vacuum_element_attribute; + } + + const compactification::ExteriorDomainMap & + DomainMapperStateless::GetExteriorMap() const noexcept { + return *m_exterior_map; + } + + void DomainMapperStateless::ValidateElementData( + const ElementMappingData &element_data + ) const { + const ElementDisplacementData &displacement = element_data.displacement; + const ElementCompactificationData &compactification = + element_data.compactification; + + if (displacement.GetDimension() != m_options.dimension) { + throw std::invalid_argument( + "Displacement field dimension does not match the domain mapper " + "dimension." + ); + } + + if (displacement.GetElement().GetDim() != m_options.dimension) { + throw std::invalid_argument( + "Displacement finite element dimension does not match the " + "domain " + "mapper dimension." + ); + } + + if (compactification.GetElement().GetDim() != m_options.dimension) { + throw std::invalid_argument( + "Compactification finite element dimension does not match the " + "domain " + "mapper dimension." + ); + } + + if (displacement.GetElement().GetGeomType() != + compactification.GetElement().GetGeomType()) { + throw std::invalid_argument( + "Displacement and compactification finite elements have " + "different " + "geometries." + ); + } + + if (compactification.GetElement().GetRangeType() != + mfem::FiniteElement::SCALAR) { + throw std::invalid_argument( + "Compactification coordinate requires a scalar finite element." + ); + } + + if (compactification.GetElement().GetMapType() != + mfem::FiniteElement::VALUE) { + throw std::invalid_argument( + "Compactification coordinate requires a value-mapped finite " + "element." + ); + } + + if (compactification.GetElement().GetDerivType() != + mfem::FiniteElement::GRAD) { + throw std::invalid_argument( + "Compactification coordinate finite element does not provide a " + "gradient." + ); + } + + if (compactification.GetDofCount() != + compactification.GetElement().GetDof()) { + throw std::invalid_argument( + "Compactification coordinate DOF count does not match its " + "finite " + "element." + ); + } + } + + MappingStatus DomainMapperStateless::EvaluateCompactificationCoordinate( + const ElementCompactificationData &compactification, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + Workspace &workspace, + CompactificationPointData &point_data + ) const { + const mfem::FiniteElement &element = compactification.GetElement(); + const mfem::Vector &dofs = compactification.GetDofs(); + const int dof_count = element.GetDof(); + + if (workspace.GetDimension() != m_options.dimension || + transformation.GetSpaceDim() != m_options.dimension || + element.GetDim() != m_options.dimension) { + return MappingStatus::invalid_dimension; + } + + if (dofs.Size() != dof_count) { + return MappingStatus::invalid_dimension; + } + + for (int i = 0; i < dofs.Size(); ++i) { + if (!std::isfinite(dofs(i))) + return MappingStatus::non_finite_input; + } + + transformation.SetIntPoint(&integration_point); + + workspace.m_compactification_shape.SetSize(dof_count); + workspace.m_compactification_dshape.SetSize( + dof_count, m_options.dimension + ); + + element.CalcShape( + integration_point, workspace.m_compactification_shape + ); + element.CalcPhysDShape( + transformation, workspace.m_compactification_dshape + ); + + point_data.coordinate = dofs * workspace.m_compactification_shape; + point_data.coordinate_gradient.SetSize(m_options.dimension); + workspace.m_compactification_dshape.MultTranspose( + dofs, point_data.coordinate_gradient + ); + + if (!std::isfinite(point_data.coordinate)) { + return MappingStatus::non_finite_result; + } + + for (int d = 0; d < point_data.coordinate_gradient.Size(); ++d) { + if (!std::isfinite(point_data.coordinate_gradient(d))) + return MappingStatus::non_finite_result; + } + + return MappingStatus::valid; + } + + void DomainMapperStateless::EvaluateField( + const ElementDisplacementData &field, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + Workspace &workspace, + mfem::Vector &value, + mfem::DenseMatrix &jacobian + ) const { + transformation.SetIntPoint(&integration_point); + + const mfem::FiniteElement &element = field.GetElement(); + const mfem::DenseMatrix &dof_matrix = field.GetDofMatrix(); + + workspace.m_shape.SetSize(element.GetDof()); + workspace.m_mesh_dshape.SetSize(element.GetDof(), m_options.dimension); + + element.CalcShape(integration_point, workspace.m_shape); + element.CalcPhysDShape(transformation, workspace.m_mesh_dshape); + + value.SetSize(m_options.dimension); + dof_matrix.MultTranspose(workspace.m_shape, value); + + jacobian.SetSize(m_options.dimension, m_options.dimension); + mfem::MultAtB(dof_matrix, workspace.m_mesh_dshape, jacobian); + } + + MappingStatus DomainMapperStateless::EvaluatePoint( + const ElementMappingData &element_data, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + Workspace &workspace, + MappingPointContext &context + ) const { + ValidateElementData(element_data); + + if (workspace.GetDimension() != m_options.dimension) + throw std::invalid_argument( + "The mapping workspace has the wrong dimension." + ); + if (transformation.GetSpaceDim() != m_options.dimension) + throw std::invalid_argument( + "The element transformation has the wrong spatial dimension." + ); + if (transformation.GetGeometryType() != + element_data.displacement.GetElement().GetGeomType()) + throw std::invalid_argument( + "The element transformation geometry does not match the " + "supplied " + "element data." + ); + + transformation.SetIntPoint(&integration_point); + + context.reference_position.SetSize(m_options.dimension); + transformation.Transform(integration_point, context.reference_position); + + EvaluateField( + element_data.displacement, transformation, integration_point, + workspace, workspace.m_field_value, workspace.m_field_jacobian + ); + + if (!vector_is_finite(context.reference_position) || + !vector_is_finite(workspace.m_field_value) || + !matrix_is_finite(workspace.m_field_jacobian)) { + return MappingStatus::non_finite_input; + } + + context.displaced_position.SetSize(m_options.dimension); + context.displaced_position = context.reference_position; + context.displaced_position += workspace.m_field_value; + + context.displacement_jacobian.SetSize( + m_options.dimension, m_options.dimension + ); + context.displacement_jacobian = workspace.m_field_jacobian; + for (int i = 0; i < m_options.dimension; ++i) + context.displacement_jacobian(i, i) += 1.0; + + context.compactified = IsCompactifiedElement(transformation); + + if (context.compactified) { + const MappingStatus coordinate_status = + EvaluateCompactificationCoordinate( + element_data.compactification, transformation, + integration_point, workspace, + workspace.m_compactification_point + ); + + if (coordinate_status != MappingStatus::valid) + return coordinate_status; + + const compactification::ExteriorMapInput exterior_input{ + .reference_position = context.reference_position, + .displaced_position = context.displaced_position, + .displacement_jacobian = context.displacement_jacobian, + .compactification_coordinate = + workspace.m_compactification_point.coordinate, + .compactification_coordinate_gradient = + workspace.m_compactification_point.coordinate_gradient + }; + + const MappingStatus exterior_status = m_exterior_map->Evaluate( + exterior_input, workspace.m_exterior_result + ); + if (exterior_status != MappingStatus::valid) + return exterior_status; + + context.physical_position = + workspace.m_exterior_result.physical_position; + context.mapping_jacobian = + workspace.m_exterior_result.mapping_jacobian; + } else { + context.physical_position = context.displaced_position; + context.mapping_jacobian = context.displacement_jacobian; + } + + if (!vector_is_finite(context.physical_position) || + !matrix_is_finite(context.mapping_jacobian)) + return MappingStatus::non_finite_result; + + context.mapping_determinant = context.mapping_jacobian.Det(); + if (!std::isfinite(context.mapping_determinant)) + return MappingStatus::non_finite_result; + if (context.mapping_determinant <= 0.0) + return MappingStatus::non_positive_determinant; + + context.inverse_mapping_jacobian.SetSize( + m_options.dimension, m_options.dimension + ); + mfem::CalcInverse( + context.mapping_jacobian, context.inverse_mapping_jacobian + ); + + if (!matrix_is_finite(context.inverse_mapping_jacobian)) + return MappingStatus::non_finite_result; + + return MappingStatus::valid; + } + + MappingStatus DomainMapperStateless::EvaluateVolume( + const ElementMappingData &element_data, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + Workspace &workspace, + VolumeMappingContext &context + ) const { + const MappingStatus point_status = EvaluatePoint( + element_data, transformation, integration_point, workspace, + context.mapping + ); + if (point_status != MappingStatus::valid) + return point_status; + + transformation.SetIntPoint(&integration_point); + mfem::Mult( + context.mapping.mapping_jacobian, transformation.Jacobian(), + workspace.m_full_element_jacobian + ); + + context.quadrature.J_inv.SetSize( + m_options.dimension, m_options.dimension + ); + mfem::CalcInverse( + workspace.m_full_element_jacobian, context.quadrature.J_inv + ); + + context.quadrature.detJ = context.mapping.mapping_determinant; + context.quadrature.weight = integration_point.weight * + transformation.Weight() * + context.mapping.mapping_determinant; + + if (!matrix_is_finite(context.quadrature.J_inv) || + !std::isfinite(context.quadrature.weight)) + return MappingStatus::non_finite_result; + if (context.quadrature.weight <= 0.0) + return MappingStatus::non_positive_determinant; + + return MappingStatus::valid; + } + + mfem::ElementTransformation & + DomainMapperStateless::SelectFaceElementTransformation( + mfem::FaceElementTransformations &transformation, + const FaceElementSide side + ) { + if (side == FaceElementSide::element_1) { + MFEM_VERIFY( + transformation.Elem1 != nullptr, + "The face does not have an element-1 transformation." + ); + return *transformation.Elem1; + } + + MFEM_VERIFY( + transformation.Elem2 != nullptr, + "The face does not have an element-2 transformation." + ); + return *transformation.Elem2; + } + + const mfem::IntegrationPoint & + DomainMapperStateless::SelectFaceElementIntegrationPoint( + mfem::FaceElementTransformations &transformation, + const FaceElementSide side + ) { + mfem::ElementTransformation &element_transformation = + SelectFaceElementTransformation(transformation, side); + return element_transformation.GetIntPoint(); + } + + MappingStatus DomainMapperStateless::EvaluateFace( + const ElementMappingData &element_data, + mfem::FaceElementTransformations &transformation, + const FaceElementSide side, + const mfem::IntegrationPoint &integration_point, + Workspace &workspace, + FaceMappingContext &context + ) const { + transformation.SetAllIntPoints(&integration_point); + mfem::ElementTransformation &element_transformation = + SelectFaceElementTransformation(transformation, side); + const mfem::IntegrationPoint &element_integration_point = + SelectFaceElementIntegrationPoint(transformation, side); + + const MappingStatus point_status = EvaluatePoint( + element_data, element_transformation, element_integration_point, + workspace, context.mapping + ); + if (point_status != MappingStatus::valid) + return point_status; + + workspace.m_reference_normal.SetSize(m_options.dimension); + mfem::CalcOrtho( + transformation.Jacobian(), workspace.m_reference_normal + ); + if (side == FaceElementSide::element_2) + workspace.m_reference_normal *= -1.0; + + const double reference_normal_magnitude = + workspace.m_reference_normal.Norml2(); + if (!std::isfinite(reference_normal_magnitude) || + reference_normal_magnitude <= 0.0) + return MappingStatus::non_finite_result; + + context.reference_normal.SetSize(m_options.dimension); + context.reference_normal = workspace.m_reference_normal; + context.reference_normal /= reference_normal_magnitude; + + context.mapping.inverse_mapping_jacobian.MultTranspose( + workspace.m_reference_normal, workspace.m_mapped_normal + ); + workspace.m_mapped_normal *= context.mapping.mapping_determinant; + + const double mapped_normal_magnitude = + workspace.m_mapped_normal.Norml2(); + if (!std::isfinite(mapped_normal_magnitude) || + mapped_normal_magnitude <= 0.0) + return MappingStatus::non_finite_result; + + context.quadrature.normal.SetSize(m_options.dimension); + context.quadrature.normal = workspace.m_mapped_normal; + context.quadrature.normal /= mapped_normal_magnitude; + + context.reference_surface_weight = + integration_point.weight * reference_normal_magnitude; + context.physical_surface_weight = + integration_point.weight * mapped_normal_magnitude; + + context.quadrature.ds = context.reference_surface_weight; + context.quadrature.v_dot_n_scale = + mapped_normal_magnitude / reference_normal_magnitude; + + if (!vector_is_finite(context.quadrature.normal) || + !std::isfinite(context.reference_surface_weight) || + !std::isfinite(context.physical_surface_weight) || + !std::isfinite(context.quadrature.v_dot_n_scale)) { + return MappingStatus::non_finite_result; + } + + return MappingStatus::valid; + } + + MappingStatus DomainMapperStateless::EvaluatePointVariation( + const ElementMappingData &element_data, + const ElementDisplacementData &direction, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + const MappingPointContext &base_context, + Workspace &workspace, + MappingPointVariation &variation + ) const { + ValidateElementData(element_data); + const ElementMappingData direction_data{ + .displacement = direction, + .compactification = element_data.compactification + }; + ValidateElementData(direction_data); + + if (element_data.displacement.GetDofCount() != direction.GetDofCount()) + throw std::invalid_argument( + "The displacement and direction elements have different " + "degree-of-freedom counts." + ); + if (workspace.GetDimension() != m_options.dimension) + throw std::invalid_argument( + "The mapping workspace has the wrong dimension." + ); + if (base_context.compactified != IsCompactifiedElement(transformation)) + throw std::invalid_argument( + "The base mapping context does not match the current element " + "domain." + ); + + EvaluateField( + direction, transformation, integration_point, workspace, + workspace.m_field_value, workspace.m_field_jacobian + ); + + if (!vector_is_finite(workspace.m_field_value) || + !matrix_is_finite(workspace.m_field_jacobian)) + return MappingStatus::non_finite_input; + + variation.displacement_variation = workspace.m_field_value; + variation.displacement_jacobian_variation = workspace.m_field_jacobian; + + if (base_context.compactified) { + const MappingStatus coordinate_status = + EvaluateCompactificationCoordinate( + element_data.compactification, transformation, + integration_point, workspace, + workspace.m_compactification_point + ); + + if (coordinate_status != MappingStatus::valid) + return coordinate_status; + + const compactification::ExteriorMapInput exterior_input{ + .reference_position = base_context.reference_position, + .displaced_position = base_context.displaced_position, + .displacement_jacobian = base_context.displacement_jacobian, + .compactification_coordinate = + workspace.m_compactification_point.coordinate, + .compactification_coordinate_gradient = + workspace.m_compactification_point.coordinate_gradient + }; + + workspace.m_exterior_result.physical_position = + base_context.physical_position; + workspace.m_exterior_result.mapping_jacobian = + base_context.mapping_jacobian; + + const compactification::ExteriorMapDirection exterior_direction{ + .displaced_position_variation = + variation.displacement_variation, + .displacement_jacobian_variation = + variation.displacement_jacobian_variation + }; + + // ReSharper disable once CppTooWideScopeInitStatement + const MappingStatus exterior_status = + m_exterior_map->EvaluateVariation( + exterior_input, workspace.m_exterior_result, + exterior_direction, workspace.m_exterior_variation + ); + + if (exterior_status != MappingStatus::valid) { + return exterior_status; + } + + variation.physical_position_variation = + workspace.m_exterior_variation.physical_position_variation; + variation.mapping_jacobian_variation = + workspace.m_exterior_variation.mapping_jacobian_variation; + } else { + variation.physical_position_variation = + variation.displacement_variation; + variation.mapping_jacobian_variation = + variation.displacement_jacobian_variation; + } + + mfem::Mult( + base_context.inverse_mapping_jacobian, + variation.mapping_jacobian_variation, workspace.m_matrix_temp_1 + ); + + double trace = 0.0; + for (int i = 0; i < m_options.dimension; ++i) + trace += workspace.m_matrix_temp_1(i, i); + variation.mapping_determinant_variation = + base_context.mapping_determinant * trace; + + variation.inverse_mapping_jacobian_variation.SetSize( + m_options.dimension, m_options.dimension + ); + mfem::Mult( + workspace.m_matrix_temp_1, base_context.inverse_mapping_jacobian, + variation.inverse_mapping_jacobian_variation + ); + variation.inverse_mapping_jacobian_variation *= -1.0; + + if (!vector_is_finite(variation.physical_position_variation) || + !matrix_is_finite(variation.mapping_jacobian_variation) || + !matrix_is_finite(variation.inverse_mapping_jacobian_variation) || + !std::isfinite(variation.mapping_determinant_variation)) { + return MappingStatus::non_finite_result; + } + + return MappingStatus::valid; + } + + MappingStatus DomainMapperStateless::EvaluateVolumeVariation( + const ElementMappingData &element_data, + const ElementDisplacementData &direction, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + const VolumeMappingContext &base_context, + Workspace &workspace, + VolumeMappingVariation &variation + ) const { + const MappingStatus point_status = EvaluatePointVariation( + element_data, direction, transformation, integration_point, + base_context.mapping, workspace, variation.mapping + ); + if (point_status != MappingStatus::valid) + return point_status; + + transformation.SetIntPoint(&integration_point); + mfem::Mult( + variation.mapping.mapping_jacobian_variation, + transformation.Jacobian(), workspace.m_full_element_jacobian + ); + mfem::Mult( + base_context.quadrature.J_inv, workspace.m_full_element_jacobian, + workspace.m_matrix_temp_1 + ); + + variation.inverse_element_jacobian_variation.SetSize( + m_options.dimension, m_options.dimension + ); + mfem::Mult( + workspace.m_matrix_temp_1, base_context.quadrature.J_inv, + variation.inverse_element_jacobian_variation + ); + variation.inverse_element_jacobian_variation *= -1.0; + + variation.weight_variation = + integration_point.weight * transformation.Weight() * + variation.mapping.mapping_determinant_variation; + + if (!matrix_is_finite(variation.inverse_element_jacobian_variation) || + !std::isfinite(variation.weight_variation)) + return MappingStatus::non_finite_result; + + return MappingStatus::valid; + } + + MappingStatus DomainMapperStateless::EvaluateFaceVariation( + const ElementMappingData &element_data, + const ElementDisplacementData &direction, + mfem::FaceElementTransformations &transformation, + const FaceElementSide side, + const mfem::IntegrationPoint &integration_point, + const FaceMappingContext &base_context, + Workspace &workspace, + FaceMappingVariation &variation + ) const { + transformation.SetAllIntPoints(&integration_point); + mfem::ElementTransformation &element_transformation = + SelectFaceElementTransformation(transformation, side); + const mfem::IntegrationPoint &element_integration_point = + SelectFaceElementIntegrationPoint(transformation, side); + + const MappingStatus point_status = EvaluatePointVariation( + element_data, direction, element_transformation, + element_integration_point, base_context.mapping, workspace, + variation.mapping + ); + if (point_status != MappingStatus::valid) + return point_status; + + workspace.m_reference_normal.SetSize(m_options.dimension); + mfem::CalcOrtho( + transformation.Jacobian(), workspace.m_reference_normal + ); + if (side == FaceElementSide::element_2) + workspace.m_reference_normal *= -1.0; + + const double reference_normal_magnitude = + workspace.m_reference_normal.Norml2(); + if (!std::isfinite(reference_normal_magnitude) || + reference_normal_magnitude <= 0.0) + return MappingStatus::non_finite_result; + + base_context.mapping.inverse_mapping_jacobian.MultTranspose( + workspace.m_reference_normal, workspace.m_vector_temp + ); + workspace.m_mapped_normal = workspace.m_vector_temp; + workspace.m_mapped_normal *= base_context.mapping.mapping_determinant; + + variation.physical_normal_variation.SetSize(m_options.dimension); + variation.mapping.inverse_mapping_jacobian_variation.MultTranspose( + workspace.m_reference_normal, variation.physical_normal_variation + ); + variation.physical_normal_variation *= + base_context.mapping.mapping_determinant; + variation.physical_normal_variation.Add( + variation.mapping.mapping_determinant_variation, + workspace.m_vector_temp + ); + + const double mapped_normal_magnitude = + workspace.m_mapped_normal.Norml2(); + if (!std::isfinite(mapped_normal_magnitude) || + mapped_normal_magnitude <= 0.0) + return MappingStatus::non_finite_result; + + const double mapped_normal_magnitude_variation = + base_context.quadrature.normal * + variation.physical_normal_variation; + + variation.physical_normal_variation.Add( + -mapped_normal_magnitude_variation, base_context.quadrature.normal + ); + variation.physical_normal_variation /= mapped_normal_magnitude; + + variation.physical_surface_weight_variation = + integration_point.weight * mapped_normal_magnitude_variation; + variation.normal_flux_scale_variation = + mapped_normal_magnitude_variation / reference_normal_magnitude; + + if (!vector_is_finite(variation.physical_normal_variation) || + !std::isfinite(variation.physical_surface_weight_variation) || + !std::isfinite(variation.normal_flux_scale_variation)) { + return MappingStatus::non_finite_result; + } + + return MappingStatus::valid; + } +} // namespace mean_field::mapping \ No newline at end of file diff --git a/libmeanfield/impl/mapping/transformations.cpp b/libmeanfield/impl/mapping/transformations.cpp new file mode 100644 index 0000000..e41f963 --- /dev/null +++ b/libmeanfield/impl/mapping/transformations.cpp @@ -0,0 +1,276 @@ +module; +#include + +module mean_field; +import :mapping.types; + +namespace mean_field::mapping { + void MapHDivFluxToPhysical( + const MappingPointContext &context, + const mfem::Vector &reference_flux, + mfem::Vector &physical_flux + ) { + MFEM_VERIFY( + reference_flux.Size() == context.mapping_jacobian.Width(), + "The reference H(div) flux has the wrong dimension." + ); + + physical_flux.SetSize(reference_flux.Size()); + context.mapping_jacobian.Mult(reference_flux, physical_flux); + physical_flux /= context.mapping_determinant; + } + + void MapPhysicalFluxToHDivReference( + const MappingPointContext &context, + const mfem::Vector &physical_flux, + mfem::Vector &reference_flux + ) { + MFEM_VERIFY( + physical_flux.Size() == context.inverse_mapping_jacobian.Width(), + "The physical H(div) flux has the wrong dimension." + ); + + reference_flux.SetSize(physical_flux.Size()); + context.inverse_mapping_jacobian.Mult(physical_flux, reference_flux); + reference_flux *= context.mapping_determinant; + } + + void MapReferenceGradientToPhysical( + const MappingPointContext &context, + const mfem::Vector &reference_gradient, + mfem::Vector &physical_gradient + ) { + MFEM_VERIFY( + reference_gradient.Size() == + context.inverse_mapping_jacobian.Height(), + "The reference scalar gradient has the wrong dimension." + ); + + physical_gradient.SetSize(reference_gradient.Size()); + context.inverse_mapping_jacobian.MultTranspose( + reference_gradient, physical_gradient + ); + } + + void MapPhysicalGradientToReference( + const MappingPointContext &context, + const mfem::Vector &physical_gradient, + mfem::Vector &reference_gradient + ) { + MFEM_VERIFY( + physical_gradient.Size() == context.mapping_jacobian.Height(), + "The physical scalar gradient has the wrong dimension." + ); + + reference_gradient.SetSize(physical_gradient.Size()); + context.mapping_jacobian.MultTranspose( + physical_gradient, reference_gradient + ); + } + + void MapReferenceVectorGradientToPhysical( + const MappingPointContext &context, + const mfem::DenseMatrix &reference_gradient, + mfem::DenseMatrix &physical_gradient + ) { + MFEM_VERIFY( + reference_gradient.Width() == + context.inverse_mapping_jacobian.Height(), + "The reference vector gradient has the wrong dimension." + ); + + physical_gradient.SetSize( + reference_gradient.Height(), + context.inverse_mapping_jacobian.Width() + ); + mfem::Mult( + reference_gradient, context.inverse_mapping_jacobian, + physical_gradient + ); + } + + void MapPhysicalVectorGradientToReference( + const MappingPointContext &context, + const mfem::DenseMatrix &physical_gradient, + mfem::DenseMatrix &reference_gradient + ) { + MFEM_VERIFY( + physical_gradient.Width() == context.mapping_jacobian.Height(), + "The physical vector gradient has the wrong dimension." + ); + + reference_gradient.SetSize( + physical_gradient.Height(), context.mapping_jacobian.Width() + ); + mfem::Mult( + physical_gradient, context.mapping_jacobian, reference_gradient + ); + } + + double MapHDivDivergenceToPhysical( + const MappingPointContext &context, + const double reference_divergence + ) { + return reference_divergence / context.mapping_determinant; + } + + void ComputeHDivMassTensor( + const MappingPointContext &context, + mfem::DenseMatrix &mass_tensor + ) { + const int dimension = context.mapping_jacobian.Height(); + + MFEM_VERIFY( + context.mapping_jacobian.Width() == dimension, + "The mapping Jacobian must be square." + ); + MFEM_VERIFY( + context.mapping_determinant > 0.0, + "The mapping determinant must be positive." + ); + + mass_tensor.SetSize(dimension, dimension); + mfem::MultAtB( + context.mapping_jacobian, context.mapping_jacobian, mass_tensor + ); + mass_tensor *= 1 / context.mapping_determinant; + } + + void ComputeScalarDiffusionTensor( + const MappingPointContext &context, + mfem::DenseMatrix &diffusion_tensor + ) { + const int dimension = context.inverse_mapping_jacobian.Height(); + + MFEM_VERIFY( + context.inverse_mapping_jacobian.Width() == dimension, + "The inverse mapping Jacobian must be square." + ); + MFEM_VERIFY( + context.mapping_determinant > 0.0, + "The mapping determinant must be positive." + ); + + diffusion_tensor.SetSize(dimension, dimension); + mfem::MultABt( + context.inverse_mapping_jacobian, context.inverse_mapping_jacobian, + diffusion_tensor + ); + diffusion_tensor *= context.mapping_determinant; + } + + void MapHCurlFieldToPhysical( + const MappingPointContext &context, + const mfem::Vector &reference_field, + mfem::Vector &physical_field + ) { + MFEM_VERIFY( + reference_field.Size() == context.inverse_mapping_jacobian.Height(), + "The reference H(curl) field has the wrong dimension." + ); + + physical_field.SetSize(reference_field.Size()); + context.inverse_mapping_jacobian.MultTranspose( + reference_field, physical_field + ); + } + + void MapPhysicalFieldToHCurlReference( + const MappingPointContext &context, + const mfem::Vector &physical_field, + mfem::Vector &reference_field + ) { + MFEM_VERIFY( + physical_field.Size() == context.mapping_jacobian.Height(), + "The physical H(curl) field has the wrong dimension." + ); + + reference_field.SetSize(physical_field.Size()); + context.mapping_jacobian.MultTranspose(physical_field, reference_field); + } + + void MapHCurlCurlToPhysical( + const MappingPointContext &context, + const mfem::Vector &reference_curl, + mfem::Vector &physical_curl + ) { + MFEM_VERIFY( + reference_curl.Size() == context.mapping_jacobian.Width(), + "The reference H(curl) curl has the wrong dimension." + ); + + physical_curl.SetSize(reference_curl.Size()); + context.mapping_jacobian.Mult(reference_curl, physical_curl); + physical_curl /= context.mapping_determinant; + } + + void MapPhysicalCurlToHCurlReference( + const MappingPointContext &context, + const mfem::Vector &physical_curl, + mfem::Vector &reference_curl + ) { + MFEM_VERIFY( + physical_curl.Size() == context.inverse_mapping_jacobian.Width(), + "The physical H(curl) curl has the wrong dimension." + ); + + reference_curl.SetSize(physical_curl.Size()); + context.inverse_mapping_jacobian.Mult(physical_curl, reference_curl); + reference_curl *= context.mapping_determinant; + } + + // TODO: Investigate these + void ComputeHCurlMassTensor( + const MappingPointContext &context, + mfem::DenseMatrix &mass_tensor + ) { + ComputeScalarDiffusionTensor(context, mass_tensor); + } + + void ComputeHCurlCurlTensor( + const MappingPointContext &context, + mfem::DenseMatrix &curl_tensor + ) { + ComputeHDivMassTensor(context, curl_tensor); + } + + void ComputeHDivMassTensorVariation( + const MappingPointContext &context, + const MappingPointVariation &variation, + mfem::DenseMatrix &mass_tensor_variation + ) { + const double determinant = context.mapping_determinant; + const double determinant_variation = + variation.mapping_determinant_variation; + const int dimension = context.inverse_mapping_jacobian.Width(); + + mass_tensor_variation.SetSize(dimension, dimension); + + MFEM_VERIFY( + std::isfinite(determinant) && determinant > 0.0, + "The mapping determinant must be positive and finite." + ); + MFEM_VERIFY( + std::isfinite(determinant_variation), + "The mapping determinant variation must be finite." + ); + + mfem::DenseMatrix determinant_correction(dimension, dimension); + ComputeHDivMassTensor(context, determinant_correction); + determinant_correction *= determinant_variation / determinant; + + mfem::DenseMatrix right_jacobian_variation(dimension, dimension); + mfem::MultAtB( + context.mapping_jacobian, variation.mapping_jacobian_variation, + right_jacobian_variation + ); + mfem::MultAtB( + variation.mapping_jacobian_variation, context.mapping_jacobian, + mass_tensor_variation + ); + + mass_tensor_variation += right_jacobian_variation; + mass_tensor_variation *= 1 / determinant; + mass_tensor_variation -= determinant_correction; + } +} // namespace mean_field::mapping \ No newline at end of file diff --git a/libmeanfield/impl/operators/contexts/barotropic_closure_linearization_context.cpp b/libmeanfield/impl/operators/contexts/barotropic_closure_linearization_context.cpp new file mode 100644 index 0000000..a72cbd3 --- /dev/null +++ b/libmeanfield/impl/operators/contexts/barotropic_closure_linearization_context.cpp @@ -0,0 +1,135 @@ +module; + +#include + +#include + +module mean_field; +import :operators.context.barotropic_closure_linearization; + +namespace mean_field::operators::context::barotropic { + BarotropicClosureLinearizationContext:: + BarotropicClosureLinearizationContext( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope + ) + : m_f(f), + m_operator( + f, + domainMapper, + barotrope + ) { + MFEM_VERIFY( + m_f.densityFes != nullptr, + "The closure linearization context requires the " + "density finite-element space." + ); + + MFEM_VERIFY( + m_f.enthalpyFes != nullptr, + "The closure linearization context requires the " + "enthalpy finite-element space." + ); + + MFEM_VERIFY( + m_f.displacementFes != nullptr, + "The closure linearization context requires the " + "displacement finite-element space." + ); + } + + void BarotropicClosureLinearizationContext::Prepare( + const mfem::Vector &baseDensityTrue, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &displacementTrue, + const BarotropicClosureRevisions &revisions + ) { + MFEM_VERIFY( + baseDensityTrue.Size() == m_f.densityFes->GetTrueVSize(), + "The closure base-density vector has the wrong size." + ); + + MFEM_VERIFY( + baseEnthalpyTrue.Size() == m_f.enthalpyFes->GetTrueVSize(), + "The closure base-enthalpy vector has the wrong size." + ); + + MFEM_VERIFY( + displacementTrue.Size() == m_f.displacementFes->GetTrueVSize(), + "The closure displacement vector has the wrong size." + ); + + if (m_isPrepared && revisions == m_revisions) { + return; + } + + m_operator.Prepare(baseDensityTrue, baseEnthalpyTrue, displacementTrue); + + m_baseDensityTrue = baseDensityTrue; + m_baseEnthalpyTrue = baseEnthalpyTrue; + m_displacementTrue = displacementTrue; + + m_revisions = revisions; + m_isPrepared = true; + ++m_preparationCount; + } + + bool BarotropicClosureLinearizationContext::IsPrepared() const noexcept { + return m_isPrepared; + } + + bool BarotropicClosureLinearizationContext::MatchesRevisions( + const BarotropicClosureRevisions &revisions + ) const noexcept { + return m_isPrepared && revisions == m_revisions; + } + + std::uint64_t BarotropicClosureLinearizationContext:: + GetPreparationCount() const noexcept { + return m_preparationCount; + } + + const BarotropicClosureRevisions & + BarotropicClosureLinearizationContext::GetRevisions() const { + VerifyPrepared(); + return m_revisions; + } + + const mfem::Vector & + BarotropicClosureLinearizationContext::GetBaseDensityTrue() const { + VerifyPrepared(); + return m_baseDensityTrue; + } + + const mfem::Vector & + BarotropicClosureLinearizationContext::GetBaseEnthalpyTrue() const { + VerifyPrepared(); + return m_baseEnthalpyTrue; + } + + const mfem::Vector & + BarotropicClosureLinearizationContext::GetDisplacementTrue() const { + VerifyPrepared(); + return m_displacementTrue; + } + + const PreparedBarotropicClosureOperator & + BarotropicClosureLinearizationContext::GetOperator() const noexcept { + return m_operator; + } + + void BarotropicClosureLinearizationContext::BuildResidual( + mfem::Vector &residual + ) const { + VerifyPrepared(); + m_operator.BuildResidual(residual); + } + + void BarotropicClosureLinearizationContext::VerifyPrepared() const { + MFEM_VERIFY( + m_isPrepared, "The barotropic-closure linearization context " + "has not been prepared." + ); + } +} // namespace mean_field::operators::context::barotropic \ No newline at end of file diff --git a/libmeanfield/impl/operators/contexts/gravity_field_context.cpp b/libmeanfield/impl/operators/contexts/gravity_field_context.cpp new file mode 100644 index 0000000..07ee7b6 --- /dev/null +++ b/libmeanfield/impl/operators/contexts/gravity_field_context.cpp @@ -0,0 +1,442 @@ +module; +#include +#include +#include + +module mean_field; +import :operators.context.gravity_field; + +namespace { + void validate_displacement( + const mean_field::fem::FEM &f, + const mfem::Vector &displacement_true + ) { + MFEM_VERIFY( + f.displacementFes != nullptr, + "GravityFieldGeometryContext requires the " + "displacement finite-element space." + ); + MFEM_VERIFY( + displacement_true.Size() == f.displacementFes->GetTrueVSize(), + "GravityFieldGeometryContext received a displacement vector with " + "the " + "wrong size." + ); + + for (int i = 0; i < displacement_true.Size(); ++i) { + MFEM_VERIFY( + std::isfinite(displacement_true(i)), + "GravityFieldGeometryContext received a non-finite " + "displacement " + "value." + ); + } + } + + void validate_linearization_state( + const mean_field::fem::FEM &f, + const mean_field::operators::context::gravity_field:: + GravityFieldStateView &state + ) { + MFEM_VERIFY( + f.densityFes != nullptr, "GravityFieldLinearizationContext " + "requires the density finite-element " + "space." + ); + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "GravityFieldLinearizationContext requires the gravity-potential " + "finite-element space." + ); + MFEM_VERIFY( + f.gravityFluxFes != nullptr, + "GravityFieldLinearizationContext requires the " + "gravity-gradient finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, + "GravityFieldLinearizationContext requires " + "the displacement finite-element space." + ); + + MFEM_VERIFY( + state.density.Size() == f.densityFes->GetTrueVSize(), + "GravityFieldLinearizationContext received a density vector with " + "the " + "wrong size." + ); + MFEM_VERIFY( + state.displacement.Size() == f.displacementFes->GetTrueVSize(), + "GravityFieldLinearizationContext received a displacement vector " + "with " + "the wrong size." + ); + MFEM_VERIFY( + state.gravity_gradient.Size() == f.gravityFluxFes->GetTrueVSize(), + "GravityFieldLinearizationContext received a gravity-gradient " + "vector " + "with the wrong size." + ); + MFEM_VERIFY( + state.gravity_potential.Size() == + f.gravityPotentialFes->GetTrueVSize(), + "GravityFieldLinearizationContext received a gravity-potential " + "vector " + "with the wrong size." + ); + + for (int i = 0; i < state.density.Size(); ++i) { + MFEM_VERIFY( + std::isfinite(state.density(i)), + "GravityFieldLinearizationContext received a non-finite " + "density " + "value." + ); + } + + for (int i = 0; i < state.displacement.Size(); ++i) { + MFEM_VERIFY( + std::isfinite(state.displacement(i)), + "GravityFieldLinearizationContext received a non-finite " + "displacement " + "value." + ); + } + + for (int i = 0; i < state.gravity_gradient.Size(); ++i) { + MFEM_VERIFY( + std::isfinite(state.gravity_gradient(i)), + "GravityFieldLinearizationContext received a non-finite " + "gravity-gradient value." + ); + } + + for (int i = 0; i < state.gravity_potential.Size(); ++i) { + MFEM_VERIFY( + std::isfinite(state.gravity_potential(i)), + "GravityFieldLinearizationContext received a non-finite " + "gravity-potential value." + ); + } + } +} // namespace + +namespace mean_field::operators::context::gravity_field { + GravityFieldGeometryContext::GravityFieldGeometryContext( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper + ) + : m_fem(f), + m_domain_mapper(domain_mapper) { + MFEM_VERIFY( + f.mesh != nullptr, "GravityFieldGeometryContext requires a mesh." + ); + MFEM_VERIFY( + f.gravityFluxFes != nullptr, + "GravityFieldGeometryContext requires the " + "gravity-gradient finite-element space." + ); + MFEM_VERIFY( + f.densityFes != nullptr, + "GravityFieldGeometryContext requires the density finite-element " + "space." + ); + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "GravityFieldGeometryContext requires the gravity-potential " + "finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, + "GravityFieldGeometryContext requires the " + "displacement finite-element space." + ); + MFEM_VERIFY( + f.compactificationFes != nullptr, + "GravityFieldGeometryContext requires the compactification " + "finite-element space." + ); + MFEM_VERIFY( + f.compactificationCoordinate != nullptr, + "GravityFieldGeometryContext requires the compactification " + "coordinate." + ); + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "GravityFieldGeometryContext requires the quadrature-rule factory." + ); + MFEM_VERIFY( + domain_mapper.GetDimension() == f.mesh->Dimension(), + "The stateless domain-mapper dimension does not match the mesh " + "dimension." + ); + } + + GravityFieldGeometryPreparation GravityFieldGeometryContext::Prepare( + const mfem::Vector &displacement_true, + const DiscretizationRevision discretization_revision, + const DisplacementRevision displacement_revision + ) { + validate_displacement(m_fem, displacement_true); + + if (m_is_prepared) { + MFEM_VERIFY( + discretization_revision >= m_discretization_revision, + "GravityFieldGeometryContext received an older discretization " + "revision." + ); + MFEM_VERIFY( + displacement_revision >= m_displacement_revision, + "GravityFieldGeometryContext received an older displacement " + "revision." + ); + } + + const bool discretization_changed = + !m_is_prepared || + discretization_revision != m_discretization_revision; + const bool displacement_changed = + !m_is_prepared || displacement_revision != m_displacement_revision; + + GravityFieldGeometryPreparation preparation; + + if (!discretization_changed && !displacement_changed) { + return preparation; + } + + if (discretization_changed) { + auto mass_operator = + std::make_unique( + m_fem, m_domain_mapper + ); + auto source_operator = + std::make_unique( + m_fem, m_domain_mapper + ); + + mass_operator->Prepare(displacement_true); + source_operator->Prepare(displacement_true); + + m_mass_operator = std::move(mass_operator); + m_source_operator = std::move(source_operator); + + preparation.reconstructed_operators = true; + preparation.rebuilt_mass_operator = true; + preparation.rebuilt_source_operator = true; + } else { + MFEM_VERIFY( + m_mass_operator != nullptr, "GravityFieldGeometryContext has " + "no prepared H(div) mass operator." + ); + MFEM_VERIFY( + m_source_operator != nullptr, + "GravityFieldGeometryContext has no prepared gravity source " + "operator." + ); + + m_mass_operator->Prepare(displacement_true); + m_source_operator->Prepare(displacement_true); + + preparation.rebuilt_mass_operator = true; + preparation.rebuilt_source_operator = true; + } + + m_displacement_true = displacement_true; + m_discretization_revision = discretization_revision; + m_displacement_revision = displacement_revision; + m_is_prepared = true; + + preparation.refreshed_variation_state = true; + + return preparation; + } + + const PreparedMappedHDivMassOperator & + GravityFieldGeometryContext::GetMassOperator() const { + MFEM_VERIFY( + m_is_prepared, + "GravityFieldGeometryContext must be prepared before " + "accessing its mass operator." + ); + MFEM_VERIFY( + m_mass_operator != nullptr, + "GravityFieldGeometryContext has no prepared H(div) mass operator." + ); + return *m_mass_operator; + } + + const PreparedMappedGravitySourceOperator & + GravityFieldGeometryContext::GetSourceOperator() const { + MFEM_VERIFY( + m_is_prepared, + "GravityFieldGeometryContext must be prepared before " + "accessing its source operator." + ); + MFEM_VERIFY( + m_source_operator != nullptr, "GravityFieldGeometryContext has no " + "prepared gravity source operator." + ); + return *m_source_operator; + } + + const mfem::Vector &GravityFieldGeometryContext::GetDisplacement() const { + MFEM_VERIFY( + m_is_prepared, + "GravityFieldGeometryContext must be prepared before " + "accessing its displacement." + ); + return m_displacement_true; + } + + DiscretizationRevision + GravityFieldGeometryContext::GetDiscretizationRevision() const noexcept { + return m_discretization_revision; + } + + DisplacementRevision + GravityFieldGeometryContext::GetDisplacementRevision() const noexcept { + return m_displacement_revision; + } + + bool GravityFieldGeometryContext::IsPrepared() const noexcept { + return m_is_prepared; + } + + GravityFieldLinearizationContext::GravityFieldLinearizationContext( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper + ) + : m_fem(f), + m_geometry_context( + f, + domain_mapper + ) { + MFEM_VERIFY( + f.densityFes != nullptr, "GravityFieldLinearizationContext " + "requires the density finite-element " + "space." + ); + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "GravityFieldLinearizationContext requires the gravity-potential " + "finite-element space." + ); + MFEM_VERIFY( + f.gravityFluxFes != nullptr, + "GravityFieldLinearizationContext requires the " + "gravity-gradient finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, + "GravityFieldLinearizationContext requires " + "the displacement finite-element space." + ); + } + + GravityFieldPreparationReport GravityFieldLinearizationContext::Prepare( + const GravityFieldStateView &state, + const GravityFieldRevisions &revisions + ) { + validate_linearization_state(m_fem, state); + + if (m_is_prepared) { + MFEM_VERIFY( + revisions.discretization >= m_revisions.discretization, + "GravityFieldLinearizationContext received an older " + "discretization " + "revision." + ); + MFEM_VERIFY( + revisions.displacement >= m_revisions.displacement, + "GravityFieldLinearizationContext received an older " + "displacement " + "revision." + ); + MFEM_VERIFY( + revisions.density >= m_revisions.density, + "GravityFieldLinearizationContext received an older density " + "revision." + ); + MFEM_VERIFY( + revisions.gravity_gradient >= m_revisions.gravity_gradient, + "GravityFieldLinearizationContext received an older " + "gravity-gradient " + "revision." + ); + MFEM_VERIFY( + revisions.gravity_potential >= m_revisions.gravity_potential, + "GravityFieldLinearizationContext received an older " + "gravity-potential revision." + ); + } + + const bool discretization_changed = + !m_is_prepared || + revisions.discretization != m_revisions.discretization; + const bool density_changed = !m_is_prepared || discretization_changed || + revisions.density != m_revisions.density; + const bool gravity_gradient_changed = + !m_is_prepared || discretization_changed || + revisions.gravity_gradient != m_revisions.gravity_gradient; + + GravityFieldPreparationReport report; + + report.geometry = m_geometry_context.Prepare( + state.displacement, revisions.discretization, revisions.displacement + ); + + if (density_changed) { + m_density_true = state.density; + report.updated_density = true; + } + + if (gravity_gradient_changed) { + m_gravity_gradient_true = state.gravity_gradient; + report.updated_gravity_gradient = true; + } + + m_revisions = revisions; + m_is_prepared = true; + + return report; + } + + const GravityFieldGeometryContext & + GravityFieldLinearizationContext::GetGeometryContext() const { + MFEM_VERIFY( + m_is_prepared, "GravityFieldLinearizationContext must be prepared " + "before accessing its geometry context." + ); + return m_geometry_context; + } + + const mfem::Vector &GravityFieldLinearizationContext::GetDensity() const { + MFEM_VERIFY( + m_is_prepared, "GravityFieldLinearizationContext must be prepared " + "before accessing its density." + ); + return m_density_true; + } + + const mfem::Vector & + GravityFieldLinearizationContext::GetGravityGradient() const { + MFEM_VERIFY( + m_is_prepared, "GravityFieldLinearizationContext must be prepared " + "before accessing its gravity gradient." + ); + return m_gravity_gradient_true; + } + + const GravityFieldRevisions & + GravityFieldLinearizationContext::GetRevisions() const { + MFEM_VERIFY( + m_is_prepared, "GravityFieldLinearizationContext must be prepared " + "before accessing its revisions." + ); + return m_revisions; + } + + bool GravityFieldLinearizationContext::IsPrepared() const noexcept { + return m_is_prepared; + } +} // namespace mean_field::operators::context::gravity_field diff --git a/libmeanfield/impl/operators/contexts/hydrostatic_equilibrium_context.cpp b/libmeanfield/impl/operators/contexts/hydrostatic_equilibrium_context.cpp new file mode 100644 index 0000000..67886ef --- /dev/null +++ b/libmeanfield/impl/operators/contexts/hydrostatic_equilibrium_context.cpp @@ -0,0 +1,309 @@ +module; + +#include + +#include + +module mean_field; + +import :operators.context.hydrostatic_equilibrium; + +namespace { + void validate_finite_vector( + const mfem::Vector &vector, + const char *message + ) { + for (int i = 0; i < vector.Size(); ++i) { + MFEM_VERIFY(std::isfinite(vector(i)), message); + } + } + + void validate_state( + const mean_field::fem::FEM &f, + const mean_field::operators::context::hydrostatic:: + HydrostaticEquilibriumStateView &state + ) { + MFEM_VERIFY( + f.enthalpyFes != nullptr, + "HydrostaticEquilibriumContext requires the " + "enthalpy finite-element space." + ); + + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "HydrostaticEquilibriumContext requires the " + "gravity-potential finite-element space." + ); + + MFEM_VERIFY( + f.displacementFes != nullptr, + "HydrostaticEquilibriumContext requires the " + "displacement finite-element space." + ); + + MFEM_VERIFY( + state.enthalpy.Size() == f.enthalpyFes->GetTrueVSize(), + "HydrostaticEquilibriumContext received an " + "enthalpy vector with the wrong size." + ); + + MFEM_VERIFY( + state.gravityPotential.Size() == + f.gravityPotentialFes->GetTrueVSize(), + "HydrostaticEquilibriumContext received a " + "gravity-potential vector with the wrong size." + ); + + MFEM_VERIFY( + state.displacement.Size() == f.displacementFes->GetTrueVSize(), + "HydrostaticEquilibriumContext received a " + "displacement vector with the wrong size." + ); + + validate_finite_vector( + state.enthalpy, "HydrostaticEquilibriumContext received a " + "non-finite enthalpy value." + ); + + validate_finite_vector( + state.gravityPotential, "HydrostaticEquilibriumContext received a " + "non-finite gravity-potential value." + ); + + validate_finite_vector( + state.displacement, "HydrostaticEquilibriumContext received a " + "non-finite displacement value." + ); + + MFEM_VERIFY( + std::isfinite(state.bernoulliConstant), + "HydrostaticEquilibriumContext received a " + "non-finite Bernoulli constant." + ); + } + + template + void validate_dependency_transition( + const Stamp &prepared, + const Stamp &requested, + const char *message + ) { + MFEM_VERIFY(requested.CanFollow(prepared), message); + } +} // namespace + +namespace mean_field::operators::context::hydrostatic { + HydrostaticEquilibriumContext::HydrostaticEquilibriumContext( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper + ) + : m_f(f), + m_domainMapper(domainMapper) { + MFEM_VERIFY( + m_f.mesh != nullptr, + "HydrostaticEquilibriumContext requires a mesh." + ); + + MFEM_VERIFY( + m_f.enthalpyFes != nullptr, + "HydrostaticEquilibriumContext requires the " + "enthalpy finite-element space." + ); + + MFEM_VERIFY( + m_f.gravityPotentialFes != nullptr, + "HydrostaticEquilibriumContext requires the " + "gravity-potential finite-element space." + ); + + MFEM_VERIFY( + m_f.displacementFes != nullptr, + "HydrostaticEquilibriumContext requires the " + "displacement finite-element space." + ); + + MFEM_VERIFY( + m_domainMapper.GetDimension() == m_f.mesh->Dimension(), + "The hydrostatic context's stateless " + "domain-mapper dimension does not match the mesh " + "dimension." + ); + } + + HydrostaticPreparationReport HydrostaticEquilibriumContext::Prepare( + const HydrostaticEquilibriumStateView &state, + const HydrostaticEquilibriumDependencies &dependencies + ) { + validate_state(m_f, state); + + if (m_isPrepared) { + validate_dependency_transition( + m_dependencies.discretization, dependencies.discretization, + "HydrostaticEquilibriumContext received an older " + "discretization revision for the same identity." + ); + + validate_dependency_transition( + m_dependencies.enthalpy, dependencies.enthalpy, + "HydrostaticEquilibriumContext received an older " + "enthalpy revision for the same identity." + ); + + validate_dependency_transition( + m_dependencies.gravityPotential, dependencies.gravityPotential, + "HydrostaticEquilibriumContext received an older " + "gravity-potential revision for the same identity." + ); + + validate_dependency_transition( + m_dependencies.displacement, dependencies.displacement, + "HydrostaticEquilibriumContext received an older " + "displacement revision for the same identity." + ); + + validate_dependency_transition( + m_dependencies.rotation, dependencies.rotation, + "HydrostaticEquilibriumContext received an older " + "rotation revision for the same identity." + ); + + validate_dependency_transition( + m_dependencies.bernoulliConstant, + dependencies.bernoulliConstant, + "HydrostaticEquilibriumContext received an older " + "Bernoulli-constant revision for the same identity." + ); + } + + const bool staticChanged = + !m_isPrepared || + dependencies.discretization != m_dependencies.discretization; + + const bool enthalpyChanged = + !m_isPrepared || dependencies.enthalpy != m_dependencies.enthalpy; + + const bool gravityPotentialChanged = + !m_isPrepared || + dependencies.gravityPotential != m_dependencies.gravityPotential; + + const bool displacementChanged = + !m_isPrepared || + dependencies.displacement != m_dependencies.displacement; + + const bool rotationChanged = + !m_isPrepared || dependencies.rotation != m_dependencies.rotation; + + const bool bernoulliConstantChanged = + !m_isPrepared || + dependencies.bernoulliConstant != m_dependencies.bernoulliConstant; + + const bool geometryPreparationRequired = + staticChanged || displacementChanged; + + const bool rotationPreparationRequired = + geometryPreparationRequired || rotationChanged; + + const bool baseStatePreparationRequired = + rotationPreparationRequired || enthalpyChanged || + gravityPotentialChanged || bernoulliConstantChanged; + + HydrostaticPreparationReport report; + + report.preparedStaticDependencies = staticChanged; + report.preparedGeometryState = geometryPreparationRequired; + report.preparedRotationDependencies = rotationPreparationRequired; + report.preparedBaseState = baseStatePreparationRequired; + + if (staticChanged || enthalpyChanged) { + m_baseEnthalpyTrue = state.enthalpy; + report.updatedEnthalpy = true; + } + + if (staticChanged || gravityPotentialChanged) { + m_baseGravityPotentialTrue = state.gravityPotential; + + report.updatedGravityPotential = true; + } + + if (geometryPreparationRequired) { + m_displacementTrue = state.displacement; + report.updatedDisplacement = true; + } + + if (staticChanged || bernoulliConstantChanged) { + m_bernoulliConstant = state.bernoulliConstant; + report.updatedBernoulliConstant = true; + } + + if (report.preparedStaticDependencies) { + ++m_statistics.staticPreparations; + } + + if (report.preparedGeometryState) { + ++m_statistics.geometryPreparations; + } + + if (report.preparedRotationDependencies) { + ++m_statistics.rotationPreparations; + } + + if (report.preparedBaseState) { + ++m_statistics.baseStatePreparations; + } + + m_dependencies = dependencies; + m_isPrepared = true; + + return report; + } + + bool HydrostaticEquilibriumContext::IsPrepared() const noexcept { + return m_isPrepared; + } + + bool HydrostaticEquilibriumContext::MatchesDependencies( + const HydrostaticEquilibriumDependencies &dependencies + ) const noexcept { + return m_isPrepared && dependencies == m_dependencies; + } + + const HydrostaticEquilibriumDependencies & + HydrostaticEquilibriumContext::GetDependencies() const { + VerifyPrepared(); + return m_dependencies; + } + + const HydrostaticPreparationStatistics & + HydrostaticEquilibriumContext::GetPreparationStatistics() const noexcept { + return m_statistics; + } + + const mfem::Vector & + HydrostaticEquilibriumContext::GetBaseEnthalpyTrue() const { + VerifyPrepared(); + return m_baseEnthalpyTrue; + } + + const mfem::Vector & + HydrostaticEquilibriumContext::GetBaseGravityPotentialTrue() const { + VerifyPrepared(); + return m_baseGravityPotentialTrue; + } + + const mfem::Vector & + HydrostaticEquilibriumContext::GetDisplacementTrue() const { + VerifyPrepared(); + return m_displacementTrue; + } + + double HydrostaticEquilibriumContext::GetBernoulliConstant() const { + VerifyPrepared(); + return m_bernoulliConstant; + } + + void HydrostaticEquilibriumContext::VerifyPrepared() const { + MFEM_VERIFY( + m_isPrepared, "HydrostaticEquilibriumContext has not been prepared." + ); + } +} // namespace mean_field::operators::context::hydrostatic diff --git a/libmeanfield/impl/operators/gravity_field.cpp b/libmeanfield/impl/operators/gravity_field.cpp new file mode 100644 index 0000000..e8be7a8 --- /dev/null +++ b/libmeanfield/impl/operators/gravity_field.cpp @@ -0,0 +1,790 @@ +module; +#include "profile.h" +#include +#include +#include +#include + +module mean_field; +import :operators.gravity_field; +import :solver.fields; +import :operators.kernels.gravity_field; + +namespace { + using namespace mean_field; + int get_state_width(const mfem::Array &state_true_offsets) { + MFEM_VERIFY( + state_true_offsets.Size() >= 2, + "The coupled state requires at least one block." + ); + MFEM_VERIFY( + state_true_offsets[0] == 0, + "The coupled state offsets must begin at zero." + ); + + for (int i = 0; i < state_true_offsets.Size() - 1; ++i) { + MFEM_VERIFY( + state_true_offsets[i + 1] >= state_true_offsets[i], + "The coupled state offsets must be nondecreasing." + ); + } + + MFEM_VERIFY( + state_true_offsets.Last() > 0, "The coupled state cannot be empty." + ); + return state_true_offsets.Last(); + } + + int get_gravity_residual_height(const fem::FEM &f) { + MFEM_VERIFY( + f.gravityFluxFes != nullptr, + "GravityFieldOperator requires the gravity-gradient finite-element " + "space (RT: Raviart-Thomas)." + ); + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "GravityFieldOperator requires the gravity-potential " + "finite-element " + "space (L2: Lebesgue " + "space of square-integrable functions)." + ); + return f.gravityFluxFes->GetTrueVSize() + + f.gravityPotentialFes->GetTrueVSize(); + } + + mfem::Array make_gravity_residual_offsets(const fem::FEM &f) { + mfem::Array offsets(operators::gravity_residual_block_count + 1); + offsets[0] = 0; + offsets[1] = f.gravityFluxFes->GetTrueVSize(); + offsets[2] = offsets[1] + f.gravityPotentialFes->GetTrueVSize(); + return offsets; + } + + template + int get_state_block_size( + const mfem::Array &state_true_offsets, + const utils::blocks::value_block + ) { + MFEM_VERIFY( + index + 1 < state_true_offsets.Size(), + "Value block is not present in the state offsets." + ); + return state_true_offsets[index + 1] - state_true_offsets[index]; + } + + void validate_state_offsets( + const fem::FEM &f, + const mfem::Array &state_true_offsets + ) { + MFEM_VERIFY( + f.densityFes != nullptr, + "GravityFieldOperator requires the density finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, "GravityFieldOperator requires the " + "displacement finite-element space." + ); + + using form = utils::blocks::gravity_field_form; + + constexpr auto density_block = utils::blocks::get_value_block
( + utils::blocks::density_field.mass_term + ); + constexpr auto displacement_block = + utils::blocks::get_value_block( + utils::blocks::displacement_field.geometry_term + ); + constexpr auto gravity_gradient_block = + utils::blocks::get_value_block( + utils::blocks::gravity_field.gradient_term + ); + constexpr auto gravity_potential_block = + utils::blocks::get_value_block( + utils::blocks::gravity_field.poisson_term + ); + + MFEM_VERIFY( + state_true_offsets.Size() == form::value_block_count + 1, + "The gravity state offsets do not match gravity_field_form." + ); + MFEM_VERIFY( + get_state_block_size(state_true_offsets, density_block) == + f.densityFes->GetTrueVSize(), + "The density block does not match the density finite-element space." + ); + MFEM_VERIFY( + get_state_block_size(state_true_offsets, displacement_block) == + f.displacementFes->GetTrueVSize(), + "The displacement block does not match the displacement " + "finite-element " + "space." + ); + MFEM_VERIFY( + get_state_block_size(state_true_offsets, gravity_gradient_block) == + f.gravityFluxFes->GetTrueVSize(), + "The gravity-gradient block does not match the RT finite-element " + "space." + ); + MFEM_VERIFY( + get_state_block_size(state_true_offsets, gravity_potential_block) == + f.gravityPotentialFes->GetTrueVSize(), + "The gravity-potential block does not match the potential " + "finite-element space." + ); + } + + void validate_gravity_context(const fem::FEM &f) { + MFEM_VERIFY( + f.gravityContext.b_form != nullptr, + "GravityFieldOperator requires the divergence operator." + ); + MFEM_VERIFY( + f.gravityContext.BT != nullptr, + "GravityFieldOperator requires the transpose divergence operator." + ); + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "GravityFieldOperator requires the quadrature-rule factory." + ); + } + + template + mfem::Vector make_read_only_value_view( + const mfem::Vector &vector, + const mfem::Array &offsets, + const utils::blocks::value_block + ) { + MFEM_VERIFY( + index + 1 < offsets.Size(), + "Value block is not present in the supplied offset array." + ); + + const int begin = offsets[index]; + const int size = offsets[index + 1] - begin; + + MFEM_VERIFY( + vector.Size() == offsets.Last(), + "Vector size does not match the value-block offsets." + ); + return mfem::Vector( + const_cast(vector.GetData()) + begin, size + ); + } + + template + mfem::Vector make_read_only_residual_view( + const mfem::Vector &vector, + const mfem::Array &offsets, + const utils::blocks::residual_block block + ) { + const int block_id = block; + const int begin = offsets[block_id]; + const int size = offsets[block_id + 1] - begin; + + MFEM_VERIFY( + vector.Size() == offsets.Last(), + "The vector does not match the residual-block layout." + ); + + mfem::Vector view; + view.MakeRef(const_cast(vector), begin, size); + return view; + } + + template + mfem::Vector make_residual_view( + mfem::Vector &vector, + const mfem::Array &offsets, + const utils::blocks::residual_block + ) { + MFEM_VERIFY( + index + 1 < offsets.Size(), + "Residual block is not present in the supplied offset array." + ); + + const int begin = offsets[index]; + const int size = offsets[index + 1] - begin; + + MFEM_VERIFY( + vector.Size() == offsets.Last(), + "Vector size does not match the residual-block offsets." + ); + return mfem::Vector(vector.GetData() + begin, size); + } +} // namespace + +namespace mean_field::operators { + GravityFieldOperator::GravityFieldOperator( + fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + context::gravity_field::GravityFieldLinearizationContext + &linearization_context, + const mfem::Array &state_true_offsets, + GravityFieldJacobianOperator &jacobian + ) + : Operator( + get_gravity_residual_height(f), + get_state_width(state_true_offsets) + ), + m_fem(f), + m_domain_mapper(domain_mapper), + m_linearization_context(linearization_context), + m_state_true_offsets(state_true_offsets), + m_residual_true_offsets(make_gravity_residual_offsets(f)), + m_jacobian(jacobian) { + MFEM_VERIFY(f.mesh != nullptr, "GravityFieldOperator requires a mesh."); + MFEM_VERIFY( + f.displacementFes != nullptr, "GravityFieldOperator requires the " + "displacement finite-element space." + ); + MFEM_VERIFY( + f.smesh.exterior_coordinate != nullptr, + "GravityFieldOperator requires the STROID exterior coordinate." + ); + MFEM_VERIFY( + f.smesh.exterior_coordinate->space != nullptr, + "GravityFieldOperator requires the exterior-coordinate " + "finite-element " + "space." + ); + MFEM_VERIFY( + f.smesh.exterior_coordinate->values != nullptr, + "GravityFieldOperator requires the exterior-coordinate values." + ); + MFEM_VERIFY( + domain_mapper.GetDimension() == f.mesh->Dimension(), + "GravityFieldOperator received a domain mapper with the wrong " + "dimension." + ); + + validate_state_offsets(f, m_state_true_offsets); + validate_gravity_context(f); + + bool has_vacuum_domain = false; + + for (int i = 0; i < f.mesh->attributes.Size(); ++i) { + if (f.mesh->attributes[i] == + domain_mapper.GetVacuumElementAttribute()) { + has_vacuum_domain = true; + break; + } + } + + MFEM_VERIFY( + has_vacuum_domain, + "GravityFieldOperator requires a compactified vacuum domain." + ); + MFEM_VERIFY( + m_residual_true_offsets.Last() == Height(), + "The gravity residual offsets do not match the operator height." + ); + MFEM_VERIFY( + m_state_true_offsets.Last() == Width(), + "The coupled state offsets do not match the operator width." + ); + } + + context::gravity_field::GravityFieldPreparationReport + GravityFieldOperator::Prepare( + const mfem::Vector &state, + const context::gravity_field::GravityFieldRevisions &revisions + ) { + using form = utils::blocks::gravity_field_form; + + constexpr auto density_block = utils::blocks::get_value_block( + utils::blocks::density_field.mass_term + ); + constexpr auto displacement_block = + utils::blocks::get_value_block( + utils::blocks::displacement_field.geometry_term + ); + constexpr auto gravity_gradient_block = + utils::blocks::get_value_block( + utils::blocks::gravity_field.gradient_term + ); + constexpr auto gravity_potential_block = + utils::blocks::get_value_block( + utils::blocks::gravity_field.poisson_term + ); + + MFEM_VERIFY( + state.Size() == Width(), "GravityFieldOperator received a " + "preparation state with the wrong size." + ); + + const mfem::Vector density = make_read_only_value_view( + state, m_state_true_offsets, density_block + ); + const mfem::Vector displacement = make_read_only_value_view( + state, m_state_true_offsets, displacement_block + ); + const mfem::Vector gravity_gradient = make_read_only_value_view( + state, m_state_true_offsets, gravity_gradient_block + ); + const mfem::Vector gravity_potential = make_read_only_value_view( + state, m_state_true_offsets, gravity_potential_block + ); + + return m_linearization_context.Prepare( + {.density = density, + .displacement = displacement, + .gravity_gradient = gravity_gradient, + .gravity_potential = gravity_potential}, + revisions + ); + } + + const mfem::Array & + GravityFieldOperator::GetStateTrueOffsets() const noexcept { + return m_state_true_offsets; + } + + const mfem::Array & + GravityFieldOperator::GetResidualTrueOffsets() const noexcept { + return m_residual_true_offsets; + } + + void GravityFieldOperator::ApplyGravityUnknowns( + const mfem::Vector &gravity_gradient, + const mfem::Vector &gravity_potential, + const context::gravity_field::GravityFieldGeometryContext + &geometry_context, + mfem::Vector &action + ) const { + using form = utils::blocks::gravity_field_form; + + constexpr auto gravity_gradient_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.gradient_term + ); + constexpr auto gravity_poisson_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.poisson_term + ); + + MFEM_VERIFY( + geometry_context.IsPrepared(), + "GravityFieldOperator received an unprepared geometry context." + ); + MFEM_VERIFY( + gravity_gradient.Size() == m_fem.gravityFluxFes->GetTrueVSize(), + "GravityFieldOperator received a gravity-gradient vector with the " + "wrong size." + ); + MFEM_VERIFY( + gravity_potential.Size() == + m_fem.gravityPotentialFes->GetTrueVSize(), + "GravityFieldOperator received a gravity-potential vector with the " + "wrong size." + ); + + action.SetSize(Height()); + action = 0.0; + + mfem::Vector gravity_gradient_action = make_residual_view( + action, m_residual_true_offsets, gravity_gradient_residual_block + ); + mfem::Vector gravity_poisson_action = make_residual_view( + action, m_residual_true_offsets, gravity_poisson_residual_block + ); + mfem::Vector transpose_divergence_action( + gravity_gradient_action.Size() + ); + + geometry_context.GetMassOperator().Mult( + gravity_gradient, gravity_gradient_action + ); + m_fem.gravityContext.BT->Mult( + gravity_potential, transpose_divergence_action + ); + gravity_gradient_action += transpose_divergence_action; + m_fem.gravityContext.b_form->Mult( + gravity_gradient, gravity_poisson_action + ); + } + + void GravityFieldOperator::ApplyDensitySource( + const mfem::Vector &density, + const context::gravity_field::GravityFieldGeometryContext + &geometry_context, + mfem::Vector &action + ) const { + using form = utils::blocks::gravity_field_form; + + constexpr auto gravity_poisson_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.poisson_term + ); + + MFEM_VERIFY( + geometry_context.IsPrepared(), + "GravityFieldOperator received an unprepared geometry context." + ); + MFEM_VERIFY( + density.Size() == m_fem.densityFes->GetTrueVSize(), + "GravityFieldOperator received a density vector with the wrong " + "size." + ); + + action.SetSize(Height()); + action = 0.0; + + mfem::Vector gravity_poisson_action = make_residual_view( + action, m_residual_true_offsets, gravity_poisson_residual_block + ); + geometry_context.GetSourceOperator().Mult( + density, gravity_poisson_action + ); + } + + void GravityFieldOperator::Mult( + const mfem::Vector &state, + mfem::Vector &residual + ) const { + MEAN_FIELD_PROFILE_SCOPE("GravityFieldOperator::Mult"); + + using form = utils::blocks::gravity_field_form; + + constexpr auto density_block = utils::blocks::get_value_block( + utils::blocks::density_field.mass_term + ); + constexpr auto gravity_gradient_block = + utils::blocks::get_value_block( + utils::blocks::gravity_field.gradient_term + ); + constexpr auto gravity_potential_block = + utils::blocks::get_value_block( + utils::blocks::gravity_field.poisson_term + ); + + MFEM_VERIFY( + state.Size() == Width(), + "GravityFieldOperator received a state with the wrong size." + ); + MFEM_VERIFY( + m_linearization_context.IsPrepared(), + "GravityFieldOperator must be prepared before Mult is called." + ); + + const mfem::Vector density = make_read_only_value_view( + state, m_state_true_offsets, density_block + ); + const mfem::Vector gravity_gradient = make_read_only_value_view( + state, m_state_true_offsets, gravity_gradient_block + ); + const mfem::Vector gravity_potential = make_read_only_value_view( + state, m_state_true_offsets, gravity_potential_block + ); + const context::gravity_field::GravityFieldGeometryContext + &geometry_context = m_linearization_context.GetGeometryContext(); + + mfem::Vector source; + + ApplyGravityUnknowns( + gravity_gradient, gravity_potential, geometry_context, residual + ); + ApplyDensitySource(density, geometry_context, source); + + residual -= source; + } + + context::gravity_field::GravityFieldLinearizationContext & + GravityFieldOperator::GetLinearizationContext() noexcept { + return m_linearization_context; + } + + const context::gravity_field::GravityFieldLinearizationContext & + GravityFieldOperator::GetLinearizationContext() const noexcept { + return m_linearization_context; + } + + mfem::Operator & + GravityFieldOperator::GetGradient(const mfem::Vector &state) const { + MFEM_VERIFY( + state.Size() == Width(), "GravityFieldOperator received a " + "linearization state with the wrong size." + ); + MFEM_VERIFY( + m_linearization_context.IsPrepared(), + "GravityFieldOperator must be prepared before GetGradient is " + "called." + ); + + return m_jacobian; + } + ReducedGravityFieldOperator::ReducedGravityFieldOperator( + GravityFieldOperator &gravity_field_operator, + context::gravity_field::GravityFieldGeometryContext + &gravity_field_geometry_context, + const mfem::Vector &displacement + ) + : Operator( + gravity_field_operator.Height(), + gravity_field_operator.Height() + ), + m_gravity_field_operator(gravity_field_operator), + m_gravity_true_offsets( + gravity_field_operator.GetResidualTrueOffsets() + ), + m_gravity_field_geometry_context(gravity_field_geometry_context) { + using form = utils::blocks::gravity_field_form; + + constexpr auto gravity_gradient_block = + utils::blocks::get_value_block( + utils::blocks::gravity_field.gradient_term + ); + constexpr auto gravity_potential_block = + utils::blocks::get_value_block( + utils::blocks::gravity_field.poisson_term + ); + constexpr auto gravity_gradient_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.gradient_term + ); + constexpr auto gravity_poisson_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.poisson_term + ); + + const mfem::Array &state_offsets = + m_gravity_field_operator.GetStateTrueOffsets(); + + MFEM_VERIFY( + state_offsets.Size() == form::value_block_count + 1, + "ReducedGravityFieldOperator received an invalid full-state layout." + ); + MFEM_VERIFY( + m_gravity_true_offsets.Size() == form::residual_block_count + 1, + "ReducedGravityFieldOperator received an invalid gravity-residual " + "layout." + ); + MFEM_VERIFY( + state_offsets[0] == 0, "The full-state offsets must begin at zero." + ); + MFEM_VERIFY( + m_gravity_true_offsets[0] == 0, + "The reduced gravity offsets must begin at zero." + ); + MFEM_VERIFY( + state_offsets.Last() == m_gravity_field_operator.Width(), + "The full-state offsets do not match the gravity-field operator " + "width." + ); + MFEM_VERIFY( + m_gravity_true_offsets.Last() == m_gravity_field_operator.Height(), + "The reduced gravity offsets do not match the gravity-field " + "operator " + "height." + ); + MFEM_VERIFY( + Width() == Height(), "ReducedGravityFieldOperator must be square." + ); + + const int full_gradient_size = + state_offsets[static_cast(gravity_gradient_block) + 1] - + state_offsets[gravity_gradient_block]; + const int full_potential_size = + state_offsets[static_cast(gravity_potential_block) + 1] - + state_offsets[gravity_potential_block]; + const int reduced_gradient_size = + m_gravity_true_offsets + [static_cast(gravity_gradient_residual_block) + 1] - + m_gravity_true_offsets[gravity_gradient_residual_block]; + const int reduced_potential_size = + m_gravity_true_offsets + [static_cast(gravity_poisson_residual_block) + 1] - + m_gravity_true_offsets[gravity_poisson_residual_block]; + + MFEM_VERIFY( + full_gradient_size == reduced_gradient_size, + "The reduced gravity-gradient block does not match the full-state " + "gravity-gradient block." + ); + MFEM_VERIFY( + full_potential_size == reduced_potential_size, + "The reduced gravity-potential block does not match the Poisson " + "residual block." + ); + + SetDisplacement(displacement); + } + + void ReducedGravityFieldOperator::SetDisplacement( + const mfem::Vector &displacement + ) { + ValidateDisplacement(displacement); + + context::gravity_field::DiscretizationRevision discretization_revision; + context::gravity_field::DisplacementRevision displacement_revision; + + if (m_gravity_field_geometry_context.IsPrepared()) { + discretization_revision = + m_gravity_field_geometry_context.GetDiscretizationRevision(); + displacement_revision = + m_gravity_field_geometry_context.GetDisplacementRevision(); + + MFEM_VERIFY( + displacement_revision.value < + std::numeric_limits::max(), + "The reduced gravity displacement revision has overflowed." + ); + ++displacement_revision.value; + } + + m_gravity_field_geometry_context.Prepare( + displacement, discretization_revision, displacement_revision + ); + } + + const mfem::Vector &ReducedGravityFieldOperator::GetDisplacement() const { + return m_gravity_field_geometry_context.GetDisplacement(); + } + + void ReducedGravityFieldOperator::BuildRightHandSide( + const mfem::Vector &density, + mfem::Vector &right_hand_side + ) const { + ValidateDensity(density); + + m_gravity_field_operator.ApplyDensitySource( + density, m_gravity_field_geometry_context, right_hand_side + ); + + MFEM_VERIFY( + right_hand_side.Size() == Height(), + "ReducedGravityFieldOperator produced a right-hand side with the " + "wrong " + "size." + ); + } + + void ReducedGravityFieldOperator::Mult( + const mfem::Vector &gravity_state, + mfem::Vector &action + ) const { + MEAN_FIELD_PROFILE_SCOPE("ReducedGravityFieldOperator::Mult"); + + using form = utils::blocks::gravity_field_form; + + constexpr auto gravity_gradient_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.gradient_term + ); + constexpr auto gravity_poisson_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.poisson_term + ); + + ValidateGravityState(gravity_state); + + const mfem::Vector gravity_gradient_true = make_read_only_residual_view( + gravity_state, m_gravity_true_offsets, + gravity_gradient_residual_block + ); + const mfem::Vector gravity_potential_true = + make_read_only_residual_view( + gravity_state, m_gravity_true_offsets, + gravity_poisson_residual_block + ); + + m_gravity_field_operator.ApplyGravityUnknowns( + gravity_gradient_true, gravity_potential_true, + m_gravity_field_geometry_context, action + ); + + MFEM_VERIFY( + action.Size() == Height(), "ReducedGravityFieldOperator produced " + "an action with the wrong size." + ); + } + + GravityFieldOperator & + ReducedGravityFieldOperator::GetGravityFieldOperator() noexcept { + return m_gravity_field_operator; + } + + const GravityFieldOperator & + ReducedGravityFieldOperator::GetGravityFieldOperator() const noexcept { + return m_gravity_field_operator; + } + + context::gravity_field::GravityFieldGeometryContext & + ReducedGravityFieldOperator::GetGeometryContext() noexcept { + return m_gravity_field_geometry_context; + } + + const context::gravity_field::GravityFieldGeometryContext & + ReducedGravityFieldOperator::GetGeometryContext() const noexcept { + return m_gravity_field_geometry_context; + } + + const mfem::Array & + ReducedGravityFieldOperator::GetGravityTrueOffsets() const noexcept { + return m_gravity_true_offsets; + } + + void ReducedGravityFieldOperator::ValidateDisplacement( + const mfem::Vector &displacement + ) const { + using form = utils::blocks::gravity_field_form; + + constexpr auto displacement_block = + utils::blocks::get_value_block( + utils::blocks::displacement_field.geometry_term + ); + + const mfem::Array &state_offsets = + m_gravity_field_operator.GetStateTrueOffsets(); + const int expected_size = + state_offsets[static_cast(displacement_block) + 1] - + state_offsets[displacement_block]; + + MFEM_VERIFY( + displacement.Size() == expected_size, + "ReducedGravityFieldOperator received a displacement with the " + "wrong " + "size." + ); + + for (int i = 0; i < displacement.Size(); ++i) { + MFEM_VERIFY( + std::isfinite(displacement(i)), + "ReducedGravityFieldOperator received a non-finite " + "displacement " + "value." + ); + } + } + + void ReducedGravityFieldOperator::ValidateDensity( + const mfem::Vector &density + ) const { + using form = utils::blocks::gravity_field_form; + + constexpr auto density_block = utils::blocks::get_value_block( + utils::blocks::density_field.mass_term + ); + + const mfem::Array &state_offsets = + m_gravity_field_operator.GetStateTrueOffsets(); + const int expected_size = + state_offsets[static_cast(density_block) + 1] - + state_offsets[density_block]; + + MFEM_VERIFY( + density.Size() == expected_size, + "ReducedGravityFieldOperator received a density with the wrong " + "size." + ); + } + + void ReducedGravityFieldOperator::ValidateGravityState( + const mfem::Vector &gravity_state + ) const { + MFEM_VERIFY( + gravity_state.Size() == Width(), + "ReducedGravityFieldOperator received " + "a gravity state with the wrong size." + ); + } +} // namespace mean_field::operators diff --git a/libmeanfield/impl/operators/gravity_field_jacobian.cpp b/libmeanfield/impl/operators/gravity_field_jacobian.cpp new file mode 100644 index 0000000..00bae60 --- /dev/null +++ b/libmeanfield/impl/operators/gravity_field_jacobian.cpp @@ -0,0 +1,317 @@ +module; +#include + +module mean_field; +import :operators.gravity_field_jacobian; +import :operators.kernels.gravity_field; +import :utils.blocks; + +namespace { + template + mfem::Vector make_read_only_value_view( + const mfem::Vector &vector, + const mfem::Array &offsets, + const mean_field::utils::blocks::value_block + ) { + const int offset = offsets[index]; + const int size = offsets[index + 1] - offset; + return mfem::Vector( + const_cast(vector.GetData()) + offset, size + ); + } + + template + mfem::Vector make_residual_view( + mfem::Vector &vector, + const mfem::Array &offsets, + const mean_field::utils::blocks::residual_block + ) { + const int offset = offsets[index]; + const int size = offsets[index + 1] - offset; + return mfem::Vector(vector.GetData() + offset, size); + } + + template + int get_block_size( + const mfem::Array &offsets, + const mean_field::utils::blocks::value_block + ) { + return offsets[index + 1] - offsets[index]; + } + + template + int get_block_size( + const mfem::Array &offsets, + const mean_field::utils::blocks::residual_block + ) { + return offsets[index + 1] - offsets[index]; + } + + void validate_offsets( + const mfem::Array &offsets, + const int block_count, + const char *message + ) { + MFEM_VERIFY(offsets.Size() == block_count + 1, message); + MFEM_VERIFY(offsets[0] == 0, "Block offsets must begin at zero."); + + for (int i = 0; i < block_count; ++i) + MFEM_VERIFY( + offsets[i + 1] >= offsets[i], + "Block offsets must be nondecreasing." + ); + } + + void validate_layout( + const mean_field::fem::FEM &f, + const mfem::Array &state_offsets, + const mfem::Array &residual_offsets + ) { + using form = mean_field::utils::blocks::gravity_field_form; + + constexpr auto density_block = + mean_field::utils::blocks::get_value_block( + mean_field::utils::blocks::density_field.mass_term + ); + constexpr auto displacement_block = + mean_field::utils::blocks::get_value_block( + mean_field::utils::blocks::displacement_field.geometry_term + ); + constexpr auto gravity_gradient_block = + mean_field::utils::blocks::get_value_block( + mean_field::utils::blocks::gravity_field.gradient_term + ); + constexpr auto gravity_potential_block = + mean_field::utils::blocks::get_value_block( + mean_field::utils::blocks::gravity_field.poisson_term + ); + constexpr auto gravity_gradient_residual_block = + mean_field::utils::blocks::get_residual_block( + mean_field::utils::blocks::gravity_field.gradient_term + ); + constexpr auto gravity_poisson_residual_block = + mean_field::utils::blocks::get_residual_block( + mean_field::utils::blocks::gravity_field.poisson_term + ); + + validate_offsets( + state_offsets, form::value_block_count, + "Gravity Jacobian state offsets do not match the gravity field " + "form." + ); + validate_offsets( + residual_offsets, form::residual_block_count, + "Gravity Jacobian residual offsets do not match the gravity field " + "form." + ); + + MFEM_VERIFY( + get_block_size(state_offsets, density_block) == + f.densityFes->GetTrueVSize(), + "The Jacobian density block has the wrong size." + ); + MFEM_VERIFY( + get_block_size(state_offsets, displacement_block) == + f.displacementFes->GetTrueVSize(), + "The Jacobian displacement block has the wrong size." + ); + MFEM_VERIFY( + get_block_size(state_offsets, gravity_gradient_block) == + f.gravityFluxFes->GetTrueVSize(), + "The Jacobian gravity-gradient block has the wrong size." + ); + MFEM_VERIFY( + get_block_size(state_offsets, gravity_potential_block) == + f.gravityPotentialFes->GetTrueVSize(), + "The Jacobian gravity-potential block has the wrong size." + ); + MFEM_VERIFY( + get_block_size(residual_offsets, gravity_gradient_residual_block) == + f.gravityFluxFes->GetTrueVSize(), + "The Jacobian gradient-residual block has the wrong size." + ); + MFEM_VERIFY( + get_block_size(residual_offsets, gravity_poisson_residual_block) == + f.gravityPotentialFes->GetTrueVSize(), + "The Jacobian Poisson-residual block has the wrong size." + ); + } +} // namespace + +namespace mean_field::operators { + GravityFieldJacobianOperator::GravityFieldJacobianOperator( + fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const context::gravity_field::GravityFieldLinearizationContext + &linearization_context, + const mfem::Array &state_true_offsets, + const mfem::Array &residual_true_offsets + ) + : Operator( + residual_true_offsets.Last(), + state_true_offsets.Last() + ), + m_fem(f), + m_domain_mapper(domain_mapper), + m_linearization_context(linearization_context), + m_state_true_offsets(state_true_offsets), + m_residual_true_offsets(residual_true_offsets) { + MFEM_VERIFY( + f.densityFes != nullptr, + "GravityFieldJacobianOperator requires the density finite-element " + "space." + ); + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "GravityFieldJacobianOperator requires the gravity-potential " + "finite-element space." + ); + MFEM_VERIFY( + f.gravityFluxFes != nullptr, + "GravityFieldJacobianOperator requires the " + "gravity-gradient finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, + "GravityFieldJacobianOperator requires the " + "displacement finite-element space." + ); + MFEM_VERIFY( + f.gravityContext.b_form != nullptr, + "GravityFieldJacobianOperator requires the divergence operator." + ); + MFEM_VERIFY( + f.gravityContext.BT != nullptr, + "GravityFieldJacobianOperator requires the transpose divergence " + "operator." + ); + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "GravityFieldJacobianOperator requires the quadrature-rule factory." + ); + MFEM_VERIFY( + domain_mapper.GetDimension() == f.mesh->Dimension(), + "GravityFieldJacobianOperator received a domain mapper with the " + "wrong " + "dimension." + ); + + validate_layout(f, m_state_true_offsets, m_residual_true_offsets); + } + + void GravityFieldJacobianOperator::Mult( + const mfem::Vector &direction, + mfem::Vector &action + ) const { + MFEM_VERIFY( + m_linearization_context.IsPrepared(), + "GravityFieldJacobianOperator requires a prepared linearization " + "context." + ); + MFEM_VERIFY( + direction.Size() == Width(), + "GravityFieldJacobianOperator received a direction with the wrong " + "size." + ); + + using form = utils::blocks::gravity_field_form; + + constexpr auto density_block = utils::blocks::get_value_block( + utils::blocks::density_field.mass_term + ); + constexpr auto displacement_block = + utils::blocks::get_value_block( + utils::blocks::displacement_field.geometry_term + ); + constexpr auto gravity_gradient_block = + utils::blocks::get_value_block( + utils::blocks::gravity_field.gradient_term + ); + constexpr auto gravity_potential_block = + utils::blocks::get_value_block( + utils::blocks::gravity_field.poisson_term + ); + constexpr auto gravity_gradient_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.gradient_term + ); + constexpr auto gravity_poisson_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.poisson_term + ); + + const context::gravity_field::GravityFieldGeometryContext + &geometry_context = m_linearization_context.GetGeometryContext(); + const mfem::Vector &density = m_linearization_context.GetDensity(); + const mfem::Vector &displacement = geometry_context.GetDisplacement(); + const mfem::Vector &gravity_gradient = + m_linearization_context.GetGravityGradient(); + + const mfem::Vector density_direction = make_read_only_value_view( + direction, m_state_true_offsets, density_block + ); + const mfem::Vector displacement_direction = make_read_only_value_view( + direction, m_state_true_offsets, displacement_block + ); + const mfem::Vector gravity_gradient_direction = + make_read_only_value_view( + direction, m_state_true_offsets, gravity_gradient_block + ); + const mfem::Vector gravity_potential_direction = + make_read_only_value_view( + direction, m_state_true_offsets, gravity_potential_block + ); + + action.SetSize(Height()); + action = 0.0; + + mfem::Vector gravity_gradient_action = make_residual_view( + action, m_residual_true_offsets, gravity_gradient_residual_block + ); + mfem::Vector gravity_poisson_action = make_residual_view( + action, m_residual_true_offsets, gravity_poisson_residual_block + ); + + mfem::Vector transpose_divergence_action; + mfem::Vector source_action; + mfem::Vector mass_variation_action; + mfem::Vector source_variation_action; + + geometry_context.GetMassOperator().Mult( + gravity_gradient_direction, gravity_gradient_action + ); + geometry_context.GetSourceOperator().Mult( + density_direction, source_action + ); + + kernels::apply_mapped_hdiv_mass_variation( + m_fem, m_domain_mapper, gravity_gradient, displacement, + displacement_direction, mass_variation_action + ); + + kernels::apply_mapped_source_variation( + m_fem, m_domain_mapper, density, displacement, + displacement_direction, source_variation_action + ); + + transpose_divergence_action.SetSize(gravity_gradient_action.Size()); + m_fem.gravityContext.BT->Mult( + gravity_potential_direction, transpose_divergence_action + ); + + gravity_gradient_action += transpose_divergence_action; + gravity_gradient_action += mass_variation_action; + + m_fem.gravityContext.b_form->Mult( + gravity_gradient_direction, gravity_poisson_action + ); + + gravity_poisson_action -= source_action; + gravity_poisson_action -= source_variation_action; + } + + const context::gravity_field::GravityFieldLinearizationContext & + GravityFieldJacobianOperator::GetLinearizationContext() const noexcept { + return m_linearization_context; + } +} // namespace mean_field::operators diff --git a/libmeanfield/impl/operators/kernels/barotropic_closure_kernels.cpp b/libmeanfield/impl/operators/kernels/barotropic_closure_kernels.cpp new file mode 100644 index 0000000..4390193 --- /dev/null +++ b/libmeanfield/impl/operators/kernels/barotropic_closure_kernels.cpp @@ -0,0 +1,811 @@ +module; + +#include +#include +#include +#include + +module mean_field; + +import :operators.kernels.barotropic_closure; + +namespace { + enum class ClosureAction { residual, density, enthalpy }; + + void true_to_local( + const mfem::ParFiniteElementSpace &finiteElementSpace, + const mfem::Vector &trueVector, + mfem::Vector &localVector + ) { + MFEM_VERIFY( + trueVector.Size() == finiteElementSpace.GetTrueVSize(), + "True vector has the wrong size." + ); + + localVector.SetSize(finiteElementSpace.GetVSize()); + + const mfem::Operator *prolongation = + finiteElementSpace.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->Mult(trueVector, localVector); + } else { + localVector = trueVector; + } + } + + void local_to_true( + const mfem::ParFiniteElementSpace &finiteElementSpace, + const mfem::Vector &localVector, + mfem::Vector &trueVector + ) { + MFEM_VERIFY( + localVector.Size() == finiteElementSpace.GetVSize(), + "Local vector has the wrong size." + ); + + trueVector.SetSize(finiteElementSpace.GetTrueVSize()); + trueVector = 0.0; + + const mfem::Operator *prolongation = + finiteElementSpace.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->MultTranspose(localVector, trueVector); + } else { + trueVector = localVector; + } + } + + int get_eos_extra_order( + const mean_field::physics::PolytropicBarotrope &barotrope + ) { + const double extraOrder = + (barotrope.polytropic_index() - 1.0) * + static_cast( + mean_field::field::Enthalpy::Scalar::familyOrder + ); + + MFEM_VERIFY( + std::isfinite(extraOrder) && extraOrder >= 0.0 && + extraOrder <= + static_cast(std::numeric_limits::max()), + "The EOS effective polynomial order is invalid." + ); + + return static_cast(std::ceil(extraOrder)); + } + + const mfem::IntegrationRule &get_eos_rule( + const mean_field::fem::FEM &f, + const mean_field::physics::PolytropicBarotrope &barotrope, + const mfem::FiniteElement &densityElement, + const mfem::FiniteElement &enthalpyElement, + const mfem::ElementTransformation &transformation + ) { + using EnthalpyField = + mean_field::field::Field; + + MFEM_VERIFY( + densityElement.GetOrder() == + mean_field::field::Density::Scalar::familyOrder, + "The EOS test element does not match the " + "registered density field." + ); + + MFEM_VERIFY( + enthalpyElement.GetOrder() == + mean_field::field::Enthalpy::Scalar::familyOrder, + "The EOS trial element does not match the " + "registered enthalpy field." + ); + + const mean_field::quadrature::Query query = EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::EosClosureSource>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), + std::array{get_eos_extra_order(barotrope)}, + mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + const auto resolution = + f.quadratureFactory->get(query, transformation.GetGeometryType()); + + MFEM_VERIFY( + resolution.integration_rule != nullptr, + "The quadrature policy did not return an " + "EOS-closure integration rule." + ); + + return *resolution.integration_rule; + } + + void validate_common_inputs( + const mean_field::fem::FEM &f, + const mean_field::mapping::DomainMapperStateless &domainMapper, + const mfem::Vector &displacementTrue + ) { + MFEM_VERIFY( + f.mesh != nullptr, "The EOS closure kernel requires a mesh." + ); + MFEM_VERIFY( + f.densityFes != nullptr, + "The EOS closure kernel requires the density " + "finite-element space." + ); + MFEM_VERIFY( + f.enthalpyFes != nullptr, + "The EOS closure kernel requires the enthalpy " + "finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, + "The EOS closure kernel requires the displacement " + "finite-element space." + ); + MFEM_VERIFY( + f.compactificationFes != nullptr, + "The EOS closure kernel requires the " + "compactification finite-element space." + ); + MFEM_VERIFY( + f.compactificationCoordinate != nullptr, + "The EOS closure kernel requires the " + "compactification coordinate." + ); + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "The EOS closure kernel requires the quadrature " + "rule factory." + ); + MFEM_VERIFY( + displacementTrue.Size() == f.displacementFes->GetTrueVSize(), + "The displacement vector has the wrong size." + ); + MFEM_VERIFY( + domainMapper.GetDimension() == f.mesh->Dimension(), + "The domain-mapper dimension does not match " + "the mesh dimension." + ); + } + + void apply_closure_action( + const mean_field::fem::FEM &f, + const mean_field::mapping::DomainMapperStateless &domainMapper, + const mean_field::physics::PolytropicBarotrope &barotrope, + const ClosureAction closureAction, + const mfem::Vector *densityInputTrue, + const mfem::Vector *baseEnthalpyTrue, + const mfem::Vector *enthalpyVariationTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &action + ) { + validate_common_inputs(f, domainMapper, displacementTrue); + + if (closureAction == ClosureAction::residual || + closureAction == ClosureAction::density) { + MFEM_VERIFY( + densityInputTrue != nullptr && + densityInputTrue->Size() == f.densityFes->GetTrueVSize(), + "The density input has the wrong size." + ); + } + + if (closureAction == ClosureAction::residual || + closureAction == ClosureAction::enthalpy) { + MFEM_VERIFY( + baseEnthalpyTrue != nullptr && + baseEnthalpyTrue->Size() == f.enthalpyFes->GetTrueVSize(), + "The base enthalpy has the wrong size." + ); + } + + if (closureAction == ClosureAction::enthalpy) { + MFEM_VERIFY( + enthalpyVariationTrue != nullptr && + enthalpyVariationTrue->Size() == + f.enthalpyFes->GetTrueVSize(), + "The enthalpy variation has the wrong size." + ); + } + + mfem::Vector densityInputLocal; + mfem::Vector baseEnthalpyLocal; + mfem::Vector enthalpyVariationLocal; + mfem::Vector displacementLocal; + + if (densityInputTrue != nullptr) { + true_to_local(*f.densityFes, *densityInputTrue, densityInputLocal); + } + + if (baseEnthalpyTrue != nullptr) { + true_to_local(*f.enthalpyFes, *baseEnthalpyTrue, baseEnthalpyLocal); + } + + if (enthalpyVariationTrue != nullptr) { + true_to_local( + *f.enthalpyFes, *enthalpyVariationTrue, enthalpyVariationLocal + ); + } + + true_to_local(*f.displacementFes, displacementTrue, displacementLocal); + + mfem::Vector localAction(f.densityFes->GetVSize()); + localAction = 0.0; + + mean_field::mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + mfem::Array densityDofs; + mfem::Array enthalpyDofs; + mfem::Array displacementDofs; + mfem::Array compactificationDofs; + + mfem::Vector elementDensityInput; + mfem::Vector elementBaseEnthalpy; + mfem::Vector elementEnthalpyVariation; + mfem::Vector elementDisplacement; + mfem::Vector elementCompactification; + mfem::Vector elementAction; + + mfem::Vector densityShape; + mfem::Vector enthalpyShape; + + const int vacuumAttribute = domainMapper.GetVacuumElementAttribute(); + + for (int elementId = 0; elementId < f.mesh->GetNE(); ++elementId) { + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(elementId); + + MFEM_VERIFY( + transformation != nullptr, + "The EOS closure kernel received a null " + "element transformation." + ); + + if (transformation->Attribute == vacuumAttribute) { + continue; + } + + const mfem::FiniteElement &densityElement = + *f.densityFes->GetFE(elementId); + const mfem::FiniteElement &enthalpyElement = + *f.enthalpyFes->GetFE(elementId); + const mfem::FiniteElement &displacementElement = + *f.displacementFes->GetFE(elementId); + const mfem::FiniteElement &compactificationElement = + *f.compactificationFes->GetFE(elementId); + + mfem::DofTransformation *densityDofTransformation = + f.densityFes->GetElementDofs(elementId, densityDofs); + + mfem::DofTransformation *enthalpyDofTransformation = + f.enthalpyFes->GetElementDofs(elementId, enthalpyDofs); + + mfem::DofTransformation *displacementDofTransformation = + f.displacementFes->GetElementVDofs(elementId, displacementDofs); + + mfem::DofTransformation *compactificationDofTransformation = + f.compactificationFes->GetElementDofs( + elementId, compactificationDofs + ); + + if (densityInputTrue != nullptr) { + densityInputLocal.GetSubVector( + densityDofs, elementDensityInput + ); + + if (densityDofTransformation != nullptr) { + densityDofTransformation->InvTransformPrimal( + elementDensityInput + ); + } + } + + if (baseEnthalpyTrue != nullptr) { + baseEnthalpyLocal.GetSubVector( + enthalpyDofs, elementBaseEnthalpy + ); + + if (enthalpyDofTransformation != nullptr) { + enthalpyDofTransformation->InvTransformPrimal( + elementBaseEnthalpy + ); + } + } + + if (enthalpyVariationTrue != nullptr) { + enthalpyVariationLocal.GetSubVector( + enthalpyDofs, elementEnthalpyVariation + ); + + if (enthalpyDofTransformation != nullptr) { + enthalpyDofTransformation->InvTransformPrimal( + elementEnthalpyVariation + ); + } + } + + displacementLocal.GetSubVector( + displacementDofs, elementDisplacement + ); + + f.compactificationCoordinate->GetSubVector( + compactificationDofs, elementCompactification + ); + + if (displacementDofTransformation != nullptr) { + displacementDofTransformation->InvTransformPrimal( + elementDisplacement + ); + } + + if (compactificationDofTransformation != nullptr) { + compactificationDofTransformation->InvTransformPrimal( + elementCompactification + ); + } + + const mean_field::mapping::ElementDisplacementData + displacementData = mean_field::mapping:: + ElementDisplacementDataFromElementVDofs( + displacementElement, elementDisplacement + ); + + const mean_field::mapping::ElementCompactificationData + compactificationData( + compactificationElement, elementCompactification + ); + + const mean_field::mapping::ElementMappingData mappingData{ + .displacement = displacementData, + .compactification = compactificationData + }; + + densityShape.SetSize(densityElement.GetDof()); + enthalpyShape.SetSize(enthalpyElement.GetDof()); + elementAction.SetSize(densityElement.GetDof()); + elementAction = 0.0; + + const mfem::IntegrationRule &integrationRule = get_eos_rule( + f, barotrope, densityElement, enthalpyElement, *transformation + ); + + for (int quadratureIndex = 0; + quadratureIndex < integrationRule.GetNPoints(); + ++quadratureIndex) { + const mfem::IntegrationPoint &integrationPoint = + integrationRule.IntPoint(quadratureIndex); + + transformation->SetIntPoint(&integrationPoint); + + mean_field::mapping::VolumeMappingContext mappingContext; + + const mean_field::mapping::MappingStatus mappingStatus = + domainMapper.EvaluateVolume( + mappingData, *transformation, integrationPoint, + workspace, mappingContext + ); + + MFEM_VERIFY( + mappingStatus == mean_field::mapping::MappingStatus::valid, + "Stateless mapping failed in the EOS " + "closure kernel. Element: " + << elementId + << ", attribute: " << transformation->Attribute + << ", quadrature point: " << quadratureIndex + << ", status: " << static_cast(mappingStatus) + ); + + densityElement.CalcShape(integrationPoint, densityShape); + + double integrand = 0.0; + + if (closureAction == ClosureAction::density) { + integrand = elementDensityInput * densityShape; + } else { + enthalpyElement.CalcShape(integrationPoint, enthalpyShape); + + const double baseEnthalpy = + elementBaseEnthalpy * enthalpyShape; + + if (closureAction == ClosureAction::residual) { + const double density = + elementDensityInput * densityShape; + + integrand = + density - + barotrope.density_from_enthalpy(baseEnthalpy); + } else { + const double enthalpyVariation = + elementEnthalpyVariation * enthalpyShape; + + integrand = -barotrope.density_derivative_from_enthalpy( + baseEnthalpy + ) * + enthalpyVariation; + } + } + + const double weightedIntegrand = + mappingContext.quadrature.weight * integrand; + + for (int densityDof = 0; densityDof < densityElement.GetDof(); + ++densityDof) { + elementAction(densityDof) += + weightedIntegrand * densityShape(densityDof); + } + } + + if (densityDofTransformation != nullptr) { + densityDofTransformation->TransformDual(elementAction); + } + + localAction.AddElementVector(densityDofs, elementAction); + } + + local_to_true(*f.densityFes, localAction, action); + } +} // namespace + +namespace mean_field::operators::kernels { + void apply_barotropic_closure( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope, + const mfem::Vector &densityTrue, + const mfem::Vector &enthalpyTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &residual + ) { + apply_closure_action( + f, domainMapper, barotrope, ClosureAction::residual, &densityTrue, + &enthalpyTrue, nullptr, displacementTrue, residual + ); + } + + void apply_barotropic_closure_density_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope, + const mfem::Vector &densityVariationTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &action + ) { + apply_closure_action( + f, domainMapper, barotrope, ClosureAction::density, + &densityVariationTrue, nullptr, nullptr, displacementTrue, action + ); + } + + void apply_barotropic_closure_enthalpy_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &enthalpyVariationTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &action + ) { + apply_closure_action( + f, domainMapper, barotrope, ClosureAction::enthalpy, nullptr, + &baseEnthalpyTrue, &enthalpyVariationTrue, displacementTrue, action + ); + } + + void apply_barotropic_closure_displacement_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope, + const mfem::Vector &baseDensityTrue, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &displacementTrue, + const mfem::Vector &displacementVariationTrue, + mfem::Vector &action + ) { + MFEM_VERIFY( + f.mesh != nullptr, "The barotropic-closure displacement action " + "requires a mesh." + ); + + MFEM_VERIFY( + f.densityFes != nullptr, + "The barotropic-closure displacement action " + "requires the density finite-element space." + ); + + MFEM_VERIFY( + f.enthalpyFes != nullptr, + "The barotropic-closure displacement action " + "requires the enthalpy finite-element space." + ); + + MFEM_VERIFY( + f.displacementFes != nullptr, + "The barotropic-closure displacement action " + "requires the displacement finite-element space." + ); + + MFEM_VERIFY( + f.compactificationFes != nullptr, + "The barotropic-closure displacement action " + "requires the compactification finite-element space." + ); + + MFEM_VERIFY( + f.compactificationCoordinate != nullptr, + "The barotropic-closure displacement action " + "requires the compactification coordinate." + ); + + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "The barotropic-closure displacement action " + "requires the quadrature-rule factory." + ); + + MFEM_VERIFY( + baseDensityTrue.Size() == f.densityFes->GetTrueVSize(), + "The base-density vector has the wrong size." + ); + + MFEM_VERIFY( + baseEnthalpyTrue.Size() == f.enthalpyFes->GetTrueVSize(), + "The base-enthalpy vector has the wrong size." + ); + + MFEM_VERIFY( + displacementTrue.Size() == f.displacementFes->GetTrueVSize(), + "The displacement vector has the wrong size." + ); + + MFEM_VERIFY( + displacementVariationTrue.Size() == + f.displacementFes->GetTrueVSize(), + "The displacement-variation vector has the wrong size." + ); + + MFEM_VERIFY( + domainMapper.GetDimension() == f.mesh->Dimension(), + "The domain-mapper dimension does not match the " + "mesh dimension." + ); + + mfem::Vector baseDensityLocal; + mfem::Vector baseEnthalpyLocal; + mfem::Vector displacementLocal; + mfem::Vector displacementVariationLocal; + + true_to_local(*f.densityFes, baseDensityTrue, baseDensityLocal); + + true_to_local(*f.enthalpyFes, baseEnthalpyTrue, baseEnthalpyLocal); + + true_to_local(*f.displacementFes, displacementTrue, displacementLocal); + + true_to_local( + *f.displacementFes, displacementVariationTrue, + displacementVariationLocal + ); + + mfem::Vector localAction(f.densityFes->GetVSize()); + localAction = 0.0; + + mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + mfem::Array densityDofs; + mfem::Array enthalpyDofs; + mfem::Array displacementDofs; + mfem::Array compactificationDofs; + + mfem::Vector elementBaseDensity; + mfem::Vector elementBaseEnthalpy; + mfem::Vector elementDisplacement; + mfem::Vector elementDisplacementVariation; + mfem::Vector elementCompactification; + + mfem::Vector densityShape; + mfem::Vector enthalpyShape; + mfem::Vector elementAction; + + mapping::VolumeMappingContext mappingContext; + mapping::VolumeMappingVariation mappingVariation; + + const int vacuumAttribute = domainMapper.GetVacuumElementAttribute(); + + for (int elementId = 0; elementId < f.mesh->GetNE(); ++elementId) { + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(elementId); + + MFEM_VERIFY( + transformation != nullptr, + "The barotropic-closure displacement action " + "received a null element transformation." + ); + + if (transformation->Attribute == vacuumAttribute) { + continue; + } + + const mfem::FiniteElement &densityElement = + *f.densityFes->GetFE(elementId); + + const mfem::FiniteElement &enthalpyElement = + *f.enthalpyFes->GetFE(elementId); + + const mfem::FiniteElement &displacementElement = + *f.displacementFes->GetFE(elementId); + + const mfem::FiniteElement &compactificationElement = + *f.compactificationFes->GetFE(elementId); + + mfem::DofTransformation *densityDofTransformation = + f.densityFes->GetElementDofs(elementId, densityDofs); + + mfem::DofTransformation *enthalpyDofTransformation = + f.enthalpyFes->GetElementDofs(elementId, enthalpyDofs); + + mfem::DofTransformation *displacementDofTransformation = + f.displacementFes->GetElementVDofs(elementId, displacementDofs); + + mfem::DofTransformation *compactificationDofTransformation = + f.compactificationFes->GetElementDofs( + elementId, compactificationDofs + ); + + baseDensityLocal.GetSubVector(densityDofs, elementBaseDensity); + + baseEnthalpyLocal.GetSubVector(enthalpyDofs, elementBaseEnthalpy); + + displacementLocal.GetSubVector( + displacementDofs, elementDisplacement + ); + + displacementVariationLocal.GetSubVector( + displacementDofs, elementDisplacementVariation + ); + + f.compactificationCoordinate->GetSubVector( + compactificationDofs, elementCompactification + ); + + if (densityDofTransformation != nullptr) { + densityDofTransformation->InvTransformPrimal( + elementBaseDensity + ); + } + + if (enthalpyDofTransformation != nullptr) { + enthalpyDofTransformation->InvTransformPrimal( + elementBaseEnthalpy + ); + } + + if (displacementDofTransformation != nullptr) { + displacementDofTransformation->InvTransformPrimal( + elementDisplacement + ); + + displacementDofTransformation->InvTransformPrimal( + elementDisplacementVariation + ); + } + + if (compactificationDofTransformation != nullptr) { + compactificationDofTransformation->InvTransformPrimal( + elementCompactification + ); + } + + const mapping::ElementDisplacementData displacementData = + mapping::ElementDisplacementDataFromElementVDofs( + displacementElement, elementDisplacement + ); + + const mapping::ElementDisplacementData displacementVariationData = + mapping::ElementDisplacementDataFromElementVDofs( + displacementElement, elementDisplacementVariation + ); + + const mapping::ElementCompactificationData compactificationData( + compactificationElement, elementCompactification + ); + + const mapping::ElementMappingData mappingData{ + .displacement = displacementData, + .compactification = compactificationData + }; + + densityShape.SetSize(densityElement.GetDof()); + + enthalpyShape.SetSize(enthalpyElement.GetDof()); + + elementAction.SetSize(densityElement.GetDof()); + elementAction = 0.0; + + const mfem::IntegrationRule &integrationRule = get_eos_rule( + f, barotrope, densityElement, enthalpyElement, *transformation + ); + + for (int quadraturePoint = 0; + quadraturePoint < integrationRule.GetNPoints(); + ++quadraturePoint) { + const mfem::IntegrationPoint &integrationPoint = + integrationRule.IntPoint(quadraturePoint); + + transformation->SetIntPoint(&integrationPoint); + + const mapping::MappingStatus mappingStatus = + domainMapper.EvaluateVolume( + mappingData, *transformation, integrationPoint, + workspace, mappingContext + ); + + MFEM_VERIFY( + mappingStatus == mapping::MappingStatus::valid, + "The base mapping is invalid while applying " + "the barotropic-closure displacement action. " + "Element: " + << elementId + << ", attribute: " << transformation->Attribute + << ", quadrature point: " << quadraturePoint + << ", status: " << static_cast(mappingStatus) + ); + + const mapping::MappingStatus variationStatus = + domainMapper.EvaluateVolumeVariation( + mappingData, displacementVariationData, *transformation, + integrationPoint, mappingContext, workspace, + mappingVariation + ); + + MFEM_VERIFY( + variationStatus == mapping::MappingStatus::valid, + "The mapping variation is invalid while " + "applying the barotropic-closure " + "displacement action. Element: " + << elementId + << ", attribute: " << transformation->Attribute + << ", quadrature point: " << quadraturePoint + << ", status: " << static_cast(variationStatus) + ); + + densityElement.CalcShape(integrationPoint, densityShape); + + enthalpyElement.CalcShape(integrationPoint, enthalpyShape); + + const double densityValue = elementBaseDensity * densityShape; + + const double enthalpyValue = + elementBaseEnthalpy * enthalpyShape; + + const double closureValue = + densityValue - + barotrope.density_from_enthalpy(enthalpyValue); + + const double geometryActionValue = + closureValue * mappingVariation.weight_variation; + + MFEM_VERIFY( + std::isfinite(closureValue) && + std::isfinite(geometryActionValue), + "The barotropic-closure displacement action " + "encountered a non-finite quadrature value." + ); + + elementAction.Add(geometryActionValue, densityShape); + } + + if (densityDofTransformation != nullptr) { + densityDofTransformation->TransformDual(elementAction); + } + + localAction.AddElementVector(densityDofs, elementAction); + } + + local_to_true(*f.densityFes, localAction, action); + } +} // namespace mean_field::operators::kernels \ No newline at end of file diff --git a/libmeanfield/impl/operators/kernels/gravity_kernels.cpp b/libmeanfield/impl/operators/kernels/gravity_kernels.cpp new file mode 100644 index 0000000..50d7c02 --- /dev/null +++ b/libmeanfield/impl/operators/kernels/gravity_kernels.cpp @@ -0,0 +1,1030 @@ +module; +#include +#include + +module mean_field; +import :operators.kernels.gravity_field; + +namespace { + void true_to_local( + const mfem::ParFiniteElementSpace &finite_element_space, + const mfem::Vector &true_vector, + mfem::Vector &local_vector + ) { + MFEM_VERIFY( + true_vector.Size() == finite_element_space.GetTrueVSize(), + "True vector has the wrong size." + ); + + local_vector.SetSize(finite_element_space.GetVSize()); + + const mfem::Operator *prolongation = + finite_element_space.GetProlongationMatrix(); + if (prolongation != nullptr) { + prolongation->Mult(true_vector, local_vector); + } else { + local_vector = true_vector; + } + } + + void local_to_true( + const mfem::ParFiniteElementSpace &finite_element_space, + const mfem::Vector &local_vector, + mfem::Vector &true_vector + ) { + MFEM_VERIFY( + local_vector.Size() == finite_element_space.GetVSize(), + "Local vector has the wrong size." + ); + + true_vector.SetSize(finite_element_space.GetTrueVSize()); + true_vector = 0.0; + + const mfem::Operator *prolongation = + finite_element_space.GetProlongationMatrix(); + if (prolongation != nullptr) { + prolongation->MultTranspose(local_vector, true_vector); + } else { + true_vector = local_vector; + } + } + + void add_local_to_true( + const mfem::ParFiniteElementSpace &fes, + const mfem::Vector &local_vector, + mfem::Vector &true_vector + ) { + const mfem::Operator *prolongation = fes.GetProlongationMatrix(); + if (prolongation != nullptr) { + prolongation->AddMultTranspose(local_vector, true_vector); + } else { + true_vector += local_vector; + } + } + + mean_field::quadrature::MappingKind get_mapping_kind( + const mean_field::mapping::DomainMapperStateless &domain_mapper, + const mfem::ElementTransformation &transformation + ) { + return transformation.Attribute == + domain_mapper.GetVacuumElementAttribute() + ? mean_field::quadrature::MappingKind::kelvin + : mean_field::quadrature::MappingKind::general; + } + + const mfem::IntegrationRule &get_hdiv_mass_rule( + const mean_field::fem::FEM &f, + const mean_field::mapping::DomainMapperStateless &domain_mapper, + const mfem::FiniteElement &element, + const mfem::ElementTransformation &transformation + ) { + using GravityField = + mean_field::field::Field; + MFEM_VERIFY( + element.GetOrder() == + mean_field::field::Gravity::Flux::familyOrder + 1, + "The H(div) kernel element does not match the registered gravity " + "flux." + ); + const mean_field::quadrature::Query query = GravityField::make_query< + mean_field::field::Gravity::Form::HDivMass>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), {}, mean_field::utils::DOMAINS::ALL, + get_mapping_kind(domain_mapper, transformation) + ); + + const auto resolution = + f.quadratureFactory->get(query, transformation.GetGeometryType()); + MFEM_VERIFY( + resolution.integration_rule != nullptr, + "The quadrature policy did not return an H(div) mass integration " + "rule." + ); + return *resolution.integration_rule; + } + + const mfem::IntegrationRule &get_source_rule( + const mean_field::fem::FEM &f, + const mfem::FiniteElement &density_element, + const mfem::FiniteElement &potential_element, + const mfem::ElementTransformation &transformation + ) { + using GravityField = + mean_field::field::Field; + MFEM_VERIFY( + density_element.GetOrder() == + mean_field::field::Density::Scalar::familyOrder, + "The source-kernel trial element does not match the registered " + "density " + "field." + ); + MFEM_VERIFY( + potential_element.GetOrder() == + mean_field::field::Gravity::Potential::familyOrder, + "The source-kernel test element does not match the registered " + "gravity " + "potential." + ); + const mean_field::quadrature::Query query = GravityField::make_query< + mean_field::field::Gravity::Form::SourceProjection>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), {}, mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + const auto resolution = + f.quadratureFactory->get(query, transformation.GetGeometryType()); + MFEM_VERIFY( + resolution.integration_rule != nullptr, + "The quadrature policy did not return a gravity-source integration " + "rule." + ); + return *resolution.integration_rule; + } +} // namespace + +namespace mean_field::operators::kernels { + void apply_mapped_hdiv_mass( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &gravity_gradient_true, + const mfem::Vector &displacement_true, + mfem::Vector &action + ) { + MFEM_VERIFY( + f.gravityFluxFes != nullptr, + "The H(div) mass kernel requires the " + "gravity-gradient finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, "The H(div) mass kernel requires the " + "displacement finite-element space." + ); + MFEM_VERIFY( + f.compactificationFes != nullptr, + "The H(div) mass kernel requires the compactification " + "finite-element " + "space." + ); + MFEM_VERIFY( + f.compactificationCoordinate != nullptr, + "The H(div) mass kernel requires the compactification field." + ); + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "The H(div) mass kernel requires the quadrature rule factory." + ); + MFEM_VERIFY( + gravity_gradient_true.Size() == f.gravityFluxFes->GetTrueVSize(), + "The gravity-gradient vector has the wrong size." + ); + MFEM_VERIFY( + displacement_true.Size() == f.displacementFes->GetTrueVSize(), + "The displacement vector has the wrong size." + ); + + mfem::Vector gravity_gradient_local; + mfem::Vector displacement_local; + true_to_local( + *f.gravityFluxFes, gravity_gradient_true, gravity_gradient_local + ); + true_to_local( + *f.displacementFes, displacement_true, displacement_local + ); + + mfem::Vector local_action(f.gravityFluxFes->GetVSize()); + local_action = 0.0; + + mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + mfem::Array gravity_dofs; + mfem::Array displacement_dofs; + mfem::Array compactification_dofs; + + mfem::Vector element_gravity_gradient; + mfem::Vector element_displacement; + mfem::Vector element_compactification; + mfem::Vector element_action; + mfem::Vector gravity_gradient_value; + mfem::Vector mapped_gravity_gradient_value; + + mfem::DenseMatrix vector_shape; + mfem::DenseMatrix mapped_mass_tensor; + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + const mfem::FiniteElement &gravity_element = + *f.gravityFluxFes->GetFE(element_id); + const mfem::FiniteElement &displacement_element = + *f.displacementFes->GetFE(element_id); + const mfem::FiniteElement &compactification_element = + *f.compactificationFes->GetFE(element_id); + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + + mfem::DofTransformation *gravity_dof_transformation = + f.gravityFluxFes->GetElementVDofs(element_id, gravity_dofs); + mfem::DofTransformation *displacement_dof_transformation = + f.displacementFes->GetElementVDofs( + element_id, displacement_dofs + ); + mfem::DofTransformation *compactification_dof_transformation = + f.compactificationFes->GetElementDofs( + element_id, compactification_dofs + ); + + gravity_gradient_local.GetSubVector( + gravity_dofs, element_gravity_gradient + ); + displacement_local.GetSubVector( + displacement_dofs, element_displacement + ); + f.compactificationCoordinate->GetSubVector( + compactification_dofs, element_compactification + ); + + if (gravity_dof_transformation != nullptr) + gravity_dof_transformation->InvTransformPrimal( + element_gravity_gradient + ); + if (displacement_dof_transformation != nullptr) + displacement_dof_transformation->InvTransformPrimal( + element_displacement + ); + if (compactification_dof_transformation != nullptr) + compactification_dof_transformation->InvTransformPrimal( + element_compactification + ); + + // const mapping::ElementDisplacementData + // displacement_data(displacement_element, element_displacement, + // mfem::Ordering::byVDIM); + + const mapping::ElementDisplacementData displacement_data = + mapping::ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement + ); + + const mapping::ElementCompactificationData compactification_data( + compactification_element, element_compactification + ); + const mapping::ElementMappingData mapping_data{ + .displacement = displacement_data, + .compactification = compactification_data + }; + + const int gravity_dof_count = gravity_element.GetDof(); + const int dimension = transformation->GetSpaceDim(); + + element_action.SetSize(gravity_dof_count); + gravity_gradient_value.SetSize(dimension); + mapped_gravity_gradient_value.SetSize(dimension); + vector_shape.SetSize(gravity_dof_count, dimension); + mapped_mass_tensor.SetSize(dimension); + element_action = 0.0; + + const mfem::IntegrationRule &integration_rule = get_hdiv_mass_rule( + f, domain_mapper, gravity_element, *transformation + ); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + transformation->SetIntPoint(&integration_point); + + mapping::VolumeMappingContext mapping_context; + const mapping::MappingStatus status = + domain_mapper.EvaluateVolume( + mapping_data, *transformation, integration_point, + workspace, mapping_context + ); + MFEM_VERIFY( + status == mapping::MappingStatus::valid, + "Stateless mapping failed in the matrix-free H(div) mass " + "kernel. " + "Element: " + << element_id + << ", attribute: " << transformation->Attribute + << ", quadrature point: " << q + << ", status: " << static_cast(status) + ); + + gravity_element.CalcVShape(*transformation, vector_shape); + mapping::ComputeHDivMassTensor( + mapping_context.mapping, mapped_mass_tensor + ); + + vector_shape.MultTranspose( + element_gravity_gradient, gravity_gradient_value + ); + mapped_mass_tensor.Mult( + gravity_gradient_value, mapped_gravity_gradient_value + ); + + const double weight = + integration_point.weight * transformation->Weight(); + + for (int i = 0; i < gravity_dof_count; ++i) { + double value = 0.0; + for (int component = 0; component < dimension; ++component) + value += vector_shape(i, component) * + mapped_gravity_gradient_value(component); + element_action(i) += weight * value; + } + } + + if (gravity_dof_transformation != nullptr) + gravity_dof_transformation->TransformDual(element_action); + local_action.AddElementVector(gravity_dofs, element_action); + } + + local_to_true(*f.gravityFluxFes, local_action, action); + } + + void apply_mapped_source( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &density_true, + const mfem::Vector &displacement_true, + mfem::Vector &action + ) { + MFEM_VERIFY( + f.densityFes != nullptr, "The gravity-source kernel requires the " + "density finite-element space." + ); + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "The gravity-source kernel requires the gravity-potential " + "finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, + "The gravity-source kernel requires the " + "displacement finite-element space." + ); + MFEM_VERIFY( + f.compactificationFes != nullptr, + "The gravity-source kernel requires the compactification " + "finite-element space." + ); + MFEM_VERIFY( + f.compactificationCoordinate != nullptr, + "The gravity-source kernel requires the compactification field." + ); + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "The gravity-source kernel requires the quadrature rule factory." + ); + MFEM_VERIFY( + density_true.Size() == f.densityFes->GetTrueVSize(), + "The density vector has the wrong size." + ); + MFEM_VERIFY( + displacement_true.Size() == f.displacementFes->GetTrueVSize(), + "The displacement vector has the wrong size." + ); + + mfem::Vector density_local; + mfem::Vector displacement_local; + true_to_local(*f.densityFes, density_true, density_local); + true_to_local( + *f.displacementFes, displacement_true, displacement_local + ); + + mfem::Vector local_action(f.gravityPotentialFes->GetVSize()); + local_action = 0.0; + + mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + mfem::Array density_dofs; + mfem::Array potential_dofs; + mfem::Array displacement_dofs; + mfem::Array compactification_dofs; + + mfem::Vector element_density; + mfem::Vector element_displacement; + mfem::Vector element_compactification; + mfem::Vector element_action; + mfem::Vector density_shape; + mfem::Vector potential_shape; + + const int vacuum_attribute = domain_mapper.GetVacuumElementAttribute(); + constexpr double source_scale = 4.0 * M_PI * utils::G; + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + if (transformation->Attribute == vacuum_attribute) + continue; + + const mfem::FiniteElement &density_element = + *f.densityFes->GetFE(element_id); + const mfem::FiniteElement &potential_element = + *f.gravityPotentialFes->GetFE(element_id); + const mfem::FiniteElement &displacement_element = + *f.displacementFes->GetFE(element_id); + const mfem::FiniteElement &compactification_element = + *f.compactificationFes->GetFE(element_id); + + mfem::DofTransformation *density_dof_transformation = + f.densityFes->GetElementDofs(element_id, density_dofs); + mfem::DofTransformation *potential_dof_transformation = + f.gravityPotentialFes->GetElementDofs( + element_id, potential_dofs + ); + mfem::DofTransformation *displacement_dof_transformation = + f.displacementFes->GetElementVDofs( + element_id, displacement_dofs + ); + mfem::DofTransformation *compactification_dof_transformation = + f.compactificationFes->GetElementDofs( + element_id, compactification_dofs + ); + + density_local.GetSubVector(density_dofs, element_density); + displacement_local.GetSubVector( + displacement_dofs, element_displacement + ); + f.compactificationCoordinate->GetSubVector( + compactification_dofs, element_compactification + ); + + if (density_dof_transformation != nullptr) + density_dof_transformation->InvTransformPrimal(element_density); + if (displacement_dof_transformation != nullptr) + displacement_dof_transformation->InvTransformPrimal( + element_displacement + ); + if (compactification_dof_transformation != nullptr) + compactification_dof_transformation->InvTransformPrimal( + element_compactification + ); + + const mapping::ElementDisplacementData displacement_data = + mapping::ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement + ); + const mapping::ElementCompactificationData compactification_data( + compactification_element, element_compactification + ); + const mapping::ElementMappingData mapping_data{ + .displacement = displacement_data, + .compactification = compactification_data + }; + + const int density_dof_count = density_element.GetDof(); + const int potential_dof_count = potential_element.GetDof(); + + density_shape.SetSize(density_dof_count); + potential_shape.SetSize(potential_dof_count); + element_action.SetSize(potential_dof_count); + element_action = 0.0; + + const mfem::IntegrationRule &integration_rule = get_source_rule( + f, density_element, potential_element, *transformation + ); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + transformation->SetIntPoint(&integration_point); + + mapping::VolumeMappingContext mapping_context; + const mapping::MappingStatus status = + domain_mapper.EvaluateVolume( + mapping_data, *transformation, integration_point, + workspace, mapping_context + ); + MFEM_VERIFY( + status == mapping::MappingStatus::valid, + "Stateless mapping failed in the matrix-free " + "gravity-source " + "kernel. Element: " + << element_id + << ", attribute: " << transformation->Attribute + << ", quadrature point: " << q + << ", status: " << static_cast(status) + ); + + density_element.CalcShape(integration_point, density_shape); + potential_element.CalcShape(integration_point, potential_shape); + + const double density_value = element_density * density_shape; + const double weight = source_scale * density_value * + mapping_context.quadrature.weight; + + for (int i = 0; i < potential_dof_count; ++i) + element_action(i) += weight * potential_shape(i); + } + + if (potential_dof_transformation != nullptr) + potential_dof_transformation->TransformDual(element_action); + local_action.AddElementVector(potential_dofs, element_action); + } + + local_to_true(*f.gravityPotentialFes, local_action, action); + } + + void apply_mapped_hdiv_mass_variation( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &gravity_gradient_true, + const mfem::Vector &displacement_true, + const mfem::Vector &displacement_variation_true, + mfem::Vector &action_variation + ) { + MFEM_VERIFY( + f.mesh != nullptr, + "The H(div) mass-variation kernel requires a mesh." + ); + MFEM_VERIFY( + f.gravityFluxFes != nullptr, + "The H(div) mass-variation kernel requires the " + "gravity-gradient finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, + "The H(div) mass-variation kernel requires " + "the displacement finite-element space." + ); + MFEM_VERIFY( + f.compactificationFes != nullptr, + "The H(div) mass-variation kernel requires the compactification " + "finite-element space." + ); + MFEM_VERIFY( + f.compactificationCoordinate != nullptr, + "The H(div) mass-variation kernel requires the compactification " + "field." + ); + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "The H(div) mass-variation kernel requires the quadrature rule " + "factory." + ); + MFEM_VERIFY( + gravity_gradient_true.Size() == f.gravityFluxFes->GetTrueVSize(), + "The gravity-gradient vector has the wrong size." + ); + MFEM_VERIFY( + displacement_true.Size() == f.displacementFes->GetTrueVSize(), + "The displacement vector has the wrong size." + ); + MFEM_VERIFY( + displacement_variation_true.Size() == + f.displacementFes->GetTrueVSize(), + "The displacement-variation vector has the wrong size." + ); + MFEM_VERIFY( + domain_mapper.GetDimension() == f.mesh->Dimension(), + "The domain-mapper dimension does not match the mesh dimension." + ); + + mfem::Vector gravity_gradient_local; + mfem::Vector displacement_local; + mfem::Vector displacement_variation_local; + + true_to_local( + *f.gravityFluxFes, gravity_gradient_true, gravity_gradient_local + ); + true_to_local( + *f.displacementFes, displacement_true, displacement_local + ); + true_to_local( + *f.displacementFes, displacement_variation_true, + displacement_variation_local + ); + + mfem::Vector local_action(f.gravityFluxFes->GetVSize()); + local_action = 0.0; + + mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + mfem::Array gravity_gradient_dofs; + mfem::Array displacement_dofs; + mfem::Array compactification_dofs; + + mfem::Vector element_gravity_gradient; + mfem::Vector element_displacement; + mfem::Vector element_displacement_variation; + mfem::Vector element_compactification; + mfem::Vector element_action; + mfem::Vector gravity_gradient_value; + mfem::Vector mass_tensor_variation_action; + + mfem::DenseMatrix gravity_gradient_shape; + mfem::DenseMatrix mass_tensor_variation; + + const int vacuum_attribute = domain_mapper.GetVacuumElementAttribute(); + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + const mfem::FiniteElement &gravity_gradient_element = + *f.gravityFluxFes->GetFE(element_id); + const mfem::FiniteElement &displacement_element = + *f.displacementFes->GetFE(element_id); + const mfem::FiniteElement &compactification_element = + *f.compactificationFes->GetFE(element_id); + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + + MFEM_VERIFY( + transformation != nullptr, + "The H(div) mass-variation kernel " + "received a null element transformation." + ); + + mfem::DofTransformation *gravity_dof_transformation = + f.gravityFluxFes->GetElementVDofs( + element_id, gravity_gradient_dofs + ); + mfem::DofTransformation *displacement_dof_transformation = + f.displacementFes->GetElementVDofs( + element_id, displacement_dofs + ); + mfem::DofTransformation *compactification_dof_transformation = + f.compactificationFes->GetElementDofs( + element_id, compactification_dofs + ); + + gravity_gradient_local.GetSubVector( + gravity_gradient_dofs, element_gravity_gradient + ); + displacement_local.GetSubVector( + displacement_dofs, element_displacement + ); + displacement_variation_local.GetSubVector( + displacement_dofs, element_displacement_variation + ); + f.compactificationCoordinate->GetSubVector( + compactification_dofs, element_compactification + ); + + if (gravity_dof_transformation != nullptr) + gravity_dof_transformation->InvTransformPrimal( + element_gravity_gradient + ); + + if (displacement_dof_transformation != nullptr) { + displacement_dof_transformation->InvTransformPrimal( + element_displacement + ); + displacement_dof_transformation->InvTransformPrimal( + element_displacement_variation + ); + } + + if (compactification_dof_transformation != nullptr) + compactification_dof_transformation->InvTransformPrimal( + element_compactification + ); + + const mapping::ElementDisplacementData displacement_data = + mapping::ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement + ); + const mapping::ElementDisplacementData displacement_variation_data = + mapping::ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement_variation + ); + const mapping::ElementCompactificationData compactification_data( + compactification_element, element_compactification + ); + const mapping::ElementMappingData mapping_data{ + .displacement = displacement_data, + .compactification = compactification_data + }; + + const int gravity_gradient_dof_count = + gravity_gradient_element.GetDof(); + const int dimension = transformation->GetSpaceDim(); + + element_action.SetSize(gravity_gradient_dof_count); + element_action = 0.0; + + gravity_gradient_value.SetSize(dimension); + mass_tensor_variation_action.SetSize(dimension); + + gravity_gradient_shape.SetSize( + gravity_gradient_dof_count, dimension + ); + mass_tensor_variation.SetSize(dimension, dimension); + + const mfem::IntegrationRule &integration_rule = get_hdiv_mass_rule( + f, domain_mapper, gravity_gradient_element, *transformation + ); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + transformation->SetIntPoint(&integration_point); + + mapping::VolumeMappingContext mapping_context; + const mapping::MappingStatus status = + domain_mapper.EvaluateVolume( + mapping_data, *transformation, integration_point, + workspace, mapping_context + ); + MFEM_VERIFY( + status == mapping::MappingStatus::valid, + "Stateless mapping failed in the matrix-free H(div) mass " + "kernel. " + "Element: " + << element_id + << ", attribute: " << transformation->Attribute + << ", quadrature point: " << q + << ", status: " << static_cast(status) + ); + + mapping::VolumeMappingVariation mapping_variation; + const mapping::MappingStatus variation_status = + domain_mapper.EvaluateVolumeVariation( + mapping_data, displacement_variation_data, + *transformation, integration_point, mapping_context, + workspace, mapping_variation + ); + MFEM_VERIFY( + variation_status == mapping::MappingStatus::valid, + "The mapping variation is invalid while applying the " + "H(div) mass " + "variation." + ); + + mapping::ComputeHDivMassTensorVariation( + mapping_context.mapping, mapping_variation.mapping, + mass_tensor_variation + ); + + gravity_gradient_element.CalcVShape( + *transformation, gravity_gradient_shape + ); + gravity_gradient_shape.MultTranspose( + element_gravity_gradient, gravity_gradient_value + ); + mass_tensor_variation.Mult( + gravity_gradient_value, mass_tensor_variation_action + ); + const double reference_weight = + integration_point.weight * transformation->Weight(); + + gravity_gradient_shape.AddMult( + mass_tensor_variation_action, element_action, + reference_weight + ); + } + + if (gravity_dof_transformation != nullptr) + gravity_dof_transformation->TransformDual(element_action); + local_action.AddElementVector( + gravity_gradient_dofs, element_action + ); + } + + action_variation.SetSize(f.gravityFluxFes->GetTrueVSize()); + action_variation = 0.0; + add_local_to_true(*f.gravityFluxFes, local_action, action_variation); + } + + void apply_mapped_source_variation( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &density_true, + const mfem::Vector &displacement_true, + const mfem::Vector &displacement_variation_true, + mfem::Vector &action_variation + ) { + MFEM_VERIFY( + f.mesh != nullptr, "The source-variation kernel requires a mesh." + ); + MFEM_VERIFY( + f.densityFes != nullptr, + "The source-variation kernel requires the density finite-element " + "space." + ); + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "The source-variation kernel requires the gravity-potential " + "finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, + "The source-variation kernel requires the " + "displacement finite-element space." + ); + MFEM_VERIFY( + f.compactificationFes != nullptr, + "The source-variation kernel requires the compactification " + "finite-element space." + ); + MFEM_VERIFY( + f.compactificationCoordinate != nullptr, + "The source-variation kernel requires the compactification field." + ); + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "The source-variation kernel requires the quadrature rule factory." + ); + MFEM_VERIFY( + density_true.Size() == f.densityFes->GetTrueVSize(), + "The density vector has the wrong size." + ); + MFEM_VERIFY( + displacement_true.Size() == f.displacementFes->GetTrueVSize(), + "The displacement vector has the wrong size." + ); + MFEM_VERIFY( + displacement_variation_true.Size() == + f.displacementFes->GetTrueVSize(), + "The displacement-variation vector has the wrong size." + ); + MFEM_VERIFY( + domain_mapper.GetDimension() == f.mesh->Dimension(), + "The domain-mapper dimension does not match the mesh dimension." + ); + + mfem::Vector density_local; + mfem::Vector displacement_local; + mfem::Vector displacement_variation_local; + + true_to_local(*f.densityFes, density_true, density_local); + true_to_local( + *f.displacementFes, displacement_true, displacement_local + ); + true_to_local( + *f.displacementFes, displacement_variation_true, + displacement_variation_local + ); + + mfem::Vector local_action(f.gravityPotentialFes->GetVSize()); + local_action = 0.0; + + mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + mfem::Array density_dofs; + mfem::Array potential_dofs; + mfem::Array displacement_dofs; + mfem::Array compactification_dofs; + + mfem::Vector element_density; + mfem::Vector element_displacement; + mfem::Vector element_displacement_variation; + mfem::Vector element_compactification; + mfem::Vector element_action; + mfem::Vector density_shape; + mfem::Vector potential_shape; + + mapping::VolumeMappingContext mapping_context; + mapping::VolumeMappingVariation mapping_variation; + + const int vacuum_attribute = domain_mapper.GetVacuumElementAttribute(); + constexpr double gravitational_source_scale = 4.0 * M_PI * utils::G; + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + MFEM_VERIFY( + transformation != nullptr, + "The source-variation kernel received a null element " + "transformation." + ); + + if (transformation->Attribute == vacuum_attribute) + continue; + + const mfem::FiniteElement &density_element = + *f.densityFes->GetFE(element_id); + const mfem::FiniteElement &potential_element = + *f.gravityPotentialFes->GetFE(element_id); + const mfem::FiniteElement &displacement_element = + *f.displacementFes->GetFE(element_id); + const mfem::FiniteElement &compactification_element = + *f.compactificationFes->GetFE(element_id); + + mfem::DofTransformation *density_dof_transformation = + f.densityFes->GetElementDofs(element_id, density_dofs); + mfem::DofTransformation *potential_dof_transformation = + f.gravityPotentialFes->GetElementDofs( + element_id, potential_dofs + ); + mfem::DofTransformation *displacement_dof_transformation = + f.displacementFes->GetElementVDofs( + element_id, displacement_dofs + ); + mfem::DofTransformation *compactification_dof_transformation = + f.compactificationFes->GetElementDofs( + element_id, compactification_dofs + ); + + density_local.GetSubVector(density_dofs, element_density); + displacement_local.GetSubVector( + displacement_dofs, element_displacement + ); + displacement_variation_local.GetSubVector( + displacement_dofs, element_displacement_variation + ); + f.compactificationCoordinate->GetSubVector( + compactification_dofs, element_compactification + ); + + if (density_dof_transformation != nullptr) + density_dof_transformation->InvTransformPrimal(element_density); + + if (displacement_dof_transformation != nullptr) { + displacement_dof_transformation->InvTransformPrimal( + element_displacement + ); + displacement_dof_transformation->InvTransformPrimal( + element_displacement_variation + ); + } + + if (compactification_dof_transformation != nullptr) + compactification_dof_transformation->InvTransformPrimal( + element_compactification + ); + + const mapping::ElementDisplacementData displacement_data = + mapping::ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement + ); + const mapping::ElementDisplacementData displacement_variation_data = + mapping::ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement_variation + ); + const mapping::ElementCompactificationData compactification_data( + compactification_element, element_compactification + ); + const mapping::ElementMappingData mapping_data{ + .displacement = displacement_data, + .compactification = compactification_data + }; + + element_action.SetSize(potential_element.GetDof()); + element_action = 0.0; + + density_shape.SetSize(density_element.GetDof()); + potential_shape.SetSize(potential_element.GetDof()); + + const mfem::IntegrationRule &integration_rule = get_source_rule( + f, density_element, potential_element, *transformation + ); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + transformation->SetIntPoint(&integration_point); + + const mapping::MappingStatus mapping_status = + domain_mapper.EvaluateVolume( + mapping_data, *transformation, integration_point, + workspace, mapping_context + ); + MFEM_VERIFY( + mapping_status == mapping::MappingStatus::valid, + "The base mapping is invalid while applying the source " + "variation." + ); + + const mapping::MappingStatus variation_status = + domain_mapper.EvaluateVolumeVariation( + mapping_data, displacement_variation_data, + *transformation, integration_point, mapping_context, + workspace, mapping_variation + ); + + MFEM_VERIFY( + variation_status == mapping::MappingStatus::valid, + "The mapping variation is invalid while applying the " + "source " + "variation." + ); + + density_element.CalcShape(integration_point, density_shape); + potential_element.CalcShape(integration_point, potential_shape); + + const double density_value = density_shape * element_density; + const double source_variation_value = + gravitational_source_scale * density_value * + mapping_variation.weight_variation; + + element_action.Add(source_variation_value, potential_shape); + } + + if (potential_dof_transformation != nullptr) + potential_dof_transformation->TransformDual(element_action); + local_action.AddElementVector(potential_dofs, element_action); + } + + action_variation.SetSize(f.gravityPotentialFes->GetTrueVSize()); + action_variation = 0.0; + add_local_to_true( + *f.gravityPotentialFes, local_action, action_variation + ); + } +} // namespace mean_field::operators::kernels diff --git a/libmeanfield/impl/operators/kernels/hydrostatic_equilibrium_kernels.cpp b/libmeanfield/impl/operators/kernels/hydrostatic_equilibrium_kernels.cpp new file mode 100644 index 0000000..fd7d7b1 --- /dev/null +++ b/libmeanfield/impl/operators/kernels/hydrostatic_equilibrium_kernels.cpp @@ -0,0 +1,775 @@ +module; + +#include +#include +#include +#include +#include + +module mean_field; + +import :operators.kernels.hydrostatic_equilibrium; + +namespace { + void true_to_local( + const mfem::ParFiniteElementSpace &finiteElementSpace, + const mfem::Vector &trueVector, + mfem::Vector &localVector + ) { + MFEM_VERIFY( + trueVector.Size() == finiteElementSpace.GetTrueVSize(), + "True vector has the wrong size." + ); + + localVector.SetSize(finiteElementSpace.GetVSize()); + + const mfem::Operator *prolongation = + finiteElementSpace.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->Mult(trueVector, localVector); + } else { + localVector = trueVector; + } + } + + void local_to_true( + const mfem::ParFiniteElementSpace &finiteElementSpace, + const mfem::Vector &localVector, + mfem::Vector &trueVector + ) { + MFEM_VERIFY( + localVector.Size() == finiteElementSpace.GetVSize(), + "Local vector has the wrong size." + ); + + trueVector.SetSize(finiteElementSpace.GetTrueVSize()); + + trueVector = 0.0; + + const mfem::Operator *prolongation = + finiteElementSpace.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->MultTranspose(localVector, trueVector); + } else { + trueVector = localVector; + } + } + + void validate_fem( + const mean_field::fem::FEM &f, + const mean_field::mapping::DomainMapperStateless &domainMapper + ) { + MFEM_VERIFY( + f.mesh != nullptr, "The hydrostatic kernel requires a mesh." + ); + + MFEM_VERIFY( + f.enthalpyFes != nullptr, "The hydrostatic kernel requires the " + "enthalpy finite-element space." + ); + + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "The hydrostatic kernel requires the " + "gravity-potential finite-element space." + ); + + MFEM_VERIFY( + f.displacementFes != nullptr, "The hydrostatic kernel requires the " + "displacement finite-element space." + ); + + MFEM_VERIFY( + f.compactificationFes != nullptr, + "The hydrostatic kernel requires the " + "compactification finite-element space." + ); + + MFEM_VERIFY( + f.compactificationCoordinate != nullptr, + "The hydrostatic kernel requires the " + "compactification coordinate." + ); + + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "The hydrostatic kernel requires the " + "quadrature-rule factory." + ); + + MFEM_VERIFY( + f.mesh->Dimension() == 3, + "The rigid-rotation hydrostatic kernel " + "currently requires a three-dimensional mesh." + ); + + MFEM_VERIFY( + domainMapper.GetDimension() == f.mesh->Dimension(), + "The domain-mapper dimension does not match " + "the mesh dimension." + ); + } + + const mfem::IntegrationRule &get_hydrostatic_rule( + const mean_field::fem::FEM &f, + const mfem::FiniteElement &enthalpyElement, + const mfem::FiniteElement &potentialElement, + const mfem::ElementTransformation &transformation + ) { + using EnthalpyField = + mean_field::field::Field; + + MFEM_VERIFY( + enthalpyElement.GetOrder() == + mean_field::field::Enthalpy::Scalar::familyOrder, + "The hydrostatic test element does not match " + "the registered enthalpy field." + ); + + MFEM_VERIFY( + potentialElement.GetOrder() == + mean_field::field::Gravity::Potential::familyOrder, + "The hydrostatic potential element does not " + "match the registered gravity-potential field." + ); + + const auto enthalpyQuery = EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::EquilibriumEnthalpy>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), {}, mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + const auto gravityQuery = EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::EquilibriumGravity>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), {}, mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + const auto rotationQuery = EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::EquilibriumRotation>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), std::array{2}, + mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + const auto constantQuery = EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::EquilibriumConstant>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), {}, mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + int integrationOrder = 0; + + const auto update_order = [&f, &transformation, &integrationOrder]( + const mean_field::quadrature::Query &query + ) { + const auto rule = f.quadratureFactory->get( + query, transformation.GetGeometryType() + ); + + MFEM_VERIFY( + rule.integration_rule != nullptr, + "The quadrature policy did not return " + "a hydrostatic-equilibrium rule." + ); + + integrationOrder = + std::max(integrationOrder, rule.resolution.order); + }; + + update_order(enthalpyQuery); + update_order(gravityQuery); + update_order(rotationQuery); + update_order(constantQuery); + + return mfem::IntRules.Get( + transformation.GetGeometryType(), integrationOrder + ); + } + + struct HydrostaticAssemblyRequest { + const mean_field::physics::RigidRotation *rotation{nullptr}; + + const mfem::Vector *baseEnthalpyTrue{nullptr}; + const mfem::Vector *basePotentialTrue{nullptr}; + + const mfem::Vector *enthalpyVariationTrue{nullptr}; + const mfem::Vector *potentialVariationTrue{nullptr}; + const mfem::Vector *displacementVariationTrue{nullptr}; + + double bernoulliConstant{0.0}; + double constantVariation{0.0}; + + bool buildResidual{false}; + }; + + void assemble_hydrostatic_form( + const mean_field::fem::FEM &f, + const mean_field::mapping::DomainMapperStateless &domainMapper, + const mfem::Vector &displacementTrue, + const HydrostaticAssemblyRequest &request, + mfem::Vector &result + ) { + validate_fem(f, domainMapper); + + MFEM_VERIFY( + displacementTrue.Size() == f.displacementFes->GetTrueVSize(), + "The hydrostatic displacement vector has " + "the wrong size." + ); + + MFEM_VERIFY( + std::isfinite(request.bernoulliConstant), + "The Bernoulli constant is non-finite." + ); + + MFEM_VERIFY( + std::isfinite(request.constantVariation), + "The Bernoulli-constant variation is non-finite." + ); + + const bool requiresBaseState = + request.buildResidual || + request.displacementVariationTrue != nullptr; + + if (requiresBaseState) { + MFEM_VERIFY( + request.rotation != nullptr, + "The hydrostatic residual or geometry " + "action requires the rotation model." + ); + + MFEM_VERIFY( + request.baseEnthalpyTrue != nullptr, + "The hydrostatic residual or geometry " + "action requires the base enthalpy." + ); + + MFEM_VERIFY( + request.basePotentialTrue != nullptr, + "The hydrostatic residual or geometry " + "action requires the base potential." + ); + } + + if (request.baseEnthalpyTrue != nullptr) { + MFEM_VERIFY( + request.baseEnthalpyTrue->Size() == + f.enthalpyFes->GetTrueVSize(), + "The base enthalpy vector has the wrong size." + ); + } + + if (request.basePotentialTrue != nullptr) { + MFEM_VERIFY( + request.basePotentialTrue->Size() == + f.gravityPotentialFes->GetTrueVSize(), + "The base potential vector has the wrong size." + ); + } + + if (request.enthalpyVariationTrue != nullptr) { + MFEM_VERIFY( + request.enthalpyVariationTrue->Size() == + f.enthalpyFes->GetTrueVSize(), + "The enthalpy variation has the wrong size." + ); + } + + if (request.potentialVariationTrue != nullptr) { + MFEM_VERIFY( + request.potentialVariationTrue->Size() == + f.gravityPotentialFes->GetTrueVSize(), + "The potential variation has the wrong size." + ); + } + + if (request.displacementVariationTrue != nullptr) { + MFEM_VERIFY( + request.displacementVariationTrue->Size() == + f.displacementFes->GetTrueVSize(), + "The displacement variation has the wrong size." + ); + } + + mfem::Vector displacementLocal; + true_to_local(*f.displacementFes, displacementTrue, displacementLocal); + + mfem::Vector baseEnthalpyLocal; + mfem::Vector basePotentialLocal; + mfem::Vector enthalpyVariationLocal; + mfem::Vector potentialVariationLocal; + mfem::Vector displacementVariationLocal; + + if (request.baseEnthalpyTrue != nullptr) { + true_to_local( + *f.enthalpyFes, *request.baseEnthalpyTrue, baseEnthalpyLocal + ); + } + + if (request.basePotentialTrue != nullptr) { + true_to_local( + *f.gravityPotentialFes, *request.basePotentialTrue, + basePotentialLocal + ); + } + + if (request.enthalpyVariationTrue != nullptr) { + true_to_local( + *f.enthalpyFes, *request.enthalpyVariationTrue, + enthalpyVariationLocal + ); + } + + if (request.potentialVariationTrue != nullptr) { + true_to_local( + *f.gravityPotentialFes, *request.potentialVariationTrue, + potentialVariationLocal + ); + } + + if (request.displacementVariationTrue != nullptr) { + true_to_local( + *f.displacementFes, *request.displacementVariationTrue, + displacementVariationLocal + ); + } + + mfem::Vector localResult(f.enthalpyFes->GetVSize()); + + localResult = 0.0; + + mean_field::mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + mfem::Array enthalpyDofs; + mfem::Array potentialDofs; + mfem::Array displacementDofs; + mfem::Array compactificationDofs; + + mfem::Vector elementBaseEnthalpy; + mfem::Vector elementBasePotential; + mfem::Vector elementEnthalpyVariation; + mfem::Vector elementPotentialVariation; + mfem::Vector elementDisplacement; + mfem::Vector elementDisplacementVariation; + mfem::Vector elementCompactification; + mfem::Vector elementResult; + + mfem::Vector enthalpyShape; + mfem::Vector potentialShape; + + const int vacuumAttribute = domainMapper.GetVacuumElementAttribute(); + + for (int elementId = 0; elementId < f.mesh->GetNE(); ++elementId) { + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(elementId); + + MFEM_VERIFY( + transformation != nullptr, + "The hydrostatic kernel received a null " + "element transformation." + ); + + if (transformation->Attribute == vacuumAttribute) { + continue; + } + + const mfem::FiniteElement &enthalpyElement = + *f.enthalpyFes->GetFE(elementId); + + const mfem::FiniteElement &potentialElement = + *f.gravityPotentialFes->GetFE(elementId); + + const mfem::FiniteElement &displacementElement = + *f.displacementFes->GetFE(elementId); + + const mfem::FiniteElement &compactificationElement = + *f.compactificationFes->GetFE(elementId); + + mfem::DofTransformation *enthalpyDofTransformation = + f.enthalpyFes->GetElementDofs(elementId, enthalpyDofs); + + mfem::DofTransformation *potentialDofTransformation = + f.gravityPotentialFes->GetElementDofs(elementId, potentialDofs); + + mfem::DofTransformation *displacementDofTransformation = + f.displacementFes->GetElementVDofs(elementId, displacementDofs); + + mfem::DofTransformation *compactificationDofTransformation = + f.compactificationFes->GetElementDofs( + elementId, compactificationDofs + ); + + displacementLocal.GetSubVector( + displacementDofs, elementDisplacement + ); + + f.compactificationCoordinate->GetSubVector( + compactificationDofs, elementCompactification + ); + + if (request.baseEnthalpyTrue != nullptr) { + baseEnthalpyLocal.GetSubVector( + enthalpyDofs, elementBaseEnthalpy + ); + } + + if (request.basePotentialTrue != nullptr) { + basePotentialLocal.GetSubVector( + potentialDofs, elementBasePotential + ); + } + + if (request.enthalpyVariationTrue != nullptr) { + enthalpyVariationLocal.GetSubVector( + enthalpyDofs, elementEnthalpyVariation + ); + } + + if (request.potentialVariationTrue != nullptr) { + potentialVariationLocal.GetSubVector( + potentialDofs, elementPotentialVariation + ); + } + + if (request.displacementVariationTrue != nullptr) { + displacementVariationLocal.GetSubVector( + displacementDofs, elementDisplacementVariation + ); + } + + if (enthalpyDofTransformation != nullptr) { + if (request.baseEnthalpyTrue != nullptr) { + enthalpyDofTransformation->InvTransformPrimal( + elementBaseEnthalpy + ); + } + + if (request.enthalpyVariationTrue != nullptr) { + enthalpyDofTransformation->InvTransformPrimal( + elementEnthalpyVariation + ); + } + } + + if (potentialDofTransformation != nullptr) { + if (request.basePotentialTrue != nullptr) { + potentialDofTransformation->InvTransformPrimal( + elementBasePotential + ); + } + + if (request.potentialVariationTrue != nullptr) { + potentialDofTransformation->InvTransformPrimal( + elementPotentialVariation + ); + } + } + + if (displacementDofTransformation != nullptr) { + displacementDofTransformation->InvTransformPrimal( + elementDisplacement + ); + + if (request.displacementVariationTrue != nullptr) { + displacementDofTransformation->InvTransformPrimal( + elementDisplacementVariation + ); + } + } + + if (compactificationDofTransformation != nullptr) { + compactificationDofTransformation->InvTransformPrimal( + elementCompactification + ); + } + + const mean_field::mapping::ElementDisplacementData + displacementData = mean_field::mapping:: + ElementDisplacementDataFromElementVDofs( + displacementElement, elementDisplacement + ); + + const mean_field::mapping::ElementCompactificationData + compactificationData( + compactificationElement, elementCompactification + ); + + const mean_field::mapping::ElementMappingData mappingData{ + .displacement = displacementData, + .compactification = compactificationData + }; + + std::optional + displacementVariationData; + + if (request.displacementVariationTrue != nullptr) { + displacementVariationData.emplace( + mean_field::mapping:: + ElementDisplacementDataFromElementVDofs( + displacementElement, elementDisplacementVariation + ) + ); + } + + elementResult.SetSize(enthalpyElement.GetDof()); + + elementResult = 0.0; + + enthalpyShape.SetSize(enthalpyElement.GetDof()); + + potentialShape.SetSize(potentialElement.GetDof()); + + const mfem::IntegrationRule &integrationRule = get_hydrostatic_rule( + f, enthalpyElement, potentialElement, *transformation + ); + + for (int quadraturePoint = 0; + quadraturePoint < integrationRule.GetNPoints(); + ++quadraturePoint) { + const mfem::IntegrationPoint &integrationPoint = + integrationRule.IntPoint(quadraturePoint); + + transformation->SetIntPoint(&integrationPoint); + + mean_field::mapping::VolumeMappingContext mappingContext; + + const mean_field::mapping::MappingStatus mappingStatus = + domainMapper.EvaluateVolume( + mappingData, *transformation, integrationPoint, + workspace, mappingContext + ); + + MFEM_VERIFY( + mappingStatus == mean_field::mapping::MappingStatus::valid, + "The base mapping is invalid in the " + "hydrostatic kernel. Element: " + << elementId + << ", quadrature point: " << quadraturePoint + << ", status: " << static_cast(mappingStatus) + ); + + enthalpyElement.CalcShape(integrationPoint, enthalpyShape); + + potentialElement.CalcShape(integrationPoint, potentialShape); + + double baseIntegrand = 0.0; + + if (requiresBaseState) { + const double enthalpyValue = + elementBaseEnthalpy * enthalpyShape; + + const double potentialValue = + elementBasePotential * potentialShape; + + const double rotationPotential = + request.rotation->potential( + mappingContext.mapping.physical_position + ); + + baseIntegrand = enthalpyValue + potentialValue - + rotationPotential - + request.bernoulliConstant; + } + + if (request.buildResidual) { + elementResult.Add( + mappingContext.quadrature.weight * baseIntegrand, + enthalpyShape + ); + + continue; + } + + double materialVariation = -request.constantVariation; + + if (request.enthalpyVariationTrue != nullptr) { + materialVariation += + elementEnthalpyVariation * enthalpyShape; + } + + if (request.potentialVariationTrue != nullptr) { + materialVariation += + elementPotentialVariation * potentialShape; + } + + double weightedVariation = + mappingContext.quadrature.weight * materialVariation; + + if (request.displacementVariationTrue != nullptr) { + mean_field::mapping::VolumeMappingVariation + mappingVariation; + + const mean_field::mapping::MappingStatus variationStatus = + domainMapper.EvaluateVolumeVariation( + mappingData, *displacementVariationData, + *transformation, integrationPoint, mappingContext, + workspace, mappingVariation + ); + + MFEM_VERIFY( + variationStatus == + mean_field::mapping::MappingStatus::valid, + "The mapping variation is invalid " + "in the hydrostatic kernel." + ); + + const double rotationVariation = + request.rotation->potential_directional_derivative( + mappingContext.mapping.physical_position, + mappingVariation.mapping.physical_position_variation + ); + + weightedVariation += + baseIntegrand * mappingVariation.weight_variation - + rotationVariation * mappingContext.quadrature.weight; + } + + elementResult.Add(weightedVariation, enthalpyShape); + } + + if (enthalpyDofTransformation != nullptr) { + enthalpyDofTransformation->TransformDual(elementResult); + } + + localResult.AddElementVector(enthalpyDofs, elementResult); + } + + local_to_true(*f.enthalpyFes, localResult, result); + } +} // namespace + +namespace mean_field::operators::kernels { + void apply_hydrostatic_equilibrium( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::RigidRotation &rotation, + const mfem::Vector &enthalpyTrue, + const mfem::Vector &potentialTrue, + const mfem::Vector &displacementTrue, + const double bernoulliConstant, + mfem::Vector &residual + ) { + HydrostaticAssemblyRequest request; + + request.rotation = &rotation; + request.baseEnthalpyTrue = &enthalpyTrue; + request.basePotentialTrue = &potentialTrue; + request.bernoulliConstant = bernoulliConstant; + request.buildResidual = true; + + assemble_hydrostatic_form( + f, domainMapper, displacementTrue, request, residual + ); + } + + void apply_hydrostatic_equilibrium_enthalpy_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const mfem::Vector &enthalpyVariationTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &action + ) { + HydrostaticAssemblyRequest request; + + request.enthalpyVariationTrue = &enthalpyVariationTrue; + + assemble_hydrostatic_form( + f, domainMapper, displacementTrue, request, action + ); + } + + void apply_hydrostatic_equilibrium_potential_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const mfem::Vector &potentialVariationTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &action + ) { + HydrostaticAssemblyRequest request; + + request.potentialVariationTrue = &potentialVariationTrue; + + assemble_hydrostatic_form( + f, domainMapper, displacementTrue, request, action + ); + } + + void apply_hydrostatic_equilibrium_constant_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const double constantVariation, + const mfem::Vector &displacementTrue, + mfem::Vector &action + ) { + HydrostaticAssemblyRequest request; + + request.constantVariation = constantVariation; + + assemble_hydrostatic_form( + f, domainMapper, displacementTrue, request, action + ); + } + + void apply_hydrostatic_equilibrium_displacement_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::RigidRotation &rotation, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &basePotentialTrue, + const mfem::Vector &baseDisplacementTrue, + const double baseBernoulliConstant, + const mfem::Vector &displacementVariationTrue, + mfem::Vector &action + ) { + HydrostaticAssemblyRequest request; + + request.rotation = &rotation; + request.baseEnthalpyTrue = &baseEnthalpyTrue; + request.basePotentialTrue = &basePotentialTrue; + request.displacementVariationTrue = &displacementVariationTrue; + request.bernoulliConstant = baseBernoulliConstant; + + assemble_hydrostatic_form( + f, domainMapper, baseDisplacementTrue, request, action + ); + } + + void apply_hydrostatic_equilibrium_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::RigidRotation &rotation, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &basePotentialTrue, + const mfem::Vector &baseDisplacementTrue, + const double baseBernoulliConstant, + const mfem::Vector &enthalpyVariationTrue, + const mfem::Vector &potentialVariationTrue, + const double constantVariation, + const mfem::Vector &displacementVariationTrue, + mfem::Vector &action + ) { + HydrostaticAssemblyRequest request; + + request.rotation = &rotation; + request.baseEnthalpyTrue = &baseEnthalpyTrue; + request.basePotentialTrue = &basePotentialTrue; + request.enthalpyVariationTrue = &enthalpyVariationTrue; + request.potentialVariationTrue = &potentialVariationTrue; + request.displacementVariationTrue = &displacementVariationTrue; + request.bernoulliConstant = baseBernoulliConstant; + request.constantVariation = constantVariation; + + assemble_hydrostatic_form( + f, domainMapper, baseDisplacementTrue, request, action + ); + } +} // namespace mean_field::operators::kernels \ No newline at end of file diff --git a/libmeanfield/impl/operators/kernels/pressure_force_kernels.cpp b/libmeanfield/impl/operators/kernels/pressure_force_kernels.cpp new file mode 100644 index 0000000..a97ce6b --- /dev/null +++ b/libmeanfield/impl/operators/kernels/pressure_force_kernels.cpp @@ -0,0 +1,464 @@ +module; + +#include +#include +#include + +#include + +module mean_field; + +import :operators.kernels.pressure_force; + +namespace { + void true_to_local( + const mfem::ParFiniteElementSpace &finiteElementSpace, + const mfem::Vector &trueVector, + mfem::Vector &localVector + ) { + MFEM_VERIFY( + trueVector.Size() == finiteElementSpace.GetTrueVSize(), + "The pressure-force true vector has the wrong size." + ); + + localVector.SetSize(finiteElementSpace.GetVSize()); + + const mfem::Operator *prolongation = + finiteElementSpace.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->Mult(trueVector, localVector); + } else { + localVector = trueVector; + } + } + + void local_to_true( + const mfem::ParFiniteElementSpace &finiteElementSpace, + const mfem::Vector &localVector, + mfem::Vector &trueVector + ) { + MFEM_VERIFY( + localVector.Size() == finiteElementSpace.GetVSize(), + "The pressure-force local vector has the wrong size." + ); + + trueVector.SetSize(finiteElementSpace.GetTrueVSize()); + trueVector = 0.0; + + const mfem::Operator *prolongation = + finiteElementSpace.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->MultTranspose(localVector, trueVector); + } else { + trueVector = localVector; + } + } + + [[nodiscard]] int vector_dof_index( + const mfem::Ordering::Type ordering, + const int scalarDof, + const int component, + const int scalarDofCount, + const int dimension + ) { + if (ordering == mfem::Ordering::byNODES) { + return scalarDof + component * scalarDofCount; + } + + if (ordering == mfem::Ordering::byVDIM) { + return component + scalarDof * dimension; + } + MFEM_ABORT("The displacement space uses an unsupported ordering."); + return -1; + } + + [[nodiscard]] int get_pressure_extra_order( + const mean_field::physics::PolytropicBarotrope &barotrope + ) { + /* + * Pressure has the enthalpy dependence + * + * P(h) proportional to h^(n + 1). + * + * The registered enthalpy operand already contributes one factor + * of the enthalpy polynomial order. The remaining dynamic + * contribution is therefore n times that order. + */ + const double extraOrder = + barotrope.polytropic_index() * + static_cast( + mean_field::field::Enthalpy::Scalar::familyOrder + ); + + MFEM_VERIFY( + std::isfinite(extraOrder) && extraOrder >= 0.0 && + extraOrder <= + static_cast(std::numeric_limits::max()), + "The pressure EOS effective polynomial order is invalid." + ); + + return static_cast(std::ceil(extraOrder)); + } + + [[nodiscard]] const mfem::IntegrationRule &get_pressure_force_rule( + const mean_field::fem::FEM &f, + const mean_field::physics::PolytropicBarotrope &barotrope, + const mfem::FiniteElement &enthalpyElement, + const mfem::FiniteElement &displacementElement, + const mfem::ElementTransformation &transformation + ) { + using EnthalpyField = + mean_field::field::Field; + + MFEM_VERIFY( + enthalpyElement.GetOrder() == + mean_field::field::Enthalpy::Scalar::familyOrder, + "The pressure-force enthalpy element does not match the " + "registered enthalpy field." + ); + + MFEM_VERIFY( + displacementElement.GetOrder() == + mean_field::field::Displacement::Vector::familyOrder, + "The pressure-force test element does not match the " + "registered displacement field." + ); + + const mean_field::quadrature::Query query = EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::PressureForce>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), + std::array{get_pressure_extra_order(barotrope)}, + mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + const mean_field::quadrature::MfemRule rule = + f.quadratureFactory->get(query, transformation.GetGeometryType()); + + MFEM_VERIFY( + rule.integration_rule != nullptr, + "The quadrature policy did not return a pressure-force " + "integration rule." + ); + + return *rule.integration_rule; + } + + void validate_inputs( + const mean_field::fem::FEM &f, + const mean_field::mapping::DomainMapperStateless &domainMapper, + const mfem::Vector &enthalpyTrue, + const mfem::Vector &displacementTrue + ) { + MFEM_VERIFY( + f.mesh != nullptr, "The pressure-force kernel requires a mesh." + ); + + MFEM_VERIFY( + f.enthalpyFes != nullptr, + "The pressure-force kernel requires the enthalpy " + "finite-element space." + ); + + MFEM_VERIFY( + f.displacementFes != nullptr, + "The pressure-force kernel requires the displacement " + "finite-element space." + ); + + MFEM_VERIFY( + f.compactificationFes != nullptr, + "The pressure-force kernel requires the compactification " + "finite-element space." + ); + + MFEM_VERIFY( + f.compactificationCoordinate != nullptr, + "The pressure-force kernel requires the compactification " + "coordinate." + ); + + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "The pressure-force kernel requires the quadrature " + "rule factory." + ); + + MFEM_VERIFY( + enthalpyTrue.Size() == f.enthalpyFes->GetTrueVSize(), + "The pressure-force enthalpy vector has the wrong size." + ); + + MFEM_VERIFY( + displacementTrue.Size() == f.displacementFes->GetTrueVSize(), + "The pressure-force displacement vector has the wrong size." + ); + + MFEM_VERIFY( + domainMapper.GetDimension() == f.mesh->Dimension(), + "The pressure-force domain-mapper dimension does not match " + "the mesh dimension." + ); + + MFEM_VERIFY( + f.displacementFes->GetVDim() == f.mesh->Dimension(), + "The displacement vector dimension does not match the " + "mesh dimension." + ); + + MFEM_VERIFY( + f.displacementFes->GetOrdering() == mfem::Ordering::byNODES, + "The pressure-force kernel requires the registered byNODES " + "displacement ordering." + ); + } +} // namespace + +namespace mean_field::operators::kernels { + void apply_pressure_force_residual( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope, + const mfem::Vector &enthalpyTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &residualTrue + ) { + validate_inputs(f, domainMapper, enthalpyTrue, displacementTrue); + + mfem::Vector enthalpyLocal; + mfem::Vector displacementLocal; + + true_to_local(*f.enthalpyFes, enthalpyTrue, enthalpyLocal); + + true_to_local(*f.displacementFes, displacementTrue, displacementLocal); + + mfem::Vector localResidual(f.displacementFes->GetVSize()); + localResidual = 0.0; + + mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + mfem::Array enthalpyDofs; + mfem::Array displacementDofs; + mfem::Array compactificationDofs; + + mfem::Vector elementEnthalpy; + mfem::Vector elementDisplacement; + mfem::Vector elementCompactification; + mfem::Vector elementResidual; + mfem::Vector enthalpyShape; + + mfem::DenseMatrix displacementDShapeReference; + mfem::DenseMatrix displacementDShapePhysical; + + mapping::VolumeMappingContext mappingContext; + + const int dimension = f.mesh->Dimension(); + const int vacuumAttribute = domainMapper.GetVacuumElementAttribute(); + + const mfem::Ordering::Type displacementOrdering = + f.displacementFes->GetOrdering(); + + for (int elementId = 0; elementId < f.mesh->GetNE(); ++elementId) { + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(elementId); + + MFEM_VERIFY( + transformation != nullptr, + "The pressure-force kernel received a null element " + "transformation." + ); + + /* + * Skip vacuum before constructing or evaluating any mapping + * data for the element. + */ + if (transformation->Attribute == vacuumAttribute) { + continue; + } + + const mfem::FiniteElement &enthalpyElement = + *f.enthalpyFes->GetFE(elementId); + + const mfem::FiniteElement &displacementElement = + *f.displacementFes->GetFE(elementId); + + const mfem::FiniteElement &compactificationElement = + *f.compactificationFes->GetFE(elementId); + + mfem::DofTransformation *enthalpyDofTransformation = + f.enthalpyFes->GetElementDofs(elementId, enthalpyDofs); + + mfem::DofTransformation *displacementDofTransformation = + f.displacementFes->GetElementVDofs(elementId, displacementDofs); + + mfem::DofTransformation *compactificationDofTransformation = + f.compactificationFes->GetElementDofs( + elementId, compactificationDofs + ); + + enthalpyLocal.GetSubVector(enthalpyDofs, elementEnthalpy); + + displacementLocal.GetSubVector( + displacementDofs, elementDisplacement + ); + + f.compactificationCoordinate->GetSubVector( + compactificationDofs, elementCompactification + ); + + if (enthalpyDofTransformation != nullptr) { + enthalpyDofTransformation->InvTransformPrimal(elementEnthalpy); + } + + if (displacementDofTransformation != nullptr) { + displacementDofTransformation->InvTransformPrimal( + elementDisplacement + ); + } + + if (compactificationDofTransformation != nullptr) { + compactificationDofTransformation->InvTransformPrimal( + elementCompactification + ); + } + + const mapping::ElementDisplacementData displacementData = + mapping::ElementDisplacementDataFromElementVDofs( + displacementElement, elementDisplacement + ); + + const mapping::ElementCompactificationData compactificationData( + compactificationElement, elementCompactification + ); + + const mapping::ElementMappingData mappingData{ + .displacement = displacementData, + .compactification = compactificationData + }; + + const int scalarDisplacementDofCount = displacementElement.GetDof(); + + MFEM_VERIFY( + displacementDofs.Size() == + scalarDisplacementDofCount * dimension, + "The pressure-force element displacement vector has " + "the wrong size." + ); + + enthalpyShape.SetSize(enthalpyElement.GetDof()); + + displacementDShapeReference.SetSize( + scalarDisplacementDofCount, dimension + ); + + displacementDShapePhysical.SetSize( + scalarDisplacementDofCount, dimension + ); + + elementResidual.SetSize(displacementDofs.Size()); + elementResidual = 0.0; + + const mfem::IntegrationRule &integrationRule = + get_pressure_force_rule( + f, barotrope, enthalpyElement, displacementElement, + *transformation + ); + + for (int quadratureIndex = 0; + quadratureIndex < integrationRule.GetNPoints(); + ++quadratureIndex) { + const mfem::IntegrationPoint &integrationPoint = + integrationRule.IntPoint(quadratureIndex); + + transformation->SetIntPoint(&integrationPoint); + + const mapping::MappingStatus mappingStatus = + domainMapper.EvaluateVolume( + mappingData, *transformation, integrationPoint, + workspace, mappingContext + ); + + MFEM_VERIFY( + mappingStatus == mapping::MappingStatus::valid, + "Stateless mapping failed in the pressure-force " + "kernel. Element: " + << elementId + << ", attribute: " << transformation->Attribute + << ", quadrature point: " << quadratureIndex + << ", status: " << static_cast(mappingStatus) + ); + + enthalpyElement.CalcShape(integrationPoint, enthalpyShape); + + const double enthalpyValue = elementEnthalpy * enthalpyShape; + + const double pressureValue = + barotrope.pressure_from_enthalpy(enthalpyValue); + + displacementElement.CalcDShape( + integrationPoint, displacementDShapeReference + ); + + /* + * Row i of DShape is grad_reference(N_i). Multiplication + * by the complete inverse element Jacobian gives + * + * grad_physical(N_i) + * = grad_reference(N_i) J^{-1}. + */ + mfem::Mult( + displacementDShapeReference, + mappingContext.quadrature.J_inv, displacementDShapePhysical + ); + + const double weightedPressure = + pressureValue * mappingContext.quadrature.weight; + + MFEM_VERIFY( + std::isfinite(pressureValue) && + std::isfinite(weightedPressure), + "The pressure-force kernel encountered a non-finite " + "quadrature value." + ); + + /* + * For the vector basis N_i e_c, + * + * div(N_i e_c) = partial_c N_i. + * + * Therefore + * + * R_(i,c) + * = -integral P partial_c N_i dV. + */ + for (int scalarDof = 0; scalarDof < scalarDisplacementDofCount; + ++scalarDof) { + for (int component = 0; component < dimension; + ++component) { + const int vectorDof = vector_dof_index( + displacementOrdering, scalarDof, component, + scalarDisplacementDofCount, dimension + ); + + elementResidual(vectorDof) -= + weightedPressure * + displacementDShapePhysical(scalarDof, component); + } + } + } + + if (displacementDofTransformation != nullptr) { + displacementDofTransformation->TransformDual(elementResidual); + } + + localResidual.AddElementVector(displacementDofs, elementResidual); + } + + local_to_true(*f.displacementFes, localResidual, residualTrue); + } +} // namespace mean_field::operators::kernels \ No newline at end of file diff --git a/libmeanfield/impl/operators/prepared_barotropic_closure.cpp b/libmeanfield/impl/operators/prepared_barotropic_closure.cpp new file mode 100644 index 0000000..f26d9b8 --- /dev/null +++ b/libmeanfield/impl/operators/prepared_barotropic_closure.cpp @@ -0,0 +1,718 @@ +module; + +#include +#include +#include +#include +#include + +module mean_field; + +import :operators.prepared_barotropic_closure; + +namespace { + int get_density_size(const mean_field::fem::FEM &f) { + MFEM_VERIFY( + f.densityFes != nullptr, + "PreparedBarotropicClosureOperator requires the " + "density finite-element space." + ); + + return f.densityFes->GetTrueVSize(); + } + + int get_enthalpy_size(const mean_field::fem::FEM &f) { + MFEM_VERIFY( + f.enthalpyFes != nullptr, + "PreparedBarotropicClosureOperator requires the " + "enthalpy finite-element space." + ); + + return f.enthalpyFes->GetTrueVSize(); + } + + void validate_finite_vector( + const mfem::Vector &vector, + const char *message + ) { + for (int i = 0; i < vector.Size(); ++i) { + MFEM_VERIFY(std::isfinite(vector(i)), message); + } + } + + void true_to_local( + const mfem::ParFiniteElementSpace &finiteElementSpace, + const mfem::Vector &trueVector, + mfem::Vector &localVector + ) { + MFEM_VERIFY( + trueVector.Size() == finiteElementSpace.GetTrueVSize(), + "True vector has the wrong size." + ); + + localVector.SetSize(finiteElementSpace.GetVSize()); + + const mfem::Operator *prolongation = + finiteElementSpace.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->Mult(trueVector, localVector); + } else { + localVector = trueVector; + } + } + + void local_to_true( + const mfem::ParFiniteElementSpace &finiteElementSpace, + const mfem::Vector &localVector, + mfem::Vector &trueVector + ) { + MFEM_VERIFY( + localVector.Size() == finiteElementSpace.GetVSize(), + "Local vector has the wrong size." + ); + + trueVector.SetSize(finiteElementSpace.GetTrueVSize()); + trueVector = 0.0; + + const mfem::Operator *prolongation = + finiteElementSpace.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->MultTranspose(localVector, trueVector); + } else { + trueVector = localVector; + } + } + + int get_eos_extra_order( + const mean_field::physics::PolytropicBarotrope &barotrope + ) { + const double extraOrder = + (barotrope.polytropic_index() - 1.0) * + static_cast( + mean_field::field::Enthalpy::Scalar::familyOrder + ); + + MFEM_VERIFY( + std::isfinite(extraOrder) && extraOrder >= 0.0 && + extraOrder <= + static_cast(std::numeric_limits::max()), + "The EOS effective polynomial order is invalid." + ); + + return static_cast(std::ceil(extraOrder)); + } + + const mfem::IntegrationRule &get_eos_rule( + const mean_field::fem::FEM &f, + const mean_field::physics::PolytropicBarotrope &barotrope, + const mfem::FiniteElement &densityElement, + const mfem::FiniteElement &enthalpyElement, + const mfem::ElementTransformation &transformation + ) { + using EnthalpyField = + mean_field::field::Field; + + MFEM_VERIFY( + densityElement.GetOrder() == + mean_field::field::Density::Scalar::familyOrder, + "The prepared EOS test element does not match " + "the registered density field." + ); + + MFEM_VERIFY( + enthalpyElement.GetOrder() == + mean_field::field::Enthalpy::Scalar::familyOrder, + "The prepared EOS trial element does not match " + "the registered enthalpy field." + ); + + const mean_field::quadrature::Query query = EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::EosClosureSource>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), + std::array{get_eos_extra_order(barotrope)}, + mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + const auto resolution = + f.quadratureFactory->get(query, transformation.GetGeometryType()); + + MFEM_VERIFY( + resolution.integration_rule != nullptr, + "The quadrature policy did not return a prepared " + "EOS-closure integration rule." + ); + + return *resolution.integration_rule; + } +} // namespace + +namespace mean_field::operators { + PreparedBarotropicClosureOperator::PreparedBarotropicClosureOperator( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope + ) + : mfem::Operator( + f.densityFes->GetTrueVSize(), + f.densityFes->GetTrueVSize() + f.enthalpyFes->GetTrueVSize() + + f.displacementFes->GetTrueVSize() + ), + m_fem(f), + m_domainMapper(domainMapper), + m_barotrope(barotrope), + m_densitySize(f.densityFes->GetTrueVSize()), + m_enthalpySize(f.enthalpyFes->GetTrueVSize()) { + MFEM_VERIFY( + m_fem.densityFes != nullptr, + "PreparedBarotropicClosureOperator requires " + "a density finite-element space." + ); + + MFEM_VERIFY( + m_fem.enthalpyFes != nullptr, + "PreparedBarotropicClosureOperator requires " + "an enthalpy finite-element space." + ); + + MFEM_VERIFY( + m_fem.displacementFes != nullptr, + "PreparedBarotropicClosureOperator requires " + "a displacement finite-element space." + ); + } + + void PreparedBarotropicClosureOperator::Prepare( + const mfem::Vector &baseDensityTrue, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &displacementTrue + ) { + MFEM_VERIFY( + baseDensityTrue.Size() == m_densitySize, + "PreparedBarotropicClosureOperator received a " + "base-density vector with the wrong size." + ); + + MFEM_VERIFY( + baseEnthalpyTrue.Size() == m_enthalpySize, + "PreparedBarotropicClosureOperator received a " + "base-enthalpy vector with the wrong size." + ); + + MFEM_VERIFY( + displacementTrue.Size() == m_fem.displacementFes->GetTrueVSize(), + "PreparedBarotropicClosureOperator received a " + "displacement vector with the wrong size." + ); + MFEM_VERIFY( + baseDensityTrue.Size() == m_fem.densityFes->GetTrueVSize(), + "The base density true vector has the wrong size." + ); + + MFEM_VERIFY( + baseEnthalpyTrue.Size() == m_fem.enthalpyFes->GetTrueVSize(), + "The base enthalpy true vector has the wrong size." + ); + + MFEM_VERIFY( + displacementTrue.Size() == m_fem.displacementFes->GetTrueVSize(), + "The base displacement true vector has the wrong size." + ); + + validate_finite_vector( + baseDensityTrue, "PreparedBarotropicClosureOperator received a " + "non-finite base-density value." + ); + + validate_finite_vector( + baseEnthalpyTrue, "PreparedBarotropicClosureOperator received a " + "non-finite base-enthalpy value." + ); + + validate_finite_vector( + displacementTrue, "PreparedBarotropicClosureOperator received a " + "non-finite displacement value." + ); + + m_isPrepared = false; + m_elements.clear(); + m_elements.reserve(m_fem.mesh->GetNE()); + + mfem::Vector baseDensityLocal; + mfem::Vector baseEnthalpyLocal; + mfem::Vector displacementLocal; + + true_to_local(*m_fem.densityFes, baseDensityTrue, baseDensityLocal); + + true_to_local(*m_fem.enthalpyFes, baseEnthalpyTrue, baseEnthalpyLocal); + + true_to_local( + *m_fem.displacementFes, displacementTrue, displacementLocal + ); + + mapping::DomainMapperStateless::Workspace workspace( + m_fem.mesh->Dimension() + ); + + mfem::Array displacementDofs; + mfem::Array compactificationDofs; + + mfem::Vector elementBaseDensity; + mfem::Vector elementBaseEnthalpy; + mfem::Vector elementDisplacement; + mfem::Vector elementCompactification; + + mfem::Vector densityShape; + mfem::Vector enthalpyShape; + + const int vacuumAttribute = m_domainMapper.GetVacuumElementAttribute(); + + for (int elementId = 0; elementId < m_fem.mesh->GetNE(); ++elementId) { + mfem::ElementTransformation *transformation = + m_fem.mesh->GetElementTransformation(elementId); + + MFEM_VERIFY( + transformation != nullptr, + "PreparedBarotropicClosureOperator received " + "a null element transformation." + ); + + if (transformation->Attribute == vacuumAttribute) { + continue; + } + + m_elements.emplace_back(); + ElementPAData &data = m_elements.back(); + + data.densityDofTransformation = + m_fem.densityFes->GetElementDofs(elementId, data.densityDofs); + + data.enthalpyDofTransformation = + m_fem.enthalpyFes->GetElementDofs(elementId, data.enthalpyDofs); + + mfem::DofTransformation *displacementDofTransformation = + m_fem.displacementFes->GetElementVDofs( + elementId, displacementDofs + ); + + mfem::DofTransformation *compactificationDofTransformation = + m_fem.compactificationFes->GetElementDofs( + elementId, compactificationDofs + ); + + baseDensityLocal.GetSubVector(data.densityDofs, elementBaseDensity); + + baseEnthalpyLocal.GetSubVector( + data.enthalpyDofs, elementBaseEnthalpy + ); + + displacementLocal.GetSubVector( + displacementDofs, elementDisplacement + ); + + m_fem.compactificationCoordinate->GetSubVector( + compactificationDofs, elementCompactification + ); + + if (data.densityDofTransformation != nullptr) { + data.densityDofTransformation->InvTransformPrimal( + elementBaseDensity + ); + } + + if (data.enthalpyDofTransformation != nullptr) { + data.enthalpyDofTransformation->InvTransformPrimal( + elementBaseEnthalpy + ); + } + + if (displacementDofTransformation != nullptr) { + displacementDofTransformation->InvTransformPrimal( + elementDisplacement + ); + } + + if (compactificationDofTransformation != nullptr) { + compactificationDofTransformation->InvTransformPrimal( + elementCompactification + ); + } + + const mfem::FiniteElement &densityElement = + *m_fem.densityFes->GetFE(elementId); + + const mfem::FiniteElement &enthalpyElement = + *m_fem.enthalpyFes->GetFE(elementId); + + const mfem::FiniteElement &displacementElement = + *m_fem.displacementFes->GetFE(elementId); + + const mfem::FiniteElement &compactificationElement = + *m_fem.compactificationFes->GetFE(elementId); + + const mapping::ElementDisplacementData displacementData = + mapping::ElementDisplacementDataFromElementVDofs( + displacementElement, elementDisplacement + ); + + const mapping::ElementCompactificationData compactificationData( + compactificationElement, elementCompactification + ); + + const mapping::ElementMappingData mappingData{ + .displacement = displacementData, + .compactification = compactificationData + }; + + const mfem::IntegrationRule &integrationRule = get_eos_rule( + m_fem, m_barotrope, densityElement, enthalpyElement, + *transformation + ); + + const int quadraturePointCount = integrationRule.GetNPoints(); + + const int densityDofCount = densityElement.GetDof(); + + const int enthalpyDofCount = enthalpyElement.GetDof(); + + data.densityBasis.SetSize(quadraturePointCount, densityDofCount); + + data.enthalpyBasis.SetSize(quadraturePointCount, enthalpyDofCount); + + data.weightedResidual.SetSize(quadraturePointCount); + + data.quadratureWeights.SetSize(quadraturePointCount); + + data.weightedEnthalpyDerivative.SetSize(quadraturePointCount); + + densityShape.SetSize(densityDofCount); + + enthalpyShape.SetSize(enthalpyDofCount); + + for (int quadraturePoint = 0; + quadraturePoint < quadraturePointCount; ++quadraturePoint) { + const mfem::IntegrationPoint &integrationPoint = + integrationRule.IntPoint(quadraturePoint); + + transformation->SetIntPoint(&integrationPoint); + + mapping::VolumeMappingContext mappingContext; + + const mapping::MappingStatus mappingStatus = + m_domainMapper.EvaluateVolume( + mappingData, *transformation, integrationPoint, + workspace, mappingContext + ); + + MFEM_VERIFY( + mappingStatus == mapping::MappingStatus::valid, + "Stateless mapping failed while preparing " + "the barotropic closure operator. Element: " + << elementId + << ", attribute: " << transformation->Attribute + << ", quadrature point: " << quadraturePoint + << ", status: " << static_cast(mappingStatus) + ); + + densityElement.CalcShape(integrationPoint, densityShape); + + enthalpyElement.CalcShape(integrationPoint, enthalpyShape); + + for (int densityDof = 0; densityDof < densityDofCount; + ++densityDof) { + data.densityBasis(quadraturePoint, densityDof) = + densityShape(densityDof); + } + + for (int enthalpyDof = 0; enthalpyDof < enthalpyDofCount; + ++enthalpyDof) { + data.enthalpyBasis(quadraturePoint, enthalpyDof) = + enthalpyShape(enthalpyDof); + } + + const double density = elementBaseDensity * densityShape; + + const double enthalpy = elementBaseEnthalpy * enthalpyShape; + + const double quadratureWeight = + mappingContext.quadrature.weight; + + const double eosDensity = + m_barotrope.density_from_enthalpy(enthalpy); + + const double enthalpyDerivative = + m_barotrope.density_derivative_from_enthalpy(enthalpy); + + MFEM_VERIFY( + std::isfinite(quadratureWeight) && quadratureWeight > 0.0 && + std::isfinite(eosDensity) && + std::isfinite(enthalpyDerivative), + "PreparedBarotropicClosureOperator " + "encountered invalid quadrature data." + ); + + data.quadratureWeights(quadraturePoint) = quadratureWeight; + + data.weightedResidual(quadraturePoint) = + quadratureWeight * (density - eosDensity); + + data.weightedEnthalpyDerivative(quadraturePoint) = + quadratureWeight * enthalpyDerivative; + } + } + + MFEM_VERIFY( + !m_elements.empty(), "PreparedBarotropicClosureOperator found no " + "stellar elements." + ); + + m_baseDensityTrue = baseDensityTrue; + m_baseEnthalpyTrue = baseEnthalpyTrue; + m_baseDisplacementTrue = displacementTrue; + + m_isPrepared = true; + ++m_preparationCount; + } + + void PreparedBarotropicClosureOperator::BuildResidual( + mfem::Vector &residual + ) const { + MFEM_VERIFY( + m_isPrepared, "PreparedBarotropicClosureOperator must be " + "prepared before BuildResidual is called." + ); + + mfem::Vector localResidual(m_fem.densityFes->GetVSize()); + localResidual = 0.0; + + mfem::Vector elementResidual; + + for (const ElementPAData &data : m_elements) { + elementResidual.SetSize(data.densityDofs.Size()); + + data.densityBasis.MultTranspose( + data.weightedResidual, elementResidual + ); + + if (data.densityDofTransformation != nullptr) { + data.densityDofTransformation->TransformDual(elementResidual); + } + + localResidual.AddElementVector(data.densityDofs, elementResidual); + } + + local_to_true(*m_fem.densityFes, localResidual, residual); + } + + void PreparedBarotropicClosureOperator::Mult( + const mfem::Vector &densityVariationTrue, + const mfem::Vector &enthalpyVariationTrue, + const mfem::Vector &displacementVariationTrue, + mfem::Vector &action + ) const { + VerifyPrepared(); + + MFEM_VERIFY( + densityVariationTrue.Size() == m_densitySize, + "The density-variation true vector has " + "the wrong size." + ); + + MFEM_VERIFY( + enthalpyVariationTrue.Size() == m_enthalpySize, + "The enthalpy-variation true vector has " + "the wrong size." + ); + + MFEM_VERIFY( + displacementVariationTrue.Size() == + m_fem.displacementFes->GetTrueVSize(), + "The displacement-variation true vector has " + "the wrong size." + ); + + Mult(densityVariationTrue, enthalpyVariationTrue, action); + + mfem::Vector displacementAction; + + kernels::apply_barotropic_closure_displacement_action( + m_fem, m_domainMapper, m_barotrope, m_baseDensityTrue, + m_baseEnthalpyTrue, m_baseDisplacementTrue, + displacementVariationTrue, displacementAction + ); + + MFEM_VERIFY( + displacementAction.Size() == m_densitySize, + "The barotropic-closure displacement action " + "returned a vector with the wrong size." + ); + + action += displacementAction; + } + + void PreparedBarotropicClosureOperator::Mult( + const mfem::Vector &combinedVariation, + mfem::Vector &action + ) const { + VerifyPrepared(); + + const int displacementSize = m_fem.displacementFes->GetTrueVSize(); + + const int combinedSize = + m_densitySize + m_enthalpySize + displacementSize; + + MFEM_VERIFY( + combinedVariation.Size() == combinedSize, + "The combined barotropic-closure variation " + "vector has the wrong size. Expected " + << combinedSize << " entries but received " + << combinedVariation.Size() << "." + ); + + mfem::real_t *combinedData = + const_cast(combinedVariation.HostRead()); + + const mfem::Vector densityVariationTrue(combinedData, m_densitySize); + + const mfem::Vector enthalpyVariationTrue( + combinedData + m_densitySize, m_enthalpySize + ); + + const mfem::Vector displacementVariationTrue( + combinedData + m_densitySize + m_enthalpySize, displacementSize + ); + + Mult( + densityVariationTrue, enthalpyVariationTrue, + displacementVariationTrue, action + ); + } + + void PreparedBarotropicClosureOperator::Mult( + const mfem::Vector &densityVariationTrue, + const mfem::Vector &enthalpyVariationTrue, + mfem::Vector &action + ) const { + MFEM_VERIFY( + m_isPrepared, "PreparedBarotropicClosureOperator must be " + "prepared before Mult is called." + ); + + MFEM_VERIFY( + densityVariationTrue.Size() == m_densitySize, + "PreparedBarotropicClosureOperator received a " + "density variation with the wrong size." + ); + + MFEM_VERIFY( + enthalpyVariationTrue.Size() == m_enthalpySize, + "PreparedBarotropicClosureOperator received an " + "enthalpy variation with the wrong size." + ); + + mfem::Vector densityVariationLocal; + mfem::Vector enthalpyVariationLocal; + + true_to_local( + *m_fem.densityFes, densityVariationTrue, densityVariationLocal + ); + + true_to_local( + *m_fem.enthalpyFes, enthalpyVariationTrue, enthalpyVariationLocal + ); + + mfem::Vector localAction(m_fem.densityFes->GetVSize()); + localAction = 0.0; + + mfem::Vector elementDensityVariation; + mfem::Vector elementEnthalpyVariation; + mfem::Vector quadratureDensityVariation; + mfem::Vector quadratureEnthalpyVariation; + mfem::Vector quadratureAction; + mfem::Vector elementAction; + + for (const ElementPAData &data : m_elements) { + densityVariationLocal.GetSubVector( + data.densityDofs, elementDensityVariation + ); + + enthalpyVariationLocal.GetSubVector( + data.enthalpyDofs, elementEnthalpyVariation + ); + + if (data.densityDofTransformation != nullptr) { + data.densityDofTransformation->InvTransformPrimal( + elementDensityVariation + ); + } + + if (data.enthalpyDofTransformation != nullptr) { + data.enthalpyDofTransformation->InvTransformPrimal( + elementEnthalpyVariation + ); + } + + quadratureDensityVariation.SetSize(data.quadratureWeights.Size()); + + quadratureEnthalpyVariation.SetSize(data.quadratureWeights.Size()); + + quadratureAction.SetSize(data.quadratureWeights.Size()); + + data.densityBasis.Mult( + elementDensityVariation, quadratureDensityVariation + ); + + data.enthalpyBasis.Mult( + elementEnthalpyVariation, quadratureEnthalpyVariation + ); + + for (int quadraturePoint = 0; + quadraturePoint < quadratureAction.Size(); ++quadraturePoint) { + quadratureAction(quadraturePoint) = + data.quadratureWeights(quadraturePoint) * + quadratureDensityVariation(quadraturePoint) - + data.weightedEnthalpyDerivative(quadraturePoint) * + quadratureEnthalpyVariation(quadraturePoint); + } + + elementAction.SetSize(data.densityDofs.Size()); + + data.densityBasis.MultTranspose(quadratureAction, elementAction); + + if (data.densityDofTransformation != nullptr) { + data.densityDofTransformation->TransformDual(elementAction); + } + + localAction.AddElementVector(data.densityDofs, elementAction); + } + + local_to_true(*m_fem.densityFes, localAction, action); + } + + bool PreparedBarotropicClosureOperator::IsPrepared() const noexcept { + return m_isPrepared; + } + + std::uint64_t + PreparedBarotropicClosureOperator::GetPreparationCount() const noexcept { + return m_preparationCount; + } + + int PreparedBarotropicClosureOperator::GetDensitySize() const noexcept { + return m_densitySize; + } + + int PreparedBarotropicClosureOperator::GetEnthalpySize() const noexcept { + return m_enthalpySize; + } + + void PreparedBarotropicClosureOperator::VerifyPrepared() const { + MFEM_VERIFY( + m_isPrepared, "PreparedBarotropicClosureOperator must be " + "prepared before this operation is called." + ); + } +} // namespace mean_field::operators \ No newline at end of file diff --git a/libmeanfield/impl/operators/prepared_gravity_source.cpp b/libmeanfield/impl/operators/prepared_gravity_source.cpp new file mode 100644 index 0000000..bd86c70 --- /dev/null +++ b/libmeanfield/impl/operators/prepared_gravity_source.cpp @@ -0,0 +1,617 @@ +module; +#include +#include +#include +#include +#include + +module mean_field; +import :operators.prepared_gravity_source; + +namespace { + int get_operator_height(const mean_field::fem::FEM &f) { + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "PreparedMappedGravitySourceOperator requires the " + "gravity-potential " + "finite-element space." + ); + return f.gravityPotentialFes->GetTrueVSize(); + } + + int get_operator_width(const mean_field::fem::FEM &f) { + MFEM_VERIFY( + f.densityFes != nullptr, + "PreparedMappedGravitySourceOperator requires the density " + "finite-element space." + ); + return f.densityFes->GetTrueVSize(); + } + + void true_to_local( + const mfem::ParFiniteElementSpace &finite_element_space, + const mfem::Vector &true_vector, + mfem::Vector &local_vector + ) { + local_vector.SetSize(finite_element_space.GetVSize()); + + const mfem::Operator *prolongation = + finite_element_space.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->Mult(true_vector, local_vector); + } else { + local_vector = true_vector; + } + } + + void local_to_true( + const mfem::ParFiniteElementSpace &finite_element_space, + const mfem::Vector &local_vector, + mfem::Vector &true_vector + ) { + MFEM_VERIFY( + local_vector.Size() == finite_element_space.GetVSize(), + "Local vector has the wrong size." + ); + + true_vector.SetSize(finite_element_space.GetTrueVSize()); + true_vector = 0.0; + + const mfem::Operator *prolongation = + finite_element_space.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->MultTranspose(local_vector, true_vector); + } else { + true_vector = local_vector; + } + } + + const mfem::IntegrationRule &get_source_rule( + const mean_field::fem::FEM &f, + const mfem::FiniteElement &density_element, + const mfem::FiniteElement &potential_element, + const mfem::ElementTransformation &transformation + ) { + using GravityField = + mean_field::field::Field; + MFEM_VERIFY( + density_element.GetOrder() == + mean_field::field::Density::Scalar::familyOrder, + "The prepared source trial element does not match the registered " + "density field." + ); + MFEM_VERIFY( + potential_element.GetOrder() == + mean_field::field::Gravity::Potential::familyOrder, + "The prepared source test element does not match the registered " + "gravity potential." + ); + const mean_field::quadrature::Query query = GravityField::make_query< + mean_field::field::Gravity::Form::SourceProjection>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), {}, mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + return *f.quadratureFactory + ->get(query, transformation.GetGeometryType()) + .integration_rule; + } + + class FrozenMappedGravitySourceCoefficient final + : public mfem::Coefficient { + public: + FrozenMappedGravitySourceCoefficient( + const mean_field::fem::FEM &f, + const mean_field::mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &displacement_true + ) + : m_fem(f), + m_domain_mapper(domain_mapper), + m_workspace(domain_mapper.GetDimension()) { + true_to_local( + *m_fem.displacementFes, displacement_true, m_displacement_local + ); + } + + double Eval( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point + ) override { + transformation.SetIntPoint(&integration_point); + + const int element_id = transformation.ElementNo; + MFEM_VERIFY( + element_id >= 0 && element_id < m_fem.mesh->GetNE(), + "Mapped gravity source coefficient received an invalid element " + "ID." + ); + if (transformation.Attribute == + m_domain_mapper.GetVacuumElementAttribute()) { + return 0.0; + } + + LoadElement(element_id); + const mean_field::mapping::ElementMappingData mapping_data{ + .displacement = *m_displacement_data, + .compactification = *m_compactification_data + }; + + mean_field::mapping::VolumeMappingContext mapping_context; + + const mean_field::mapping::MappingStatus status = + m_domain_mapper.EvaluateVolume( + mapping_data, transformation, integration_point, + m_workspace, mapping_context + ); + + if (status != mean_field::mapping::MappingStatus::valid) { + const mfem::FiniteElement &displacement_element = + *m_fem.displacementFes->GetFE(element_id); + const mfem::FiniteElement &compactification_element = + *m_fem.compactificationFes->GetFE(element_id); + + mfem::Vector displacement_shape(displacement_element.GetDof()); + mfem::Vector compactification_shape( + compactification_element.GetDof() + ); + mfem::Vector reference_position(m_domain_mapper.GetDimension()); + mfem::Vector displacement_value(m_domain_mapper.GetDimension()); + + displacement_element.CalcShape( + integration_point, displacement_shape + ); + compactification_element.CalcShape( + integration_point, compactification_shape + ); + transformation.Transform(integration_point, reference_position); + m_displacement_data->GetDofMatrix().MultTranspose( + displacement_shape, displacement_value + ); + + const double compactification_coordinate = + m_compactification_data->GetDofs() * compactification_shape; + + MFEM_ABORT( + "Stateless domain mapping failed while preparing the " + "gravity " + "source operator." + << "\nMapping status = " << static_cast(status) + << "\nElement ID = " << element_id + << "\nElement attribute = " << transformation.Attribute + << "\nIntegration-point index = " << integration_point.index + << "\nIntegration point = <" << integration_point.x << ", " + << integration_point.y << ", " << integration_point.z << ">" + << "\nReference position = <" << reference_position(0) + << ", " << reference_position(1) << ", " + << reference_position(2) << ">" + << "\nReference radius = " << reference_position.Norml2() + << "\nDisplacement value = <" << displacement_value(0) + << ", " << displacement_value(1) << ", " + << displacement_value(2) << ">" + << "\nDisplacement magnitude = " + << displacement_value.Norml2() + << "\nCompactification coordinate = " + << compactification_coordinate + << "\nDisplacement ordering = " + << static_cast(m_fem.displacementFes->GetOrdering()) + ); + } + const double mapping_determinant = + mapping_context.mapping.mapping_determinant; + MFEM_VERIFY( + std::isfinite(mapping_determinant) && mapping_determinant > 0.0, + "Prepared gravity source operator encountered a non-positive " + "or " + "non-finite mapping determinant." + ); + + return 4.0 * std::numbers::pi * mean_field::utils::G * + mapping_determinant; + } + + private: + void LoadElement(const int element_id) { + if (element_id == m_cached_element_id) { + return; + } + + const mfem::FiniteElement &displacement_element = + *m_fem.displacementFes->GetFE(element_id); + const mfem::FiniteElement &compactification_element = + *m_fem.compactificationFes->GetFE(element_id); + + mfem::DofTransformation *displacement_dof_transformation = + m_fem.displacementFes->GetElementVDofs( + element_id, m_displacement_dofs + ); + mfem::DofTransformation *compactification_dof_transformation = + m_fem.compactificationFes->GetElementDofs( + element_id, m_compactification_dofs + ); + + m_displacement_local.GetSubVector( + m_displacement_dofs, m_element_displacement + ); + m_fem.compactificationCoordinate->GetSubVector( + m_compactification_dofs, m_element_compactification + ); + + if (displacement_dof_transformation != nullptr) { + displacement_dof_transformation->InvTransformPrimal( + m_element_displacement + ); + } + + if (compactification_dof_transformation != nullptr) { + compactification_dof_transformation->InvTransformPrimal( + m_element_compactification + ); + } + + m_displacement_data = std::make_unique< + mean_field::mapping::ElementDisplacementData>( + mean_field::mapping::ElementDisplacementDataFromElementVDofs( + displacement_element, m_element_displacement + ) + ); + + m_compactification_data = std::make_unique< + mean_field::mapping::ElementCompactificationData>( + compactification_element, m_element_compactification + ); + + m_cached_element_id = element_id; + } + + const mean_field::fem::FEM &m_fem; + const mean_field::mapping::DomainMapperStateless &m_domain_mapper; + + mfem::Vector m_displacement_local; + + mfem::Array m_displacement_dofs; + mfem::Array m_compactification_dofs; + + mfem::Vector m_element_displacement; + mfem::Vector m_element_compactification; + + std::unique_ptr + m_displacement_data; + std::unique_ptr + m_compactification_data; + + mean_field::mapping::DomainMapperStateless::Workspace m_workspace; + int m_cached_element_id{-1}; + }; +} // namespace + +namespace mean_field::operators { + PreparedMappedGravitySourceOperator::PreparedMappedGravitySourceOperator( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper + ) + : Operator( + get_operator_height(f), + get_operator_width(f) + ), + m_fem(f), + m_domain_mapper(domain_mapper) { + MFEM_VERIFY( + f.mesh != nullptr, + "PreparedMappedGravitySourceOperator requires a mesh." + ); + MFEM_VERIFY( + f.densityFes != nullptr, + "PreparedMappedGravitySourceOperator requires the density " + "finite-element space." + ); + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "PreparedMappedGravitySourceOperator requires the " + "gravity-potential " + "finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, + "PreparedMappedGravitySourceOperator requires " + "the displacement finite-element space." + ); + MFEM_VERIFY( + f.compactificationFes != nullptr, + "PreparedMappedGravitySourceOperator requires the compactification " + "finite-element space." + ); + MFEM_VERIFY( + f.compactificationCoordinate != nullptr, + "PreparedMappedGravitySourceOperator requires the compactification " + "coordinate." + ); + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "PreparedMappedGravitySourceOperator " + "requires the quadrature-rule factory." + ); + MFEM_VERIFY( + domain_mapper.GetDimension() == f.mesh->Dimension(), + "The stateless domain-mapper dimension does not match the mesh " + "dimension." + ); + + utils::populate_element_mask( + f.mesh.get(), utils::DOMAINS::STELLAR, m_stellar_marker + ); + } + + void PreparedMappedGravitySourceOperator::Prepare( + const mfem::Vector &displacement_true + ) { + MFEM_VERIFY( + displacement_true.Size() == m_fem.displacementFes->GetTrueVSize(), + "PreparedMappedGravitySourceOperator received a displacement " + "vector " + "with the wrong size." + ); + + for (int i = 0; i < displacement_true.Size(); ++i) { + MFEM_VERIFY( + std::isfinite(displacement_true(i)), + "PreparedMappedGravitySourceOperator received a non-finite " + "displacement value." + ); + } + + m_is_prepared = false; + m_elements.clear(); + m_elements.reserve(m_fem.mesh->GetNE()); + + FrozenMappedGravitySourceCoefficient source_coefficient( + m_fem, m_domain_mapper, displacement_true + ); + + for (int element_id = 0; element_id < m_fem.mesh->GetNE(); + ++element_id) { + const int attribute = m_fem.mesh->GetAttribute(element_id); + + if (attribute <= 0 || attribute > m_stellar_marker.Size() || + m_stellar_marker[attribute - 1] == 0) { + continue; + } + + m_elements.emplace_back(); + ElementPAData &data = m_elements.back(); + + data.element_id = element_id; + + data.density_dof_transformation = + m_fem.densityFes->GetElementDofs(element_id, data.density_dofs); + + data.potential_dof_transformation = + m_fem.gravityPotentialFes->GetElementDofs( + element_id, data.potential_dofs + ); + + const mfem::FiniteElement &density_element = + *m_fem.densityFes->GetFE(element_id); + + const mfem::FiniteElement &potential_element = + *m_fem.gravityPotentialFes->GetFE(element_id); + + mfem::ElementTransformation &transformation = + *m_fem.mesh->GetElementTransformation(element_id); + + const mfem::IntegrationRule &integration_rule = get_source_rule( + m_fem, density_element, potential_element, transformation + ); + + const int quadrature_point_count = integration_rule.GetNPoints(); + + const int density_dof_count = density_element.GetDof(); + + const int potential_dof_count = potential_element.GetDof(); + + data.density_basis.SetSize( + quadrature_point_count, density_dof_count + ); + + data.potential_basis.SetSize( + quadrature_point_count, potential_dof_count + ); + + data.quadrature_data.SetSize(quadrature_point_count); + + mfem::Vector density_shape(density_dof_count); + mfem::Vector potential_shape(potential_dof_count); + + for (int quadrature_point = 0; + quadrature_point < quadrature_point_count; + ++quadrature_point) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(quadrature_point); + + transformation.SetIntPoint(&integration_point); + + // CalcPhysShape matches the scalar mixed-mass discretization, + // including the finite-element map type. + density_element.CalcPhysShape(transformation, density_shape); + + potential_element.CalcPhysShape( + transformation, potential_shape + ); + + for (int i = 0; i < density_dof_count; ++i) { + data.density_basis(quadrature_point, i) = density_shape(i); + } + + for (int i = 0; i < potential_dof_count; ++i) { + data.potential_basis(quadrature_point, i) = + potential_shape(i); + } + + const double coefficient_value = + source_coefficient.Eval(transformation, integration_point); + + transformation.SetIntPoint(&integration_point); + + const double quadrature_value = integration_point.weight * + transformation.Weight() * + coefficient_value; + + MFEM_VERIFY( + std::isfinite(quadrature_value) && quadrature_value > 0.0, + "Prepared gravity source operator encountered invalid " + "quadrature data on element " + << element_id << ", quadrature point " + << quadrature_point << "." + ); + + data.quadrature_data(quadrature_point) = quadrature_value; + } + } + + MFEM_VERIFY( + !m_elements.empty(), + "PreparedMappedGravitySourceOperator found no stellar elements." + ); + + m_is_prepared = true; + ++m_preparation_count; + } + void PreparedMappedGravitySourceOperator::Mult( + const mfem::Vector &density_true, + mfem::Vector &action + ) const { + MFEM_VERIFY( + m_is_prepared, + "PreparedMappedGravitySourceOperator must be prepared before " + "Mult is called." + ); + + MFEM_VERIFY( + density_true.Size() == Width(), + "PreparedMappedGravitySourceOperator received a density vector " + "with the wrong size." + ); + + mfem::Vector density_local; + + true_to_local(*m_fem.densityFes, density_true, density_local); + + mfem::Vector local_action(m_fem.gravityPotentialFes->GetVSize()); + local_action = 0.0; + + mfem::Vector element_density; + mfem::Vector quadrature_density; + mfem::Vector element_action; + + for (const ElementPAData &data : m_elements) { + density_local.GetSubVector(data.density_dofs, element_density); + + if (data.density_dof_transformation != nullptr) { + data.density_dof_transformation->InvTransformPrimal( + element_density + ); + } + + quadrature_density.SetSize(data.quadrature_data.Size()); + + // B_density * x_e + data.density_basis.Mult(element_density, quadrature_density); + + // D * B_density * x_e + for (int q = 0; q < quadrature_density.Size(); ++q) { + quadrature_density(q) *= data.quadrature_data(q); + } + + element_action.SetSize(data.potential_dofs.Size()); + + // B_potential^T * D * B_density * x_e + data.potential_basis.MultTranspose( + quadrature_density, element_action + ); + + if (data.potential_dof_transformation != nullptr) { + data.potential_dof_transformation->TransformDual( + element_action + ); + } + + local_action.AddElementVector(data.potential_dofs, element_action); + } + + local_to_true(*m_fem.gravityPotentialFes, local_action, action); + } + + void PreparedMappedGravitySourceOperator::MultTranspose( + const mfem::Vector &potential_true, + mfem::Vector &action + ) const { + MFEM_VERIFY( + m_is_prepared, + "PreparedMappedGravitySourceOperator must be prepared before " + "MultTranspose is called." + ); + + MFEM_VERIFY( + potential_true.Size() == Height(), + "PreparedMappedGravitySourceOperator received a potential vector " + "with the wrong size." + ); + + mfem::Vector potential_local; + + true_to_local( + *m_fem.gravityPotentialFes, potential_true, potential_local + ); + + mfem::Vector local_action(m_fem.densityFes->GetVSize()); + local_action = 0.0; + + mfem::Vector element_potential; + mfem::Vector quadrature_potential; + mfem::Vector element_action; + + for (const ElementPAData &data : m_elements) { + potential_local.GetSubVector( + data.potential_dofs, element_potential + ); + + if (data.potential_dof_transformation != nullptr) { + data.potential_dof_transformation->InvTransformPrimal( + element_potential + ); + } + + quadrature_potential.SetSize(data.quadrature_data.Size()); + + data.potential_basis.Mult(element_potential, quadrature_potential); + + for (int q = 0; q < quadrature_potential.Size(); ++q) { + quadrature_potential(q) *= data.quadrature_data(q); + } + + element_action.SetSize(data.density_dofs.Size()); + + data.density_basis.MultTranspose( + quadrature_potential, element_action + ); + + if (data.density_dof_transformation != nullptr) { + data.density_dof_transformation->TransformDual(element_action); + } + + local_action.AddElementVector(data.density_dofs, element_action); + } + + local_to_true(*m_fem.densityFes, local_action, action); + } + bool PreparedMappedGravitySourceOperator::IsPrepared() const noexcept { + return m_is_prepared; + } + + std::uint64_t + PreparedMappedGravitySourceOperator::GetPreparationCount() const noexcept { + return m_preparation_count; + } +} // namespace mean_field::operators diff --git a/libmeanfield/impl/operators/prepared_hdiv_mass.cpp b/libmeanfield/impl/operators/prepared_hdiv_mass.cpp new file mode 100644 index 0000000..234118a --- /dev/null +++ b/libmeanfield/impl/operators/prepared_hdiv_mass.cpp @@ -0,0 +1,441 @@ +module; +#include +#include +#include +#include + +module mean_field; +import :operators.prepared_hdiv_mass; + +namespace { + int get_operator_size(const mean_field::fem::FEM &f) { + MFEM_VERIFY( + f.gravityFluxFes != nullptr, + "PreparedMappedHDivMassOperator requires the " + "gravity-gradient finite-element space." + ); + return f.gravityFluxFes->GetTrueVSize(); + } + + void true_to_local( + const mfem::ParFiniteElementSpace &finite_element_space, + const mfem::Vector &true_vector, + mfem::Vector &local_vector + ) { + local_vector.SetSize(finite_element_space.GetVSize()); + + const mfem::Operator *prolongation = + finite_element_space.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->Mult(true_vector, local_vector); + } else { + local_vector = true_vector; + } + } + + int find_representative_element( + const mean_field::fem::FEM &f, + const mfem::Array &marker + ) { + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + const int attribute = f.mesh->GetAttribute(element_id); + + if (attribute > 0 && attribute <= marker.Size() && + marker[attribute - 1] != 0) { + return element_id; + } + } + + return -1; + } + + void validate_uniform_domain_discretization( + const mean_field::fem::FEM &f, + const mfem::Array &marker, + const int representative_element_id + ) { + const mfem::FiniteElement &representative_element = + *f.gravityFluxFes->GetFE(representative_element_id); + const mfem::ElementTransformation &representative_transformation = + *f.mesh->GetElementTransformation(representative_element_id); + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + const int attribute = f.mesh->GetAttribute(element_id); + + if (attribute <= 0 || attribute > marker.Size() || + marker[attribute - 1] == 0) { + continue; + } + + const mfem::FiniteElement &element = + *f.gravityFluxFes->GetFE(element_id); + const mfem::ElementTransformation &transformation = + *f.mesh->GetElementTransformation(element_id); + + MFEM_VERIFY( + element.GetGeomType() == representative_element.GetGeomType(), + "Prepared H(div) mass domains currently require a uniform " + "element " + "geometry." + ); + MFEM_VERIFY( + element.GetOrder() == representative_element.GetOrder(), + "Prepared H(div) mass domains currently require a uniform " + "finite-element order." + ); + MFEM_VERIFY( + transformation.OrderW() == + representative_transformation.OrderW(), + "Prepared H(div) mass domains currently require a uniform " + "geometry-weight order." + ); + } + } + + class FrozenMappedHDivMassCoefficient final + : public mfem::MatrixCoefficient { + public: + FrozenMappedHDivMassCoefficient( + const mean_field::fem::FEM &f, + const mean_field::mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &displacement_true, + bool elevates_vacuum + ) + : MatrixCoefficient(domain_mapper.GetDimension()), + m_fem(f), + m_domain_mapper(domain_mapper), + m_workspace(domain_mapper.GetDimension()), + m_elevates_vacuum(elevates_vacuum) { + true_to_local( + *m_fem.displacementFes, displacement_true, m_displacement_local + ); + } + + void Eval( + mfem::DenseMatrix &mass_tensor, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point + ) override { + transformation.SetIntPoint(&integration_point); + + const int element_id = transformation.ElementNo; + MFEM_VERIFY( + element_id >= 0 && element_id < m_fem.mesh->GetNE(), + "Mapped H(div) mass coefficient received an invalid element ID." + ); + + const bool element_is_vacuum = + transformation.Attribute == + m_domain_mapper.GetVacuumElementAttribute(); + + if (element_is_vacuum != m_elevates_vacuum) { + mass_tensor.SetSize(m_domain_mapper.GetDimension()); + mass_tensor = 0.0; + return; + } + + LoadElement(element_id); + + const mean_field::mapping::ElementMappingData mapping_data{ + .displacement = *m_displacement_data, + .compactification = *m_compactification_data + }; + + mean_field::mapping::VolumeMappingContext mapping_context; + + const mean_field::mapping::MappingStatus status = + m_domain_mapper.EvaluateVolume( + mapping_data, transformation, integration_point, + m_workspace, mapping_context + ); + + MFEM_VERIFY( + status == mean_field::mapping::MappingStatus::valid, + "Stateless domain mapping failed while preparing the H(div) " + "mass " + "operator. Mapping status = " + << static_cast(status) + << ", element ID = " << element_id + << ", element attribute = " << transformation.Attribute + << ", coefficient domain = " + << (m_elevates_vacuum ? "vacuum" : "stellar") + ); + + const mfem::DenseMatrix &mapping_jacobian = + mapping_context.mapping.mapping_jacobian; + const double mapping_determinant = + mapping_context.mapping.mapping_determinant; + + MFEM_VERIFY( + std::isfinite(mapping_determinant) && mapping_determinant > 0.0, + "Prepared H(div) mass operator encountered a non-positive or " + "non-finite mapping determinant." + ); + + mfem::MultAtB(mapping_jacobian, mapping_jacobian, mass_tensor); + mass_tensor *= 1.0 / mapping_determinant; + } + + private: + void LoadElement(const int element_id) { + if (element_id == m_cached_element_id) { + return; + } + + const mfem::FiniteElement &displacement_element = + *m_fem.displacementFes->GetFE(element_id); + const mfem::FiniteElement &compactification_element = + *m_fem.compactificationFes->GetFE(element_id); + + mfem::DofTransformation *displacement_dof_transformation = + m_fem.displacementFes->GetElementVDofs( + element_id, m_displacement_dofs + ); + mfem::DofTransformation *compactification_dof_transformation = + m_fem.compactificationFes->GetElementDofs( + element_id, m_compactification_dofs + ); + + m_displacement_local.GetSubVector( + m_displacement_dofs, m_element_displacement + ); + m_fem.compactificationCoordinate->GetSubVector( + m_compactification_dofs, m_element_compactification + ); + + if (displacement_dof_transformation != nullptr) { + displacement_dof_transformation->InvTransformPrimal( + m_element_displacement + ); + } + + if (compactification_dof_transformation != nullptr) { + compactification_dof_transformation->InvTransformPrimal( + m_element_compactification + ); + } + + m_displacement_data = std::make_unique< + mean_field::mapping::ElementDisplacementData>( + mean_field::mapping::ElementDisplacementDataFromElementVDofs( + displacement_element, m_element_displacement + ) + ); + + m_compactification_data = std::make_unique< + mean_field::mapping::ElementCompactificationData>( + compactification_element, m_element_compactification + ); + + m_cached_element_id = element_id; + } + + const mean_field::fem::FEM &m_fem; + const mean_field::mapping::DomainMapperStateless &m_domain_mapper; + + mfem::Vector m_displacement_local; + + mfem::Array m_displacement_dofs; + mfem::Array m_compactification_dofs; + + mfem::Vector m_element_displacement; + mfem::Vector m_element_compactification; + + std::unique_ptr + m_displacement_data; + std::unique_ptr + m_compactification_data; + + mean_field::mapping::DomainMapperStateless::Workspace m_workspace; + int m_cached_element_id{-1}; + bool m_elevates_vacuum; + }; +} // namespace + +namespace mean_field::operators { + PreparedMappedHDivMassOperator::PreparedMappedHDivMassOperator( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper + ) + : Operator(get_operator_size(f)), + m_fem(f), + m_domain_mapper(domain_mapper) { + MFEM_VERIFY( + f.mesh != nullptr, "PreparedMappedHDivMassOperator requires a mesh." + ); + MFEM_VERIFY( + f.gravityFluxFes != nullptr, + "PreparedMappedHDivMassOperator requires the " + "gravity-gradient finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, + "PreparedMappedHDivMassOperator requires the " + "displacement finite-element space." + ); + MFEM_VERIFY( + f.compactificationFes != nullptr, + "PreparedMappedHDivMassOperator requires the compactification " + "finite-element space." + ); + MFEM_VERIFY( + f.compactificationCoordinate != nullptr, + "PreparedMappedHDivMassOperator requires the compactification " + "coordinate." + ); + MFEM_VERIFY( + f.quadratureFactory != nullptr, + "PreparedMappedHDivMassOperator requires the quadrature-rule " + "factory." + ); + MFEM_VERIFY( + domain_mapper.GetDimension() == f.mesh->Dimension(), + "The stateless domain-mapper dimension does not match the mesh " + "dimension." + ); + + utils::populate_element_mask( + f.mesh.get(), utils::DOMAINS::STELLAR, m_stellar_marker + ); + utils::populate_element_mask( + f.mesh.get(), utils::DOMAINS::VACUUM, m_vacuum_marker + ); + + const int stellar_element_id = + find_representative_element(f, m_stellar_marker); + const int vacuum_element_id = + find_representative_element(f, m_vacuum_marker); + + MFEM_VERIFY( + stellar_element_id >= 0, "PreparedMappedHDivMassOperator requires " + "at least one stellar element." + ); + MFEM_VERIFY( + vacuum_element_id >= 0, + "PreparedMappedHDivMassOperator requires at " + "least one compactified vacuum element." + ); + + validate_uniform_domain_discretization( + f, m_stellar_marker, stellar_element_id + ); + validate_uniform_domain_discretization( + f, m_vacuum_marker, vacuum_element_id + ); + } + + void PreparedMappedHDivMassOperator::Prepare( + const mfem::Vector &displacement_true + ) { + MFEM_VERIFY( + displacement_true.Size() == m_fem.displacementFes->GetTrueVSize(), + "PreparedMappedHDivMassOperator received a displacement vector " + "with " + "the wrong size." + ); + + for (int i = 0; i < displacement_true.Size(); ++i) { + MFEM_VERIFY( + std::isfinite(displacement_true(i)), + "PreparedMappedHDivMassOperator received a non-finite " + "displacement " + "value." + ); + } + + const int stellar_element_id = + find_representative_element(m_fem, m_stellar_marker); + const int vacuum_element_id = + find_representative_element(m_fem, m_vacuum_marker); + + const mfem::FiniteElement &stellar_element = + *m_fem.gravityFluxFes->GetFE(stellar_element_id); + const mfem::FiniteElement &vacuum_element = + *m_fem.gravityFluxFes->GetFE(vacuum_element_id); + + mfem::ElementTransformation &stellar_transformation = + *m_fem.mesh->GetElementTransformation(stellar_element_id); + mfem::ElementTransformation &vacuum_transformation = + *m_fem.mesh->GetElementTransformation(vacuum_element_id); + + m_mass_form.reset(); + m_stellar_mass_coefficient.reset(); + m_vacuum_mass_coefficient.reset(); + + m_stellar_mass_coefficient = + std::make_unique( + m_fem, m_domain_mapper, displacement_true, false + ); + m_vacuum_mass_coefficient = + std::make_unique( + m_fem, m_domain_mapper, displacement_true, true + ); + + m_mass_form = + std::make_unique(m_fem.gravityFluxFes.get()); + m_mass_form->SetAssemblyLevel(mfem::AssemblyLevel::PARTIAL); + + auto stellar_integrator = + std::make_unique( + *m_stellar_mass_coefficient + ); + auto vacuum_integrator = std::make_unique( + *m_vacuum_mass_coefficient + ); + + m_fem.quadratureFactory->configure_gravity_hdiv_mass( + *stellar_integrator, quadrature::QuadratureRole::discretization, + stellar_element, stellar_transformation, utils::DOMAINS::STELLAR, + quadrature::MappingKind::general + ); + + m_fem.quadratureFactory->configure_gravity_hdiv_mass( + *vacuum_integrator, quadrature::QuadratureRole::discretization, + vacuum_element, vacuum_transformation, utils::DOMAINS::VACUUM, + quadrature::MappingKind::kelvin + ); + + m_mass_form->AddDomainIntegrator( + stellar_integrator.release(), m_stellar_marker + ); + m_mass_form->AddDomainIntegrator( + vacuum_integrator.release(), m_vacuum_marker + ); + m_mass_form->Assemble(); + + m_is_prepared = true; + ++m_preparation_count; + } + + void PreparedMappedHDivMassOperator::Mult( + const mfem::Vector &gravity_gradient_true, + mfem::Vector &action + ) const { + MFEM_VERIFY( + m_is_prepared, "PreparedMappedHDivMassOperator must be prepared " + "before Mult is called." + ); + MFEM_VERIFY( + m_mass_form != nullptr, "PreparedMappedHDivMassOperator has no " + "assembled partial-assembly form." + ); + MFEM_VERIFY( + gravity_gradient_true.Size() == Width(), + "PreparedMappedHDivMassOperator received a gravity-gradient vector " + "with the wrong size." + ); + + action.SetSize(Height()); + m_mass_form->Mult(gravity_gradient_true, action); + } + + bool PreparedMappedHDivMassOperator::IsPrepared() const noexcept { + return m_is_prepared; + } + + std::uint64_t + PreparedMappedHDivMassOperator::GetPreparationCount() const noexcept { + return m_preparation_count; + } +} // namespace mean_field::operators \ No newline at end of file diff --git a/libmeanfield/impl/operators/prepared_hydrostatic_equilibrium.cpp b/libmeanfield/impl/operators/prepared_hydrostatic_equilibrium.cpp new file mode 100644 index 0000000..9454c78 --- /dev/null +++ b/libmeanfield/impl/operators/prepared_hydrostatic_equilibrium.cpp @@ -0,0 +1,1432 @@ +module; + +#include +#include +#include +#include + +#include + +module mean_field; + +import :operators.prepared_hydrostatic_equilibrium; + +namespace { + void true_to_local( + const mfem::ParFiniteElementSpace &finiteElementSpace, + const mfem::Vector &trueVector, + mfem::Vector &localVector + ) { + MFEM_VERIFY( + trueVector.Size() == finiteElementSpace.GetTrueVSize(), + "Hydrostatic true vector has the wrong size." + ); + + localVector.SetSize(finiteElementSpace.GetVSize()); + + const mfem::Operator *prolongation = + finiteElementSpace.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->Mult(trueVector, localVector); + } else { + localVector = trueVector; + } + } + + void local_to_true( + const mfem::ParFiniteElementSpace &finiteElementSpace, + const mfem::Vector &localVector, + mfem::Vector &trueVector + ) { + MFEM_VERIFY( + localVector.Size() == finiteElementSpace.GetVSize(), + "Hydrostatic local vector has the wrong size." + ); + + trueVector.SetSize(finiteElementSpace.GetTrueVSize()); + trueVector = 0.0; + + const mfem::Operator *prolongation = + finiteElementSpace.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->MultTranspose(localVector, trueVector); + } else { + trueVector = localVector; + } + } + + void copy_vector_block( + const mfem::Vector &source, + const int offset, + const int size, + mfem::Vector &block + ) { + MFEM_VERIFY( + offset >= 0 && size >= 0 && offset + size <= source.Size(), + "Hydrostatic Jacobian block lies outside the " + "input vector." + ); + + block.SetSize(size); + + for (int entry = 0; entry < size; ++entry) { + block(entry) = source(offset + entry); + } + } + + const mfem::IntegrationRule &get_hydrostatic_rule( + const mean_field::fem::FEM &f, + const mfem::FiniteElement &enthalpyElement, + const mfem::FiniteElement &gravityPotentialElement, + const mfem::ElementTransformation &transformation + ) { + using EnthalpyField = + mean_field::field::Field; + + MFEM_VERIFY( + enthalpyElement.GetOrder() == + mean_field::field::Enthalpy::Scalar::familyOrder, + "The prepared hydrostatic enthalpy element does " + "not match the registered field." + ); + + MFEM_VERIFY( + gravityPotentialElement.GetOrder() == + mean_field::field::Gravity::Potential::familyOrder, + "The prepared hydrostatic potential element does " + "not match the registered field." + ); + + const auto enthalpyQuery = EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::EquilibriumEnthalpy>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), {}, mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + const auto gravityQuery = EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::EquilibriumGravity>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), {}, mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + // A rigid-rotation potential is quadratic in physical position. + const auto rotationQuery = EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::EquilibriumRotation>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), std::array{2}, + mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + const auto constantQuery = EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::EquilibriumConstant>( + mean_field::quadrature::QuadratureRole::discretization, + transformation.OrderW(), {}, mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + const std::array candidateRules{ + f.quadratureFactory->get( + enthalpyQuery, transformation.GetGeometryType() + ), + f.quadratureFactory->get( + gravityQuery, transformation.GetGeometryType() + ), + f.quadratureFactory->get( + rotationQuery, transformation.GetGeometryType() + ), + f.quadratureFactory->get( + constantQuery, transformation.GetGeometryType() + ) + }; + + const auto selectedRule = std::max_element( + candidateRules.begin(), candidateRules.end(), + [](const auto &left, const auto &right) { + return left.resolution.order < right.resolution.order; + } + ); + + MFEM_VERIFY( + selectedRule != candidateRules.end() && + selectedRule->integration_rule != nullptr, + "The quadrature policy did not return a valid " + "hydrostatic-equilibrium integration rule." + ); + + return *selectedRule->integration_rule; + } +} // namespace + +namespace mean_field::operators { + HydrostaticJacobianBlockLayout::HydrostaticJacobianBlockLayout( + const fem::FEM &f + ) { + MFEM_VERIFY( + f.enthalpyFes != nullptr, + "HydrostaticJacobianBlockLayout requires the " + "enthalpy finite-element space." + ); + + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "HydrostaticJacobianBlockLayout requires the " + "gravity-potential finite-element space." + ); + + MFEM_VERIFY( + f.displacementFes != nullptr, + "HydrostaticJacobianBlockLayout requires the " + "displacement finite-element space." + ); + + m_enthalpySize = f.enthalpyFes->GetTrueVSize(); + m_gravityPotentialSize = f.gravityPotentialFes->GetTrueVSize(); + m_displacementSize = f.displacementFes->GetTrueVSize(); + m_residualSize = m_enthalpySize; + + m_totalSize = + m_enthalpySize + m_gravityPotentialSize + 1 + m_displacementSize; + + MFEM_VERIFY( + m_enthalpySize > 0 && m_gravityPotentialSize > 0 && + m_displacementSize > 0, + "HydrostaticJacobianBlockLayout received an empty " + "finite-element space." + ); + } + + int HydrostaticJacobianBlockLayout::Offset( + const HydrostaticJacobianInputBlock block + ) const { + switch (block) { + case HydrostaticJacobianInputBlock::enthalpy: + return 0; + + case HydrostaticJacobianInputBlock::gravityPotential: + return m_enthalpySize; + + case HydrostaticJacobianInputBlock::bernoulliConstant: + return m_enthalpySize + m_gravityPotentialSize; + + case HydrostaticJacobianInputBlock::displacement: + return m_enthalpySize + m_gravityPotentialSize + 1; + } + + MFEM_ABORT( + "HydrostaticJacobianBlockLayout received an " + "unknown input block." + ); + + return 0; + } + + int HydrostaticJacobianBlockLayout::Size( + const HydrostaticJacobianInputBlock block + ) const { + switch (block) { + case HydrostaticJacobianInputBlock::enthalpy: + return m_enthalpySize; + + case HydrostaticJacobianInputBlock::gravityPotential: + return m_gravityPotentialSize; + + case HydrostaticJacobianInputBlock::bernoulliConstant: + return 1; + + case HydrostaticJacobianInputBlock::displacement: + return m_displacementSize; + } + + MFEM_ABORT( + "HydrostaticJacobianBlockLayout received an " + "unknown input block." + ); + + return 0; + } + + int HydrostaticJacobianBlockLayout::GetTotalSize() const noexcept { + return m_totalSize; + } + + int HydrostaticJacobianBlockLayout::GetResidualSize() const noexcept { + return m_residualSize; + } + + PreparedHydrostaticEquilibriumOperator:: + PreparedHydrostaticEquilibriumOperator( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper + ) + : m_fem(f), + m_domainMapper(domainMapper), + m_context( + f, + domainMapper + ) { + MFEM_VERIFY( + m_fem.mesh != nullptr, + "PreparedHydrostaticEquilibriumOperator requires a mesh." + ); + + MFEM_VERIFY( + m_fem.enthalpyFes != nullptr, + "PreparedHydrostaticEquilibriumOperator requires " + "the enthalpy finite-element space." + ); + + MFEM_VERIFY( + m_fem.gravityPotentialFes != nullptr, + "PreparedHydrostaticEquilibriumOperator requires " + "the gravity-potential finite-element space." + ); + + MFEM_VERIFY( + m_fem.displacementFes != nullptr, + "PreparedHydrostaticEquilibriumOperator requires " + "the displacement finite-element space." + ); + + MFEM_VERIFY( + m_fem.compactificationFes != nullptr, + "PreparedHydrostaticEquilibriumOperator requires " + "the compactification finite-element space." + ); + + MFEM_VERIFY( + m_fem.compactificationCoordinate != nullptr, + "PreparedHydrostaticEquilibriumOperator requires " + "the compactification coordinate." + ); + + MFEM_VERIFY( + m_fem.quadratureFactory != nullptr, + "PreparedHydrostaticEquilibriumOperator requires " + "the quadrature-rule factory." + ); + + MFEM_VERIFY( + m_domainMapper.GetDimension() == m_fem.mesh->Dimension(), + "The hydrostatic operator's stateless mapper " + "dimension does not match the mesh dimension." + ); + } + + PreparedHydrostaticEquilibriumReport + PreparedHydrostaticEquilibriumOperator::Prepare( + const context::hydrostatic::HydrostaticEquilibriumStateView &state, + const context::hydrostatic::HydrostaticEquilibriumDependencies + &dependencies, + const physics::RigidRotation &rotation + ) { + const bool rotationObjectChanged = + !m_context.IsPrepared() || + dependencies.rotation != m_context.GetDependencies().rotation; + + PreparedHydrostaticEquilibriumReport report; + + report.contextReport = m_context.Prepare(state, dependencies); + + if (rotationObjectChanged) { + m_rotation = rotation; + report.updatedRotation = true; + } + + MFEM_VERIFY( + m_rotation.has_value(), + "The prepared hydrostatic operator has no frozen " + "rotation state." + ); + + m_isPrepared = false; + + if (report.contextReport.preparedStaticDependencies) { + PrepareStaticPlan(); + } + + if (report.contextReport.preparedGeometryState) { + PrepareGeometry(); + PrepareAlgebraicJacobianBlocks(); + report.preparedAlgebraicJacobianBlocks = true; + } + + if (report.contextReport.preparedRotationDependencies) { + PrepareRotation(); + } + + if (report.contextReport.preparedBaseState) { + PrepareBaseState(); + FinalizeDisplacementJacobianPreparation(); + AssembleCachedResidual(); + ++m_residualPreparationCount; + report.preparedDisplacementJacobianData = true; + report.preparedResidual = true; + } + + MFEM_VERIFY( + !m_elements.empty(), + "PreparedHydrostaticEquilibriumOperator found no " + "stellar elements." + ); + + MFEM_VERIFY( + m_cachedResidual.Size() == m_fem.enthalpyFes->GetTrueVSize(), + "The prepared hydrostatic residual has the wrong size." + ); + + m_isPrepared = true; + return report; + } + + void PreparedHydrostaticEquilibriumOperator::PrepareStaticPlan() { + m_elements.clear(); + m_elements.reserve(m_fem.mesh->GetNE()); + + const int vacuumAttribute = m_domainMapper.GetVacuumElementAttribute(); + + mfem::Vector enthalpyShape; + mfem::Vector gravityPotentialShape; + + for (int elementId = 0; elementId < m_fem.mesh->GetNE(); ++elementId) { + mfem::ElementTransformation *transformation = + m_fem.mesh->GetElementTransformation(elementId); + + MFEM_VERIFY( + transformation != nullptr, + "Prepared hydrostatic static planning received " + "a null element transformation." + ); + + if (transformation->Attribute == vacuumAttribute) { + continue; + } + + const mfem::FiniteElement &enthalpyElement = + *m_fem.enthalpyFes->GetFE(elementId); + + const mfem::FiniteElement &gravityPotentialElement = + *m_fem.gravityPotentialFes->GetFE(elementId); + + MFEM_VERIFY( + enthalpyElement.GetGeomType() == + gravityPotentialElement.GetGeomType() && + enthalpyElement.GetGeomType() == + transformation->GetGeometryType(), + "Hydrostatic element geometries do not agree." + ); + + m_elements.emplace_back(); + ElementPAData &data = m_elements.back(); + data.elementId = elementId; + + data.enthalpyDofTransformation = + m_fem.enthalpyFes->GetElementDofs(elementId, data.enthalpyDofs); + + data.gravityPotentialDofTransformation = + m_fem.gravityPotentialFes->GetElementDofs( + elementId, data.gravityPotentialDofs + ); + + data.displacementDofTransformation = + m_fem.displacementFes->GetElementVDofs( + elementId, data.displacementDofs + ); + + data.integrationRule = &get_hydrostatic_rule( + m_fem, enthalpyElement, gravityPotentialElement, *transformation + ); + + const int quadraturePointCount = data.integrationRule->GetNPoints(); + + const int enthalpyDofCount = enthalpyElement.GetDof(); + + const int gravityPotentialDofCount = + gravityPotentialElement.GetDof(); + + data.enthalpyBasis.SetSize(quadraturePointCount, enthalpyDofCount); + + data.gravityPotentialBasis.SetSize( + quadraturePointCount, gravityPotentialDofCount + ); + + enthalpyShape.SetSize(enthalpyDofCount); + gravityPotentialShape.SetSize(gravityPotentialDofCount); + + for (int quadraturePoint = 0; + quadraturePoint < quadraturePointCount; ++quadraturePoint) { + const mfem::IntegrationPoint &integrationPoint = + data.integrationRule->IntPoint(quadraturePoint); + + enthalpyElement.CalcShape(integrationPoint, enthalpyShape); + + gravityPotentialElement.CalcShape( + integrationPoint, gravityPotentialShape + ); + + for (int dof = 0; dof < enthalpyDofCount; ++dof) { + data.enthalpyBasis(quadraturePoint, dof) = + enthalpyShape(dof); + } + + for (int dof = 0; dof < gravityPotentialDofCount; ++dof) { + data.gravityPotentialBasis(quadraturePoint, dof) = + gravityPotentialShape(dof); + } + } + } + } + + void PreparedHydrostaticEquilibriumOperator::PrepareGeometry() { + mfem::Vector displacementLocal; + + true_to_local( + *m_fem.displacementFes, m_context.GetDisplacementTrue(), + displacementLocal + ); + + mapping::DomainMapperStateless::Workspace workspace( + m_fem.mesh->Dimension() + ); + + mfem::Array compactificationDofs; + + mfem::Vector elementDisplacement; + mfem::Vector elementCompactification; + + for (ElementPAData &data : m_elements) { + mfem::ElementTransformation *transformation = + m_fem.mesh->GetElementTransformation(data.elementId); + + MFEM_VERIFY( + transformation != nullptr && data.integrationRule != nullptr, + "Prepared hydrostatic geometry has invalid " + "static element data." + ); + + mfem::DofTransformation *compactificationDofTransformation = + m_fem.compactificationFes->GetElementDofs( + data.elementId, compactificationDofs + ); + + displacementLocal.GetSubVector( + data.displacementDofs, elementDisplacement + ); + + m_fem.compactificationCoordinate->GetSubVector( + compactificationDofs, elementCompactification + ); + + if (data.displacementDofTransformation != nullptr) { + data.displacementDofTransformation->InvTransformPrimal( + elementDisplacement + ); + } + + if (compactificationDofTransformation != nullptr) { + compactificationDofTransformation->InvTransformPrimal( + elementCompactification + ); + } + + const mfem::FiniteElement &displacementElement = + *m_fem.displacementFes->GetFE(data.elementId); + + const mfem::FiniteElement &compactificationElement = + *m_fem.compactificationFes->GetFE(data.elementId); + + data.baseDisplacementData.emplace( + mapping::ElementDisplacementDataFromElementVDofs( + displacementElement, elementDisplacement + ) + ); + + data.compactificationData.emplace( + compactificationElement, elementCompactification + ); + + const mapping::ElementMappingData mappingData{ + .displacement = *data.baseDisplacementData, + .compactification = *data.compactificationData + }; + + const int quadraturePointCount = data.integrationRule->GetNPoints(); + + data.physicalPositions.SetSize( + quadraturePointCount, m_fem.mesh->Dimension() + ); + + data.quadratureWeights.SetSize(quadraturePointCount); + + data.baseMappingContexts.resize(quadraturePointCount); + + for (int quadraturePoint = 0; + quadraturePoint < quadraturePointCount; ++quadraturePoint) { + const mfem::IntegrationPoint &integrationPoint = + data.integrationRule->IntPoint(quadraturePoint); + + transformation->SetIntPoint(&integrationPoint); + + mapping::VolumeMappingContext &mappingContext = + data.baseMappingContexts[quadraturePoint]; + + const mapping::MappingStatus mappingStatus = + m_domainMapper.EvaluateVolume( + mappingData, *transformation, integrationPoint, + workspace, mappingContext + ); + + MFEM_VERIFY( + mappingStatus == mapping::MappingStatus::valid, + "Stateless mapping failed while preparing " + "hydrostatic geometry. Element: " + << data.elementId + << ", attribute: " << transformation->Attribute + << ", quadrature point: " << quadraturePoint + << ", status: " << static_cast(mappingStatus) + ); + + const double quadratureWeight = + mappingContext.quadrature.weight; + + MFEM_VERIFY( + std::isfinite(quadratureWeight) && quadratureWeight > 0.0, + "Prepared hydrostatic geometry encountered " + "an invalid quadrature weight." + ); + + data.quadratureWeights(quadraturePoint) = quadratureWeight; + + for (int component = 0; component < m_fem.mesh->Dimension(); + ++component) { + const double position = + mappingContext.mapping.physical_position(component); + + MFEM_VERIFY( + std::isfinite(position), + "Prepared hydrostatic geometry encountered " + "a non-finite physical position." + ); + + data.physicalPositions(quadraturePoint, component) = + position; + } + } + } + } + + void + PreparedHydrostaticEquilibriumOperator::PrepareAlgebraicJacobianBlocks() { + for (ElementPAData &data : m_elements) { + const int quadraturePointCount = data.quadratureWeights.Size(); + + const int enthalpyDofCount = data.enthalpyBasis.Width(); + + const int gravityPotentialDofCount = + data.gravityPotentialBasis.Width(); + + MFEM_VERIFY( + data.enthalpyBasis.Height() == quadraturePointCount && + data.gravityPotentialBasis.Height() == quadraturePointCount, + "Prepared hydrostatic algebraic Jacobian has " + "inconsistent quadrature data." + ); + + data.enthalpyJacobian.SetSize(enthalpyDofCount, enthalpyDofCount); + + data.gravityPotentialJacobian.SetSize( + enthalpyDofCount, gravityPotentialDofCount + ); + + data.bernoulliConstantJacobian.SetSize(enthalpyDofCount); + + data.enthalpyJacobian = 0.0; + data.gravityPotentialJacobian = 0.0; + data.bernoulliConstantJacobian = 0.0; + + for (int quadraturePoint = 0; + quadraturePoint < quadraturePointCount; ++quadraturePoint) { + const double quadratureWeight = + data.quadratureWeights(quadraturePoint); + + for (int testDof = 0; testDof < enthalpyDofCount; ++testDof) { + const double weightedTestBasis = + quadratureWeight * + data.enthalpyBasis(quadraturePoint, testDof); + + data.bernoulliConstantJacobian(testDof) -= + weightedTestBasis; + + for (int trialDof = 0; trialDof < enthalpyDofCount; + ++trialDof) { + data.enthalpyJacobian(testDof, trialDof) += + weightedTestBasis * + data.enthalpyBasis(quadraturePoint, trialDof); + } + + for (int trialDof = 0; trialDof < gravityPotentialDofCount; + ++trialDof) { + data.gravityPotentialJacobian(testDof, trialDof) += + weightedTestBasis * data.gravityPotentialBasis( + quadraturePoint, trialDof + ); + } + } + } + } + + ++m_algebraicJacobianStatistics.preparations; + } + + void PreparedHydrostaticEquilibriumOperator::PrepareRotation() { + MFEM_VERIFY( + m_rotation.has_value(), + "Prepared hydrostatic rotation has no frozen state." + ); + + mfem::Vector physicalPosition(m_fem.mesh->Dimension()); + + mfem::Vector coordinateDirection(m_fem.mesh->Dimension()); + + for (ElementPAData &data : m_elements) { + const int quadraturePointCount = data.physicalPositions.Height(); + + MFEM_VERIFY( + data.physicalPositions.Width() == m_fem.mesh->Dimension(), + "Prepared hydrostatic rotation has invalid " + "geometry data." + ); + + data.rotationPotential.SetSize(quadraturePointCount); + + data.rotationGradient.SetSize( + quadraturePointCount, m_fem.mesh->Dimension() + ); + + for (int quadraturePoint = 0; + quadraturePoint < quadraturePointCount; ++quadraturePoint) { + for (int component = 0; component < physicalPosition.Size(); + ++component) { + physicalPosition(component) = + data.physicalPositions(quadraturePoint, component); + } + + const double rotationPotential = + m_rotation->potential(physicalPosition); + + MFEM_VERIFY( + std::isfinite(rotationPotential), + "Prepared hydrostatic rotation encountered " + "a non-finite potential." + ); + + data.rotationPotential(quadraturePoint) = rotationPotential; + + for (int component = 0; component < physicalPosition.Size(); + ++component) { + coordinateDirection = 0.0; + coordinateDirection(component) = 1.0; + + const double gradientComponent = + m_rotation->potential_directional_derivative( + physicalPosition, coordinateDirection + ); + + MFEM_VERIFY( + std::isfinite(gradientComponent), + "Prepared hydrostatic rotation encountered " + "a non-finite potential gradient." + ); + + data.rotationGradient(quadraturePoint, component) = + gradientComponent; + } + } + } + } + + void PreparedHydrostaticEquilibriumOperator::PrepareBaseState() { + mfem::Vector enthalpyLocal; + mfem::Vector gravityPotentialLocal; + + true_to_local( + *m_fem.enthalpyFes, m_context.GetBaseEnthalpyTrue(), enthalpyLocal + ); + + true_to_local( + *m_fem.gravityPotentialFes, m_context.GetBaseGravityPotentialTrue(), + gravityPotentialLocal + ); + + mfem::Vector elementEnthalpy; + mfem::Vector elementGravityPotential; + mfem::Vector quadratureEnthalpy; + mfem::Vector quadratureGravityPotential; + + for (ElementPAData &data : m_elements) { + enthalpyLocal.GetSubVector(data.enthalpyDofs, elementEnthalpy); + + gravityPotentialLocal.GetSubVector( + data.gravityPotentialDofs, elementGravityPotential + ); + + if (data.enthalpyDofTransformation != nullptr) { + data.enthalpyDofTransformation->InvTransformPrimal( + elementEnthalpy + ); + } + + if (data.gravityPotentialDofTransformation != nullptr) { + data.gravityPotentialDofTransformation->InvTransformPrimal( + elementGravityPotential + ); + } + + const int quadraturePointCount = data.quadratureWeights.Size(); + + quadratureEnthalpy.SetSize(quadraturePointCount); + + quadratureGravityPotential.SetSize(quadraturePointCount); + + data.enthalpyBasis.Mult(elementEnthalpy, quadratureEnthalpy); + + data.gravityPotentialBasis.Mult( + elementGravityPotential, quadratureGravityPotential + ); + + MFEM_VERIFY( + data.rotationPotential.Size() == quadraturePointCount, + "Prepared hydrostatic base state has stale " + "rotation data." + ); + + data.weightedResidual.SetSize(quadraturePointCount); + + data.hydrostaticImbalance.SetSize(quadraturePointCount); + + for (int quadraturePoint = 0; + quadraturePoint < quadraturePointCount; ++quadraturePoint) { + const double imbalance = + quadratureEnthalpy(quadraturePoint) + + quadratureGravityPotential(quadraturePoint) - + data.rotationPotential(quadraturePoint) - + m_context.GetBernoulliConstant(); + + const double weightedResidual = + data.quadratureWeights(quadraturePoint) * imbalance; + + MFEM_VERIFY( + std::isfinite(weightedResidual), + "Prepared hydrostatic base state encountered " + "a non-finite residual value." + ); + + data.weightedResidual(quadraturePoint) = weightedResidual; + + data.hydrostaticImbalance(quadraturePoint) = imbalance; + } + } + } + + void PreparedHydrostaticEquilibriumOperator:: + FinalizeDisplacementJacobianPreparation() { + const int dimension = m_fem.mesh->Dimension(); + + for (const ElementPAData &data : m_elements) { + const int quadraturePointCount = data.quadratureWeights.Size(); + + MFEM_VERIFY( + data.baseDisplacementData.has_value() && + data.compactificationData.has_value() && + static_cast(data.baseMappingContexts.size()) == + quadraturePointCount && + data.rotationGradient.Height() == quadraturePointCount && + data.rotationGradient.Width() == dimension && + data.hydrostaticImbalance.Size() == quadraturePointCount, + "Prepared hydrostatic displacement Jacobian " + "has inconsistent frozen data." + ); + } + + ++m_displacementJacobianStatistics.preparations; + } + + void PreparedHydrostaticEquilibriumOperator::AssembleCachedResidual() { + mfem::Vector localResidual(m_fem.enthalpyFes->GetVSize()); + + localResidual = 0.0; + mfem::Vector elementResidual; + + for (const ElementPAData &data : m_elements) { + elementResidual.SetSize(data.enthalpyDofs.Size()); + + data.enthalpyBasis.MultTranspose( + data.weightedResidual, elementResidual + ); + + if (data.enthalpyDofTransformation != nullptr) { + data.enthalpyDofTransformation->TransformDual(elementResidual); + } + + localResidual.AddElementVector(data.enthalpyDofs, elementResidual); + } + + local_to_true(*m_fem.enthalpyFes, localResidual, m_cachedResidual); + } + + void PreparedHydrostaticEquilibriumOperator::BuildResidual( + mfem::Vector &residual + ) const { + VerifyPrepared(); + residual = m_cachedResidual; + ++m_residualApplicationCount; + } + + void PreparedHydrostaticEquilibriumOperator::ApplyEnthalpyJacobianAction( + const mfem::Vector &enthalpyVariation, + mfem::Vector &action + ) const { + VerifyPrepared(); + + mfem::Vector enthalpyVariationLocal; + + true_to_local( + *m_fem.enthalpyFes, enthalpyVariation, enthalpyVariationLocal + ); + + mfem::Vector localAction(m_fem.enthalpyFes->GetVSize()); + + localAction = 0.0; + + mfem::Vector elementVariation; + mfem::Vector elementAction; + + for (const ElementPAData &data : m_elements) { + enthalpyVariationLocal.GetSubVector( + data.enthalpyDofs, elementVariation + ); + + if (data.enthalpyDofTransformation != nullptr) { + data.enthalpyDofTransformation->InvTransformPrimal( + elementVariation + ); + } + + elementAction.SetSize(data.enthalpyJacobian.Height()); + + data.enthalpyJacobian.Mult(elementVariation, elementAction); + + if (data.enthalpyDofTransformation != nullptr) { + data.enthalpyDofTransformation->TransformDual(elementAction); + } + + localAction.AddElementVector(data.enthalpyDofs, elementAction); + } + + local_to_true(*m_fem.enthalpyFes, localAction, action); + + ++m_algebraicJacobianStatistics.enthalpyApplications; + } + + void + PreparedHydrostaticEquilibriumOperator::ApplyGravityPotentialJacobianAction( + const mfem::Vector &gravityPotentialVariation, + mfem::Vector &action + ) const { + VerifyPrepared(); + + mfem::Vector gravityPotentialVariationLocal; + + true_to_local( + *m_fem.gravityPotentialFes, gravityPotentialVariation, + gravityPotentialVariationLocal + ); + + mfem::Vector localAction(m_fem.enthalpyFes->GetVSize()); + + localAction = 0.0; + + mfem::Vector elementVariation; + mfem::Vector elementAction; + + for (const ElementPAData &data : m_elements) { + gravityPotentialVariationLocal.GetSubVector( + data.gravityPotentialDofs, elementVariation + ); + + if (data.gravityPotentialDofTransformation != nullptr) { + data.gravityPotentialDofTransformation->InvTransformPrimal( + elementVariation + ); + } + + elementAction.SetSize(data.gravityPotentialJacobian.Height()); + + data.gravityPotentialJacobian.Mult(elementVariation, elementAction); + + if (data.enthalpyDofTransformation != nullptr) { + data.enthalpyDofTransformation->TransformDual(elementAction); + } + + localAction.AddElementVector(data.enthalpyDofs, elementAction); + } + + local_to_true(*m_fem.enthalpyFes, localAction, action); + + ++m_algebraicJacobianStatistics.gravityPotentialApplications; + } + + void PreparedHydrostaticEquilibriumOperator:: + ApplyBernoulliConstantJacobianAction( + const double bernoulliConstantVariation, + mfem::Vector &action + ) const { + VerifyPrepared(); + + MFEM_VERIFY( + std::isfinite(bernoulliConstantVariation), + "Prepared hydrostatic Bernoulli-constant Jacobian " + "received a non-finite variation." + ); + + mfem::Vector localAction(m_fem.enthalpyFes->GetVSize()); + + localAction = 0.0; + mfem::Vector elementAction; + + for (const ElementPAData &data : m_elements) { + elementAction = data.bernoulliConstantJacobian; + elementAction *= bernoulliConstantVariation; + + if (data.enthalpyDofTransformation != nullptr) { + data.enthalpyDofTransformation->TransformDual(elementAction); + } + + localAction.AddElementVector(data.enthalpyDofs, elementAction); + } + + local_to_true(*m_fem.enthalpyFes, localAction, action); + + ++m_algebraicJacobianStatistics.bernoulliConstantApplications; + } + + void PreparedHydrostaticEquilibriumOperator::ApplyAlgebraicJacobianAction( + const mfem::Vector &enthalpyVariation, + const mfem::Vector &gravityPotentialVariation, + const double bernoulliConstantVariation, + mfem::Vector &action + ) const { + VerifyPrepared(); + + MFEM_VERIFY( + std::isfinite(bernoulliConstantVariation), + "Prepared hydrostatic algebraic Jacobian received " + "a non-finite Bernoulli-constant variation." + ); + + mfem::Vector enthalpyVariationLocal; + mfem::Vector gravityPotentialVariationLocal; + + true_to_local( + *m_fem.enthalpyFes, enthalpyVariation, enthalpyVariationLocal + ); + + true_to_local( + *m_fem.gravityPotentialFes, gravityPotentialVariation, + gravityPotentialVariationLocal + ); + + mfem::Vector localAction(m_fem.enthalpyFes->GetVSize()); + + localAction = 0.0; + + mfem::Vector elementEnthalpyVariation; + mfem::Vector elementGravityPotentialVariation; + mfem::Vector elementAction; + mfem::Vector elementWorkspace; + + for (const ElementPAData &data : m_elements) { + enthalpyVariationLocal.GetSubVector( + data.enthalpyDofs, elementEnthalpyVariation + ); + + gravityPotentialVariationLocal.GetSubVector( + data.gravityPotentialDofs, elementGravityPotentialVariation + ); + + if (data.enthalpyDofTransformation != nullptr) { + data.enthalpyDofTransformation->InvTransformPrimal( + elementEnthalpyVariation + ); + } + + if (data.gravityPotentialDofTransformation != nullptr) { + data.gravityPotentialDofTransformation->InvTransformPrimal( + elementGravityPotentialVariation + ); + } + + MFEM_VERIFY( + data.enthalpyJacobian.Height() == + data.gravityPotentialJacobian.Height() && + data.enthalpyJacobian.Width() == + elementEnthalpyVariation.Size() && + data.gravityPotentialJacobian.Width() == + elementGravityPotentialVariation.Size() && + data.bernoulliConstantJacobian.Size() == + data.enthalpyJacobian.Height(), + "Prepared hydrostatic algebraic Jacobian has " + "incompatible element dimensions." + ); + + elementAction.SetSize(data.enthalpyJacobian.Height()); + + elementWorkspace.SetSize(data.gravityPotentialJacobian.Height()); + + data.enthalpyJacobian.Mult(elementEnthalpyVariation, elementAction); + + data.gravityPotentialJacobian.Mult( + elementGravityPotentialVariation, elementWorkspace + ); + + elementAction.Add(1.0, elementWorkspace); + elementAction.Add( + bernoulliConstantVariation, data.bernoulliConstantJacobian + ); + + if (data.enthalpyDofTransformation != nullptr) { + data.enthalpyDofTransformation->TransformDual(elementAction); + } + + localAction.AddElementVector(data.enthalpyDofs, elementAction); + } + + local_to_true(*m_fem.enthalpyFes, localAction, action); + + ++m_algebraicJacobianStatistics.combinedApplications; + } + + void + PreparedHydrostaticEquilibriumOperator::ApplyDisplacementJacobianAction( + const mfem::Vector &displacementVariation, + mfem::Vector &action + ) const { + VerifyPrepared(); + + mfem::Vector displacementVariationLocal; + + true_to_local( + *m_fem.displacementFes, displacementVariation, + displacementVariationLocal + ); + + mfem::Vector localAction(m_fem.enthalpyFes->GetVSize()); + + localAction = 0.0; + + mapping::DomainMapperStateless::Workspace workspace( + m_fem.mesh->Dimension() + ); + + mfem::Vector elementDisplacementVariation; + mfem::Vector weightedQuadratureVariation; + mfem::Vector elementAction; + + for (const ElementPAData &data : m_elements) { + MFEM_VERIFY( + data.baseDisplacementData.has_value() && + data.compactificationData.has_value() && + data.integrationRule != nullptr, + "Prepared hydrostatic displacement Jacobian " + "has invalid frozen element data." + ); + + mfem::ElementTransformation *transformation = + m_fem.mesh->GetElementTransformation(data.elementId); + + MFEM_VERIFY( + transformation != nullptr, + "Prepared hydrostatic displacement Jacobian " + "received a null element transformation." + ); + + displacementVariationLocal.GetSubVector( + data.displacementDofs, elementDisplacementVariation + ); + + if (data.displacementDofTransformation != nullptr) { + data.displacementDofTransformation->InvTransformPrimal( + elementDisplacementVariation + ); + } + + const mfem::FiniteElement &displacementElement = + *m_fem.displacementFes->GetFE(data.elementId); + + const mapping::ElementDisplacementData directionData = + mapping::ElementDisplacementDataFromElementVDofs( + displacementElement, elementDisplacementVariation + ); + + const mapping::ElementMappingData mappingData{ + .displacement = *data.baseDisplacementData, + .compactification = *data.compactificationData + }; + + const int quadraturePointCount = data.integrationRule->GetNPoints(); + + MFEM_VERIFY( + static_cast(data.baseMappingContexts.size()) == + quadraturePointCount && + data.quadratureWeights.Size() == quadraturePointCount && + data.hydrostaticImbalance.Size() == quadraturePointCount && + data.rotationGradient.Height() == quadraturePointCount && + data.rotationGradient.Width() == m_fem.mesh->Dimension(), + "Prepared hydrostatic displacement Jacobian " + "has inconsistent quadrature data." + ); + + weightedQuadratureVariation.SetSize(quadraturePointCount); + + for (int quadraturePoint = 0; + quadraturePoint < quadraturePointCount; ++quadraturePoint) { + const mfem::IntegrationPoint &integrationPoint = + data.integrationRule->IntPoint(quadraturePoint); + + transformation->SetIntPoint(&integrationPoint); + + mapping::VolumeMappingVariation variation; + + const mapping::MappingStatus mappingStatus = + m_domainMapper.EvaluateVolumeVariation( + mappingData, directionData, *transformation, + integrationPoint, + data.baseMappingContexts[quadraturePoint], workspace, + variation + ); + + MFEM_VERIFY( + mappingStatus == mapping::MappingStatus::valid, + "Stateless mapping variation failed while " + "applying the prepared hydrostatic " + "displacement Jacobian. Element: " + << data.elementId + << ", attribute: " << transformation->Attribute + << ", quadrature point: " << quadraturePoint + << ", status: " << static_cast(mappingStatus) + ); + + double rotationPotentialVariation = 0.0; + + for (int component = 0; component < m_fem.mesh->Dimension(); + ++component) { + rotationPotentialVariation += + data.rotationGradient(quadraturePoint, component) * + variation.mapping.physical_position_variation( + component + ); + } + + const double weightedVariation = + data.hydrostaticImbalance(quadraturePoint) * + variation.weight_variation - + data.quadratureWeights(quadraturePoint) * + rotationPotentialVariation; + + MFEM_VERIFY( + std::isfinite(weightedVariation), + "Prepared hydrostatic displacement Jacobian " + "encountered a non-finite quadrature action." + ); + + weightedQuadratureVariation(quadraturePoint) = + weightedVariation; + } + + elementAction.SetSize(data.enthalpyDofs.Size()); + + data.enthalpyBasis.MultTranspose( + weightedQuadratureVariation, elementAction + ); + + if (data.enthalpyDofTransformation != nullptr) { + data.enthalpyDofTransformation->TransformDual(elementAction); + } + + localAction.AddElementVector(data.enthalpyDofs, elementAction); + } + + local_to_true(*m_fem.enthalpyFes, localAction, action); + + ++m_displacementJacobianStatistics.applications; + } + + void PreparedHydrostaticEquilibriumOperator::ApplyCompleteJacobianAction( + const mfem::Vector &enthalpyVariation, + const mfem::Vector &gravityPotentialVariation, + const double bernoulliConstantVariation, + const mfem::Vector &displacementVariation, + mfem::Vector &action + ) const { + VerifyPrepared(); + + mfem::Vector displacementAction; + + ApplyAlgebraicJacobianAction( + enthalpyVariation, gravityPotentialVariation, + bernoulliConstantVariation, action + ); + + ApplyDisplacementJacobianAction( + displacementVariation, displacementAction + ); + + MFEM_VERIFY( + action.Size() == displacementAction.Size(), + "Prepared hydrostatic complete Jacobian produced " + "incompatible algebraic and displacement actions." + ); + + action += displacementAction; + ++m_completeJacobianStatistics.applications; + } + + bool PreparedHydrostaticEquilibriumOperator::IsPrepared() const noexcept { + return m_isPrepared; + } + + const context::hydrostatic::HydrostaticPreparationStatistics & + PreparedHydrostaticEquilibriumOperator:: + GetContextPreparationStatistics() const noexcept { + return m_context.GetPreparationStatistics(); + } + + std::uint64_t PreparedHydrostaticEquilibriumOperator:: + GetResidualPreparationCount() const noexcept { + return m_residualPreparationCount; + } + + std::uint64_t PreparedHydrostaticEquilibriumOperator:: + GetResidualApplicationCount() const noexcept { + return m_residualApplicationCount; + } + + const PreparedHydrostaticAlgebraicJacobianStatistics & + PreparedHydrostaticEquilibriumOperator:: + GetAlgebraicJacobianStatistics() const noexcept { + return m_algebraicJacobianStatistics; + } + + const PreparedHydrostaticDisplacementJacobianStatistics & + PreparedHydrostaticEquilibriumOperator:: + GetDisplacementJacobianStatistics() const noexcept { + return m_displacementJacobianStatistics; + } + + const PreparedHydrostaticCompleteJacobianStatistics & + PreparedHydrostaticEquilibriumOperator:: + GetCompleteJacobianStatistics() const noexcept { + return m_completeJacobianStatistics; + } + + std::size_t PreparedHydrostaticEquilibriumOperator:: + GetStellarElementCount() const noexcept { + return m_elements.size(); + } + + const fem::FEM & + PreparedHydrostaticEquilibriumOperator::GetFEM() const noexcept { + return m_fem; + } + + void PreparedHydrostaticEquilibriumOperator::VerifyPrepared() const { + MFEM_VERIFY( + m_isPrepared, "PreparedHydrostaticEquilibriumOperator must be " + "prepared before residual or Jacobian application." + ); + } + + PreparedHydrostaticEquilibriumJacobianOperator:: + PreparedHydrostaticEquilibriumJacobianOperator( + const fem::FEM &f, + const PreparedHydrostaticEquilibriumOperator &preparedOperator + ) + : mfem::Operator( + f.enthalpyFes != nullptr ? f.enthalpyFes->GetTrueVSize() : 0, + HydrostaticJacobianBlockLayout(f).GetTotalSize() + ), + m_layout(f), + m_preparedOperator(preparedOperator) { + MFEM_VERIFY( + &m_preparedOperator.GetFEM() == &f, + "Prepared hydrostatic MFEM adapter and prepared " + "operator must use the same FEM object." + ); + + MFEM_VERIFY( + Height() == m_layout.GetResidualSize() && + Width() == m_layout.GetTotalSize(), + "Prepared hydrostatic MFEM adapter has " + "inconsistent operator dimensions." + ); + } + + void PreparedHydrostaticEquilibriumJacobianOperator::Mult( + const mfem::Vector &direction, + mfem::Vector &action + ) const { + MFEM_VERIFY( + direction.Size() == Width(), + "Prepared hydrostatic MFEM adapter received a " + "direction with the wrong size." + ); + + mfem::Vector enthalpyVariation; + mfem::Vector gravityPotentialVariation; + mfem::Vector displacementVariation; + + copy_vector_block( + direction, m_layout.Offset(HydrostaticJacobianInputBlock::enthalpy), + m_layout.Size(HydrostaticJacobianInputBlock::enthalpy), + enthalpyVariation + ); + + copy_vector_block( + direction, + m_layout.Offset(HydrostaticJacobianInputBlock::gravityPotential), + m_layout.Size(HydrostaticJacobianInputBlock::gravityPotential), + gravityPotentialVariation + ); + + copy_vector_block( + direction, + m_layout.Offset(HydrostaticJacobianInputBlock::displacement), + m_layout.Size(HydrostaticJacobianInputBlock::displacement), + displacementVariation + ); + + const double bernoulliConstantVariation = direction( + m_layout.Offset(HydrostaticJacobianInputBlock::bernoulliConstant) + ); + + m_preparedOperator.ApplyCompleteJacobianAction( + enthalpyVariation, gravityPotentialVariation, + bernoulliConstantVariation, displacementVariation, action + ); + + MFEM_VERIFY( + action.Size() == Height(), + "Prepared hydrostatic MFEM adapter produced an " + "action with the wrong size." + ); + } + + const HydrostaticJacobianBlockLayout & + PreparedHydrostaticEquilibriumJacobianOperator::GetLayout() const noexcept { + return m_layout; + } +} // namespace mean_field::operators diff --git a/libmeanfield/impl/physics/gravity.cpp b/libmeanfield/impl/physics/gravity.cpp index 85e4c30..e60e8a8 100644 --- a/libmeanfield/impl/physics/gravity.cpp +++ b/libmeanfield/impl/physics/gravity.cpp @@ -1,21 +1,55 @@ module; #include "mfem.hpp" -#include +#include #include +#include +#include #include #include -#include module mean_field; import :mapping.coefficients; import :analysis.integral; namespace { - double centrifugal_potential(const mfem::Vector &phys_x, const double omega) { + double centrifugal_potential( + const mfem::Vector &phys_x, + const double omega + ) { const double s2 = std::pow(phys_x(0), 2) + std::pow(phys_x(1), 2); return -0.5 * s2 * std::pow(omega, 2); } -} + + void grid_function_to_true_dofs( + const mfem::ParFiniteElementSpace &finite_element_space, + const mfem::GridFunction &grid_function, + mfem::Vector &true_dofs + ) { + MFEM_VERIFY( + grid_function.Size() == finite_element_space.GetVSize(), + "The grid function does not match the requested finite-element " + "space." + ); + + true_dofs.SetSize(finite_element_space.GetTrueVSize()); + + const mfem::Operator *restriction = + finite_element_space.GetRestrictionMatrix(); + + if (restriction != nullptr) { + restriction->Mult(grid_function, true_dofs); + } else { + MFEM_VERIFY( + grid_function.Size() == true_dofs.Size(), + "A finite-element space without a restriction operator must " + "have " + "matching local and true sizes." + ); + + true_dofs = grid_function; + } + } +} // namespace namespace mean_field::physics { GravitySolution grav_potential( @@ -24,68 +58,106 @@ namespace mean_field::physics { const mfem::GridFunction &rho, const bool phi_warm ) { + MFEM_VERIFY( + f.densityFes != nullptr && rho.FESpace() == f.densityFes.get(), + "Gravity solve requires rho to use the registered density space." + ); + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "Gravity solve requires the registered gravity-potential space." + ); + mfem::Array outer_bdr_marker(f.mesh->bdr_attributes.Max()); - outer_bdr_marker = 0; + outer_bdr_marker = 0; outer_bdr_marker[1] = 1; - mfem::ParLinearForm g_rhs(f.RT_fes.get()); + mfem::ParLinearForm g_rhs(f.gravityFluxFes.get()); // ReSharper disable once CppTooWideScope std::unique_ptr boundary_potential_coeff; - if (!f.has_mapping()) { // We only need to explicitly add a boundary integrator if a mapping is not being used. In the case where the outer domain has been compactified the φ=0 boundary condition is the natural condition and MFEM automatically handles this - auto boundary_potential = [&f](const mfem::Vector& x_physical) { + if (!f.has_mapping()) { // We only need to explicitly add a boundary + // integrator if a mapping is not being used. In + // the case where the outer domain has been + // compactified the φ=0 boundary condition is + // the natural condition and MFEM automatically + // handles this + auto boundary_potential = [&f](const mfem::Vector &x_physical) { return l2_multipole_potential(f, utils::MASS, x_physical); }; - boundary_potential_coeff = std::make_unique(boundary_potential); - auto boundary_integrator = std::make_unique(*boundary_potential_coeff); - const mfem::FiniteElement& boundary_element = *f.RT_fes->GetTypicalTraceElement(); + boundary_potential_coeff = + std::make_unique(boundary_potential); + auto boundary_integrator = + std::make_unique( + *boundary_potential_coeff + ); + const mfem::FiniteElement &boundary_element = + *f.gravityFluxFes->GetTypicalTraceElement(); - f.quadrature_factory->configure_gravity_boundary(*boundary_integrator, quadrature::QuadratureRole::discretization, boundary_element, utils::DOMAINS::VACUUM, quadrature::MappingKind::none); - g_rhs.AddBoundaryIntegrator(boundary_integrator.release(), outer_bdr_marker); + f.quadratureFactory->configure_gravity_boundary( + *boundary_integrator, + quadrature::QuadratureRole::discretization, boundary_element, + utils::DOMAINS::VACUUM, quadrature::MappingKind::none + ); + g_rhs.AddBoundaryIntegrator( + boundary_integrator.release(), outer_bdr_marker + ); } g_rhs.Assemble(); mfem::GridFunctionCoefficient rho_coeff(&rho); mfem::ConstantCoefficient G4pi(4.0 * M_PI * utils::G); mfem::ProductCoefficient source_coeff(G4pi, rho_coeff); - mfem::ParLinearForm f_rhs(f.L2_fes.get()); + mfem::ParLinearForm f_rhs(f.gravityPotentialFes.get()); std::unique_ptr mapped_source_coeff; - mfem::Coefficient* active_source_coeff = &source_coeff; - quadrature::MappingKind source_mapping_kind = quadrature::MappingKind::none; + mfem::Coefficient *active_source_coeff = &source_coeff; + quadrature::MappingKind source_mapping_kind = + quadrature::MappingKind::none; if (f.has_mapping()) { - mapped_source_coeff = std::make_unique(*f.mapping, source_coeff); + mapped_source_coeff = + std::make_unique( + *f.mapping, source_coeff + ); active_source_coeff = mapped_source_coeff.get(); source_mapping_kind = quadrature::MappingKind::general; } - auto source_integrator = std::make_unique(*active_source_coeff); - const mfem::FiniteElement& source_test_element = *f.L2_fes->GetTypicalFE(); - const mfem::ElementTransformation& source_transformation = *f.mesh->GetElementTransformation(0); - const int source_coefficient_order = f.L2_fes->GetMaxElementOrder(); + auto source_integrator = + std::make_unique(*active_source_coeff); + const mfem::FiniteElement &source_test_element = + *f.gravityPotentialFes->GetTypicalFE(); + const mfem::ElementTransformation &source_transformation = + *f.mesh->GetElementTransformation(0); + const int source_coefficient_order = f.densityFes->GetMaxElementOrder(); - f.quadrature_factory->configure_gravity_source(*source_integrator, quadrature::QuadratureRole::discretization, source_test_element, source_transformation, source_coefficient_order, utils::DOMAINS::STELLAR, source_mapping_kind); - f_rhs.AddDomainIntegrator(source_integrator.release(), f.gravity_context.stellar_mask); + f.quadratureFactory->configure_gravity_source( + *source_integrator, quadrature::QuadratureRole::discretization, + source_test_element, source_transformation, + source_coefficient_order, utils::DOMAINS::STELLAR, + source_mapping_kind + ); + f_rhs.AddDomainIntegrator( + source_integrator.release(), f.gravityContext.stellar_mask + ); f_rhs.Assemble(); - mfem::BlockVector RHS(f.gravity_block_true_offsets); + mfem::BlockVector RHS(f.gravityBlockTrueOffsets); RHS.GetBlock(0) = *g_rhs.ParallelAssemble(); RHS.GetBlock(1) = *f_rhs.ParallelAssemble(); - mfem::BlockVector X(f.gravity_block_true_offsets); + mfem::BlockVector X(f.gravityBlockTrueOffsets); X = 0.0; - f.gravity_context.minres->SetOperator(*f.gravity_context.block_A); - f.gravity_context.minres->Mult(RHS, X); + f.gravityContext.minres->SetOperator(*f.gravityContext.block_A); + f.gravityContext.minres->Mult(RHS, X); GravitySolution solution(f); solution.gradPhi.SetFromTrueDofs(X.GetBlock(0)); solution.phi.SetFromTrueDofs(X.GetBlock(1)); return solution; - } mfem::GridFunction get_potential( @@ -105,18 +177,21 @@ namespace mean_field::physics { std::unique_ptr centrifugal_coeff; if (fem.has_mapping()) { - centrifugal_coeff = std::make_unique(*fem.mapping, rot); + centrifugal_coeff = std::make_unique< + mapping::PhysicalPositionFunctionCoefficient>( + *fem.mapping, rot + ); } else { - centrifugal_coeff = std::make_unique(rot); + centrifugal_coeff = + std::make_unique(rot); } - mfem::GridFunction centrifugal_gf(fem.H1_fes.get()); + mfem::GridFunction centrifugal_gf(fem.gravityPotentialFes.get()); centrifugal_gf.ProjectCoefficient(*centrifugal_coeff); phi.phi += centrifugal_gf; } return phi.phi; - } mfem::DenseMatrix compute_quadrupole_moment_tensor( @@ -128,11 +203,23 @@ namespace mean_field::physics { mfem::DenseMatrix local_Q(dim, dim); local_Q = 0.0; - for (int i = 0; i < fem.H1_fes->GetNE(); ++i) { - if (fem.mesh->GetAttribute(i) == 3) continue; + for (int i = 0; i < fem.mesh->GetNE(); ++i) { + if (fem.mesh->GetAttribute(i) == 3) + continue; - mfem::ElementTransformation *trans = fem.mesh->GetElementTransformation(i); - const mfem::IntegrationRule &ir = *fem.int_rule; + mfem::ElementTransformation *trans = + fem.mesh->GetElementTransformation(i); + using DensityField = field::Field; + const quadrature::Query query = + DensityField::make_query( + quadrature::QuadratureRole::diagnostic, trans->OrderW(), + std::array{2}, utils::DOMAINS::STELLAR, + fem.has_mapping() ? quadrature::MappingKind::general + : quadrature::MappingKind::none + ); + const mfem::IntegrationRule &ir = + *fem.quadratureFactory->get(query, trans->GetGeometryType()) + .integration_rule; for (int j = 0; j < ir.GetNPoints(); ++j) { const mfem::IntegrationPoint &ip = ir.IntPoint(j); @@ -164,7 +251,8 @@ namespace mean_field::physics { for (int m = 0; m < dim; ++m) { for (int n = 0; n < dim; ++n) { const double delta = (m == n) ? 1.0 : 0.0; - const double contrib = 3.0 * x_prime(m) * x_prime(n) - delta * r_sq; + const double contrib = + 3.0 * x_prime(m) * x_prime(n) - delta * r_sq; local_Q(m, n) += rho_val * contrib * weight; } } @@ -172,7 +260,10 @@ namespace mean_field::physics { } mfem::DenseMatrix global_Q(dim, dim); - MPI_Allreduce(local_Q.GetData(), global_Q.GetData(), dim * dim, MPI_DOUBLE, MPI_SUM, fem.H1_fes->GetComm()); + MPI_Allreduce( + local_Q.GetData(), global_Q.GetData(), dim * dim, MPI_DOUBLE, + MPI_SUM, fem.mesh->GetComm() + ); return global_Q; } @@ -183,7 +274,8 @@ namespace mean_field::physics { const mfem::Vector &phys_x ) { const double r = phys_x.Norml2(); - if (r < 1e-12) return 0.0; + if (r < 1e-12) + return 0.0; const int dim = fem.mesh->Dimension(); @@ -197,7 +289,8 @@ namespace mean_field::physics { } } - const double l2_contrib = -(utils::G / (2.0 * std::pow(r, 3))) * l2_mult_factor; + const double l2_contrib = + -(utils::G / (2.0 * std::pow(r, 3))) * l2_mult_factor; const double l0_contrib = -utils::G * total_mass / r; @@ -211,87 +304,331 @@ namespace mean_field::physics { // ========================================== // 1. Partially Assemble the High-Order Mass Block // ========================================== - f.gravity_context.m_form = std::make_unique(f.RT_fes.get()); - f.gravity_context.m_form->SetAssemblyLevel(mfem::AssemblyLevel::PARTIAL); + f.gravityContext.m_form = + std::make_unique(f.gravityFluxFes.get()); + f.gravityContext.m_form->SetAssemblyLevel(mfem::AssemblyLevel::PARTIAL); std::unique_ptr hdiv_mass_integrator; if (f.has_mapping()) { - f.gravity_context.mapped_hdiv_mass_coeff = std::make_unique(*f.mapping, f.mesh->Dimension()); - hdiv_mass_integrator = std::make_unique(*f.gravity_context.mapped_hdiv_mass_coeff); + f.gravityContext.mapped_hdiv_mass_coeff = + std::make_unique( + *f.mapping, f.mesh->Dimension() + ); + hdiv_mass_integrator = + std::make_unique( + *f.gravityContext.mapped_hdiv_mass_coeff + ); } else { - f.gravity_context.mapped_hdiv_mass_coeff.reset(); - hdiv_mass_integrator = std::make_unique(); + f.gravityContext.mapped_hdiv_mass_coeff.reset(); + hdiv_mass_integrator = + std::make_unique(); } - const mfem::FiniteElement& hdiv_element = *f.RT_fes->GetTypicalFE(); - const mfem::ElementTransformation& hdiv_transformation = *f.mesh->GetElementTransformation(0); - const quadrature::MappingKind mapping_kind = f.has_mapping() ? quadrature::MappingKind::general : quadrature::MappingKind::none; + const mfem::FiniteElement &hdiv_element = + *f.gravityFluxFes->GetTypicalFE(); + const mfem::ElementTransformation &hdiv_transformation = + *f.mesh->GetElementTransformation(0); + const quadrature::MappingKind mapping_kind = + f.has_mapping() ? quadrature::MappingKind::general + : quadrature::MappingKind::none; - f.quadrature_factory->configure_gravity_hdiv_mass(*hdiv_mass_integrator, quadrature::QuadratureRole::discretization, hdiv_element, hdiv_transformation, utils::DOMAINS::ALL, mapping_kind); - f.gravity_context.m_form->AddDomainIntegrator(hdiv_mass_integrator.release()); - f.gravity_context.m_form->Assemble(); + f.quadratureFactory->configure_gravity_hdiv_mass( + *hdiv_mass_integrator, quadrature::QuadratureRole::discretization, + hdiv_element, hdiv_transformation, utils::DOMAINS::ALL, mapping_kind + ); + f.gravityContext.m_form->AddDomainIntegrator( + hdiv_mass_integrator.release() + ); + + f.gravityContext.m_form->Assemble(); // ========================================== // 2. Partially Assemble the High-Order Divergence Block // ========================================== - f.gravity_context.b_form = std::make_unique(f.RT_fes.get(), f.L2_fes.get()); - f.gravity_context.b_form->SetAssemblyLevel(mfem::AssemblyLevel::PARTIAL); + f.gravityContext.b_form = std::make_unique( + f.gravityFluxFes.get(), f.gravityPotentialFes.get() + ); + f.gravityContext.b_form->SetAssemblyLevel(mfem::AssemblyLevel::PARTIAL); - auto divergence_discretization_integrator = std::make_unique(); - const mfem::FiniteElement& divergence_discretization_test_element = *f.L2_fes->GetTypicalFE(); + auto divergence_discretization_integrator = + std::make_unique(); + const mfem::FiniteElement &divergence_discretization_test_element = + *f.gravityPotentialFes->GetTypicalFE(); - f.quadrature_factory->configure_gravity_divergence(*divergence_discretization_integrator, quadrature::QuadratureRole::discretization, hdiv_element, divergence_discretization_test_element, hdiv_transformation, utils::DOMAINS::ALL, quadrature::MappingKind::none); - f.gravity_context.b_form->AddDomainIntegrator(divergence_discretization_integrator.release()); - f.gravity_context.b_form->Assemble(); + f.quadratureFactory->configure_gravity_divergence( + *divergence_discretization_integrator, + quadrature::QuadratureRole::discretization, hdiv_element, + divergence_discretization_test_element, hdiv_transformation, + utils::DOMAINS::ALL, quadrature::MappingKind::none + ); + f.gravityContext.b_form->AddDomainIntegrator( + divergence_discretization_integrator.release() + ); + + f.gravityContext.b_form->Assemble(); + + MFEM_VERIFY( + f.domainMapperStateless != nullptr, + "Gravity source partial assembly requires the stateless domain " + "mapper." + ); + + mfem::Vector displacement_true(f.displacementFes->GetTrueVSize()); + displacement_true = 0.0; + + const mfem::GridFunction *active_displacement = + f.mapping->GetDisplacement(); + + if (active_displacement != nullptr) { + grid_function_to_true_dofs( + *f.displacementFes, *active_displacement, displacement_true + ); + } + + auto source_form = + std::make_unique( + f, *f.domainMapperStateless + ); + + source_form->Prepare(displacement_true); + + f.gravityContext.source_form = std::move(source_form); // ========================================== // 3. Assemble Global Block Operator // ========================================== - f.gravity_context.BT = std::make_unique(f.gravity_context.b_form.get()); + f.gravityContext.BT = std::make_unique( + f.gravityContext.b_form.get() + ); - f.gravity_context.block_A = std::make_unique(f.gravity_block_true_offsets); - f.gravity_context.block_A->SetBlock(0, 0, f.gravity_context.m_form.get()); - f.gravity_context.block_A->SetBlock(0, 1, f.gravity_context.BT.get()); - f.gravity_context.block_A->SetBlock(1, 0, f.gravity_context.b_form.get()); + f.gravityContext.block_A = + std::make_unique(f.gravityBlockTrueOffsets); + f.gravityContext.block_A->SetBlock(0, 0, f.gravityContext.m_form.get()); + f.gravityContext.block_A->SetBlock(0, 1, f.gravityContext.BT.get()); + f.gravityContext.block_A->SetBlock(1, 0, f.gravityContext.b_form.get()); // ========================================== // 4. Construct a mapped Schur preconditioner // ========================================== - mfem::Vector mass_diagonal(f.RT_fes->GetTrueVSize()); - f.gravity_context.m_form->AssembleDiagonal(mass_diagonal); + mfem::Vector mass_diagonal(f.gravityFluxFes->GetTrueVSize()); + f.gravityContext.m_form->AssembleDiagonal(mass_diagonal); mfem::Vector inverse_mass_diagonal(mass_diagonal); for (int i = 0; i < inverse_mass_diagonal.Size(); ++i) { - MFEM_VERIFY(std::isfinite(inverse_mass_diagonal(i)) && inverse_mass_diagonal(i) > 0.0, "Mapped RT mass matrix has a non-positive or non-finite diagonal entry."); + MFEM_VERIFY( + std::isfinite(inverse_mass_diagonal(i)) && + inverse_mass_diagonal(i) > 0.0, + "Mapped RT mass matrix has a non-positive or non-finite " + "diagonal " + "entry." + ); inverse_mass_diagonal(i) = 1.0 / inverse_mass_diagonal(i); } - mfem::ParMixedBilinearForm b_preconditioner(f.RT_fes.get(), f.L2_fes.get()); - auto divergence_preconditioner_integrator = std::make_unique(); + mfem::ParMixedBilinearForm b_preconditioner( + f.gravityFluxFes.get(), f.gravityPotentialFes.get() + ); + auto divergence_preconditioner_integrator = + std::make_unique(); - const mfem::FiniteElement& divergence_trial_element = *f.RT_fes->GetTypicalFE(); - const mfem::FiniteElement& divergence_test_element = *f.L2_fes->GetTypicalFE(); - const mfem::ElementTransformation& divergence_transformation = *f.mesh->GetElementTransformation(0); + const mfem::FiniteElement &divergence_trial_element = + *f.gravityFluxFes->GetTypicalFE(); + const mfem::FiniteElement &divergence_test_element = + *f.gravityPotentialFes->GetTypicalFE(); + const mfem::ElementTransformation &divergence_transformation = + *f.mesh->GetElementTransformation(0); - f.quadrature_factory->configure_gravity_divergence(*divergence_preconditioner_integrator, quadrature::QuadratureRole::preconditioner, divergence_trial_element, divergence_test_element, divergence_transformation, utils::DOMAINS::ALL, quadrature::MappingKind::none); - b_preconditioner.AddDomainIntegrator(divergence_preconditioner_integrator.release()); + f.quadratureFactory->configure_gravity_divergence( + *divergence_preconditioner_integrator, + quadrature::QuadratureRole::preconditioner, + divergence_trial_element, divergence_test_element, + divergence_transformation, utils::DOMAINS::ALL, + quadrature::MappingKind::none + ); + b_preconditioner.AddDomainIntegrator( + divergence_preconditioner_integrator.release() + ); b_preconditioner.Assemble(); b_preconditioner.Finalize(); - std::unique_ptr b_matrix(b_preconditioner.ParallelAssemble()); - std::unique_ptr inverse_mass_b_transpose(b_matrix->Transpose()); + std::unique_ptr b_matrix( + b_preconditioner.ParallelAssemble() + ); + std::unique_ptr inverse_mass_b_transpose( + b_matrix->Transpose() + ); inverse_mass_b_transpose->ScaleRows(inverse_mass_diagonal); - f.gravity_context.Schur.reset(mfem::ParMult(b_matrix.get(), inverse_mass_b_transpose.get())); + f.gravityContext.Schur.reset( + mfem::ParMult(b_matrix.get(), inverse_mass_b_transpose.get()) + ); // ========================================== // 5. Wire Up the preconditioners // ========================================== - f.gravity_context.prec_M = std::make_unique(mass_diagonal, empty_tdofs); - f.gravity_context.prec_Phi->SetOperator(*f.gravity_context.Schur); - f.gravity_context.block_prec->SetDiagonalBlock(0, f.gravity_context.prec_M.get()); - f.gravity_context.block_prec->SetDiagonalBlock(1, f.gravity_context.prec_Phi.get()); + f.gravityContext.prec_M = + std::make_unique( + mass_diagonal, empty_tdofs + ); + f.gravityContext.prec_Phi->SetOperator(*f.gravityContext.Schur); + f.gravityContext.block_prec->SetDiagonalBlock( + 0, f.gravityContext.prec_M.get() + ); + f.gravityContext.block_prec->SetDiagonalBlock( + 1, f.gravityContext.prec_Phi.get() + ); } -} \ No newline at end of file + GravitySolution grav_potential_new( + fem::FEM &f, + const utils::Args &args, + const mfem::GridFunction &rho, + const mfem::GridFunction &displacement + ) { + MFEM_VERIFY( + f.mesh != nullptr, + "Gravity initialization requires a parallel mesh." + ); + MFEM_VERIFY( + f.densityFes != nullptr, + "Gravity initialization requires the density finite-element space." + ); + MFEM_VERIFY( + f.gravityPotentialFes != nullptr, + "Gravity initialization requires the gravity-potential " + "finite-element " + "space." + ); + MFEM_VERIFY( + f.gravityFluxFes != nullptr, + "Gravity initialization requires the " + "gravity-gradient finite-element space." + ); + MFEM_VERIFY( + f.displacementFes != nullptr, "Gravity initialization requires the " + "displacement finite-element space." + ); + MFEM_VERIFY( + f.domainMapperStateless != nullptr, + "Gravity initialization requires the stateless domain mapper." + ); + MFEM_VERIFY( + f.gravityContext.b_form != nullptr, + "Gravity initialization requires the divergence operator." + ); + MFEM_VERIFY( + f.gravityContext.BT != nullptr, + "Gravity initialization requires the transpose divergence operator." + ); + MFEM_VERIFY( + f.gravityContext.block_prec != nullptr, + "Gravity initialization requires the gravity block preconditioner." + ); + MFEM_VERIFY( + rho.FESpace() == f.densityFes.get(), + "Gravity initialization requires density to use the FEM density " + "space." + ); + MFEM_VERIFY( + displacement.FESpace() == f.displacementFes.get(), + "Gravity initialization requires displacement to use the FEM " + "Vec_H1 " + "space." + ); + + using form = utils::blocks::gravity_field_form; + + constexpr auto gravity_gradient_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.gradient_term + ); + + constexpr auto gravity_poisson_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.poisson_term + ); + + const std::array value_sizes{ + f.densityFes->GetTrueVSize(), f.displacementFes->GetTrueVSize(), + f.gravityFluxFes->GetTrueVSize(), + f.gravityPotentialFes->GetTrueVSize() + }; + + const std::array residual_sizes{ + f.gravityFluxFes->GetTrueVSize(), + f.gravityPotentialFes->GetTrueVSize() + }; + + const utils::blocks::form_layout layout( + value_sizes, residual_sizes + ); + + mfem::Vector density_true; + mfem::Vector displacement_true; + + grid_function_to_true_dofs(*f.densityFes, rho, density_true); + grid_function_to_true_dofs( + *f.displacementFes, displacement, displacement_true + ); + + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + operators::context::gravity_field::GravityFieldGeometryContext + reduced_geometry_context(f, *f.domainMapperStateless); + + operators::ReducedGravityFieldOperator reduced_operator( + gravity_operator, reduced_geometry_context, displacement_true + ); + + mfem::Vector right_hand_side; + reduced_operator.BuildRightHandSide(density_true, right_hand_side); + + MFEM_VERIFY( + right_hand_side.Size() == reduced_operator.Height(), + "The reduced gravity right-hand side has the wrong size." + ); + + mfem::BlockVector gravity_state( + reduced_operator.GetGravityTrueOffsets() + ); + gravity_state = 0.0; + + mfem::MINRESSolver minres(f.mesh->GetComm()); + minres.SetOperator(reduced_operator); + minres.SetPreconditioner(*f.gravityContext.block_prec); + minres.SetRelTol(args.p.rtol); + minres.SetAbsTol(args.p.atol); + minres.SetMaxIter(args.p.max_iters); + minres.SetPrintLevel(1); + minres.Mult(right_hand_side, gravity_state); + + MFEM_VERIFY( + minres.GetConverged(), + "The reduced gravity solve failed to converge." + ); + + GravitySolution solution(f); + + solution.gradPhi.SetFromTrueDofs( + gravity_state.GetBlock(gravity_gradient_residual_block) + ); + + solution.phi.SetFromTrueDofs( + gravity_state.GetBlock(gravity_poisson_residual_block) + ); + + return solution; + } +} // namespace mean_field::physics diff --git a/libmeanfield/impl/physics/solid.cpp b/libmeanfield/impl/physics/solid.cpp index e0c0c8d..4a040a7 100644 --- a/libmeanfield/impl/physics/solid.cpp +++ b/libmeanfield/impl/physics/solid.cpp @@ -1,17 +1,32 @@ module; #include "mean_field.h" +#include module mean_field; namespace mean_field::physics { - double compute_moment_of_inertia(const fem::FEM &fem, const mfem::GridFunction &rho_ref) { + double compute_moment_of_inertia( + const fem::FEM &fem, + const mfem::GridFunction &rho_ref + ) { double local_I = 0.0; for (int i = 0; i < fem.mesh->GetNE(); i++) { - if (fem.mesh->GetAttribute(i) == 3) continue; + if (fem.mesh->GetAttribute(i) == 3) + continue; - mfem::ElementTransformation *T = fem.mesh->GetElementTransformation(i); - const mfem::IntegrationRule &ir = *fem.int_rule; + mfem::ElementTransformation *T = + fem.mesh->GetElementTransformation(i); + using DensityField = field::Field; + const quadrature::Query query = + DensityField::make_query( + quadrature::QuadratureRole::diagnostic, T->OrderW(), + std::array{2}, utils::DOMAINS::STELLAR, + quadrature::MappingKind::general + ); + const mfem::IntegrationRule &ir = + *fem.quadratureFactory->get(query, T->GetGeometryType()) + .integration_rule; for (int j = 0; j < ir.GetNPoints(); j++) { const mfem::IntegrationPoint &ip = ir.IntPoint(j); @@ -22,7 +37,8 @@ namespace mean_field::physics { mfem::Vector x_phys; fem.mapping->GetPhysicalPoint(*T, ip, x_phys); - const double r_cyl_sq = x_phys(0) * x_phys(0) + x_phys(1) * x_phys(1); + const double r_cyl_sq = + x_phys(0) * x_phys(0) + x_phys(1) * x_phys(1); const double detJ = std::fabs(fem.mapping->ComputeDetJ(*T, ip)); const double weight = T->Weight() * ip.weight * detJ; @@ -31,8 +47,10 @@ namespace mean_field::physics { } double global_I = 0.0; - MPI_Allreduce(&local_I, &global_I, 1, MPI_DOUBLE, MPI_SUM, fem.H1_fes->GetComm()); + MPI_Allreduce( + &local_I, &global_I, 1, MPI_DOUBLE, MPI_SUM, fem.mesh->GetComm() + ); return global_I; } -} \ No newline at end of file +} // namespace mean_field::physics diff --git a/libmeanfield/impl/utils/domain.cpp b/libmeanfield/impl/utils/domain.cpp index 1c75009..9b19862 100644 --- a/libmeanfield/impl/utils/domain.cpp +++ b/libmeanfield/impl/utils/domain.cpp @@ -11,7 +11,7 @@ namespace mean_field::utils { mfem::Vector &x_ref ) { const int dim = fem.mesh->Dimension(); - x_ref = x_phys_target; + x_ref = x_phys_target; mfem::Array init_elem; mfem::Array init_ip; @@ -29,8 +29,10 @@ namespace mean_field::utils { mfem::Array origin_ip; fem.mesh->FindPoints(P_origin, origin_elem, origin_ip, false); - if (origin_elem.Size() > 0 && origin_elem[0] >= 0 && !fem.mapping->IsIdentity()) { - mfem::ElementTransformation *T0 = fem.mesh->GetElementTransformation(origin_elem[0]); + if (origin_elem.Size() > 0 && origin_elem[0] >= 0 && + fem.mapping->HasDisplacementField()) { + mfem::ElementTransformation *T0 = + fem.mesh->GetElementTransformation(origin_elem[0]); T0->SetIntPoint(&origin_ip[0]); mfem::DenseMatrix J0(dim, dim), J0_inv(dim, dim); @@ -81,7 +83,8 @@ namespace mean_field::utils { if (elem_ids.Size() == 0 || elem_ids[0] < 0) { find_failures++; - if (find_failures > 10) return false; + if (find_failures > 10) + return false; double norm = x_ref.Norml2(); if (norm > 1e-15) { @@ -92,10 +95,11 @@ namespace mean_field::utils { continue; } - int elemID = elem_ids[0]; + int elemID = elem_ids[0]; const mfem::IntegrationPoint &ip = ips[0]; - mfem::ElementTransformation *T = fem.mesh->GetElementTransformation(elemID); + mfem::ElementTransformation *T = + fem.mesh->GetElementTransformation(elemID); T->SetIntPoint(&ip); mfem::Vector current_x_phys(dim); @@ -135,7 +139,8 @@ namespace mean_field::utils { x_ref = x_ref_candidate; } else { find_failures++; - if (find_failures > 10) return false; + if (find_failures > 10) + return false; if (double norm = x_ref.Norml2(); norm > 1e-15) { x_ref *= 0.5 * RADIUS / norm; } else { @@ -155,7 +160,8 @@ namespace mean_field::utils { const mapping::COORDINATE_SPACE rspace ) { mfem::Vector x_search; - if (vspace == mapping::COORDINATE_SPACE::PHYSICAL && fem.has_mapping()) { + if (vspace == mapping::COORDINATE_SPACE::PHYSICAL && + fem.has_mapping()) { GetReferencePoint(fem, x, x_search); } else { x_search = x; @@ -171,18 +177,22 @@ namespace mean_field::utils { double local_val = 0.0; if (elem_ids.Size() > 0 && elem_ids[0] >= 0) { const double val = u.GetValue(elem_ids[0], ips[0]); - if (rspace == mapping::COORDINATE_SPACE::PHYSICAL && !fem.has_mapping()) { - MFEM_ABORT("Physical evaluation mode requested but no mapping provided. Check domain bounds and mapping setup."); + if (rspace == mapping::COORDINATE_SPACE::PHYSICAL && + !fem.has_mapping()) { + MFEM_ABORT( + "Physical evaluation mode requested but no mapping " + "provided. Check " + "domain bounds and mapping setup." + ); } local_val = val; } double global_val = 0.0; - MPI_Allreduce(&local_val, &global_val, 1, MPI_DOUBLE, MPI_MAX, fem.H1_fes->GetComm()); + MPI_Allreduce( + &local_val, &global_val, 1, MPI_DOUBLE, MPI_MAX, fem.mesh->GetComm() + ); return global_val; } - - - -} \ No newline at end of file +} // namespace mean_field::utils diff --git a/libmeanfield/impl/utils/misc.cpp b/libmeanfield/impl/utils/misc.cpp index d0986d8..a341c49 100644 --- a/libmeanfield/impl/utils/misc.cpp +++ b/libmeanfield/impl/utils/misc.cpp @@ -1,6 +1,6 @@ module; -#include #include +#include module mean_field; import :boundary.contexts; @@ -10,18 +10,22 @@ namespace mean_field::utils { DOMAINS lhs, DOMAINS rhs ) { - return static_cast(static_cast(lhs) | static_cast(rhs)); + return static_cast( + static_cast(lhs) | static_cast(rhs) + ); } DOMAINS operator&( DOMAINS lhs, DOMAINS rhs ) { - return static_cast(static_cast(lhs) & static_cast(rhs)); + return static_cast( + static_cast(lhs) & static_cast(rhs) + ); } void populate_element_mask( - const mfem::Mesh* mesh, + const mfem::Mesh *mesh, const DOMAINS domain, mfem::Array &mask ) { @@ -33,7 +37,8 @@ namespace mean_field::utils { mask[0] = 1; } - if ((domain & DOMAINS::ENVELOPE) == DOMAINS::ENVELOPE && max_attr >= 2) { + if ((domain & DOMAINS::ENVELOPE) == DOMAINS::ENVELOPE && + max_attr >= 2) { mask[1] = 1; } @@ -59,7 +64,8 @@ namespace mean_field::utils { for (int j = 0; j < dofs.Size(); j++) { int index = dofs[j]; - if (index < 0) index = -1 - index; + if (index < 0) + index = -1 - index; vdof_marker[index] = 1; } } @@ -68,23 +74,28 @@ namespace mean_field::utils { fes->MarkerToList(vdof_marker, ess_tdof); } - - std::expected discover_bounds( + std::expected< + boundary::Bounds, + boundary::BoundsError> + discover_bounds( const mfem::Mesh *mesh, const int vacuum_attr ) { double local_min_r = std::numeric_limits::max(); double local_max_r = -std::numeric_limits::max(); - bool found_vacuum = false; + bool found_vacuum = false; for (int i = 0; i < mesh->GetNE(); ++i) { if (mesh->GetAttribute(i) == vacuum_attr) { found_vacuum = true; mfem::Array vertices; mesh->GetElementVertices(i, vertices); - for (const int v: vertices) { + for (const int v : vertices) { const double *coords = mesh->GetVertex(v); - double r = std::sqrt(coords[0] * coords[0] + coords[1] * coords[1] + coords[2] * coords[2]); + double r = std::sqrt( + coords[0] * coords[0] + coords[1] * coords[1] + + coords[2] * coords[2] + ); local_min_r = std::min(local_min_r, r); local_max_r = std::max(local_max_r, r); } @@ -93,16 +104,22 @@ namespace mean_field::utils { double global_min_r, global_max_r; int global_found_vacuum; - int l_found = found_vacuum ? 1 : 0; + int l_found = found_vacuum ? 1 : 0; MPI_Comm comm = MPI_COMM_WORLD; if (const auto *pmesh = dynamic_cast(mesh)) { comm = pmesh->GetComm(); } - MPI_Allreduce(&local_min_r, &global_min_r, 1, MPI_DOUBLE, MPI_MIN, comm); - MPI_Allreduce(&local_max_r, &global_max_r, 1, MPI_DOUBLE, MPI_MAX, comm); - MPI_Allreduce(&l_found, &global_found_vacuum, 1, MPI_INT, MPI_MAX, comm); + MPI_Allreduce( + &local_min_r, &global_min_r, 1, MPI_DOUBLE, MPI_MIN, comm + ); + MPI_Allreduce( + &local_max_r, &global_max_r, 1, MPI_DOUBLE, MPI_MAX, comm + ); + MPI_Allreduce( + &l_found, &global_found_vacuum, 1, MPI_INT, MPI_MAX, comm + ); if (global_found_vacuum) { return boundary::Bounds(global_min_r, global_max_r); @@ -110,15 +127,11 @@ namespace mean_field::utils { return std::unexpected(boundary::BoundsError::CANNOT_FIND_VACUUM); } - int get_mesh_order( - const mfem::Mesh &mesh - ) { + int get_mesh_order(const mfem::Mesh &mesh) { if (mesh.GetNodes() != nullptr) { return mesh.GetNodes()->FESpace()->GetMaxElementOrder(); } return 1; } - - -} \ No newline at end of file +} // namespace mean_field::utils \ No newline at end of file diff --git a/libmeanfield/include/profile.h b/libmeanfield/include/profile.h new file mode 100644 index 0000000..85d53f6 --- /dev/null +++ b/libmeanfield/include/profile.h @@ -0,0 +1,194 @@ +#pragma once + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +namespace mean_field::profiling { + struct Statistics { + unsigned long long observations{0}; + unsigned long long warmups{0}; + unsigned long long samples{0}; + unsigned long long warmup_target{0}; + double total_seconds{0.0}; + double minimum_seconds{std::numeric_limits::infinity()}; + double maximum_seconds{0.0}; + }; + + class Registry { + public: + static Registry& Get() { + static Registry registry; + return registry; + } + + void Record(const std::string& label, const double seconds, const unsigned long long warmup_count) { + std::scoped_lock lock(m_mutex); + Statistics& statistics = m_statistics[label]; + + statistics.warmup_target = std::max(statistics.warmup_target, warmup_count); + const bool is_warmup = statistics.observations < statistics.warmup_target; + ++statistics.observations; + + if (is_warmup) { + ++statistics.warmups; + return; + } + + ++statistics.samples; + statistics.total_seconds += seconds; + statistics.minimum_seconds = std::min(statistics.minimum_seconds, seconds); + statistics.maximum_seconds = std::max(statistics.maximum_seconds, seconds); + } + + void Reset() { + std::scoped_lock lock(m_mutex); + m_statistics.clear(); + } + + void Print(MPI_Comm communicator) const { + const std::map snapshot = GetSnapshot(); + + int mpi_initialized = 0; + int mpi_finalized = 0; + MPI_Initialized(&mpi_initialized); + if (mpi_initialized) MPI_Finalized(&mpi_finalized); + + const bool use_mpi = mpi_initialized && !mpi_finalized; + int rank = 0; + int communicator_size = 1; + + if (use_mpi) { + MPI_Comm_rank(communicator, &rank); + MPI_Comm_size(communicator, &communicator_size); + } + + if (rank == 0) { + std::cout << '\n'; + std::cout << std::left << std::setw(42) << "Profile Region" + << std::right << std::setw(11) << "Samples" + << std::setw(10) << "Warmups" + << std::setw(14) << "Avg Max ms" + << std::setw(14) << "Min ms" + << std::setw(14) << "Max ms" + << std::setw(14) << "Total Max s" << '\n'; + std::cout << std::string(119, '-') << '\n'; + } + + for (const auto& [label, local_statistics] : snapshot) { + unsigned long long minimum_samples = local_statistics.samples; + unsigned long long maximum_samples = local_statistics.samples; + unsigned long long maximum_warmups = local_statistics.warmups; + + double local_average = local_statistics.samples > 0 ? local_statistics.total_seconds / static_cast(local_statistics.samples) : 0.0; + double local_minimum = local_statistics.samples > 0 ? local_statistics.minimum_seconds : std::numeric_limits::infinity(); + double local_maximum = local_statistics.maximum_seconds; + double local_total = local_statistics.total_seconds; + + double maximum_rank_average = local_average; + double global_minimum = local_minimum; + double global_maximum = local_maximum; + double maximum_rank_total = local_total; + + if (use_mpi) { + MPI_Allreduce(&local_statistics.samples, &minimum_samples, 1, MPI_UNSIGNED_LONG_LONG, MPI_MIN, communicator); + MPI_Allreduce(&local_statistics.samples, &maximum_samples, 1, MPI_UNSIGNED_LONG_LONG, MPI_MAX, communicator); + MPI_Allreduce(&local_statistics.warmups, &maximum_warmups, 1, MPI_UNSIGNED_LONG_LONG, MPI_MAX, communicator); + MPI_Allreduce(&local_average, &maximum_rank_average, 1, MPI_DOUBLE, MPI_MAX, communicator); + MPI_Allreduce(&local_minimum, &global_minimum, 1, MPI_DOUBLE, MPI_MIN, communicator); + MPI_Allreduce(&local_maximum, &global_maximum, 1, MPI_DOUBLE, MPI_MAX, communicator); + MPI_Allreduce(&local_total, &maximum_rank_total, 1, MPI_DOUBLE, MPI_MAX, communicator); + } + + if (!std::isfinite(global_minimum)) global_minimum = 0.0; + + if (rank == 0) { + const std::string sample_string = minimum_samples == maximum_samples + ? std::to_string(minimum_samples) + : std::to_string(minimum_samples) + "-" + std::to_string(maximum_samples); + + std::cout << std::left << std::setw(100) << label + << std::right << std::setw(11) << sample_string + << std::setw(10) << maximum_warmups + << std::setw(14) << std::fixed << std::setprecision(3) << 1.0e3 * maximum_rank_average + << std::setw(14) << 1.0e3 * global_minimum + << std::setw(14) << 1.0e3 * global_maximum + << std::setw(14) << std::setprecision(6) << maximum_rank_total << '\n'; + } + } + + if (rank == 0) { + std::cout << std::string(119, '=') << '\n'; + std::cout << "MPI ranks: " << communicator_size << "\n\n"; + } + } + + private: + [[nodiscard]] std::map GetSnapshot() const { + std::scoped_lock lock(m_mutex); + return m_statistics; + } + + private: + mutable std::mutex m_mutex; + std::map m_statistics; + }; + + class ScopedTimer { + public: + ScopedTimer(std::string label, const unsigned long long warmup_count) + : m_label(std::move(label)), + m_warmup_count(warmup_count), + m_start(std::chrono::steady_clock::now()) {} + + ScopedTimer(const ScopedTimer&) = delete; + ScopedTimer& operator=(const ScopedTimer&) = delete; + ScopedTimer(ScopedTimer&&) = delete; + ScopedTimer& operator=(ScopedTimer&&) = delete; + + ~ScopedTimer() { + try { + const auto stop = std::chrono::steady_clock::now(); + const double seconds = std::chrono::duration(stop - m_start).count(); + Registry::Get().Record(m_label, seconds, m_warmup_count); + } catch (...) {} + } + + private: + std::string m_label; + unsigned long long m_warmup_count; + std::chrono::steady_clock::time_point m_start; + }; +} + +#define MEAN_FIELD_PROFILE_JOIN_IMPL(left, right) left##right +#define MEAN_FIELD_PROFILE_JOIN(left, right) MEAN_FIELD_PROFILE_JOIN_IMPL(left, right) + +#define MEAN_FIELD_PROFILE_SCOPE_WARMUP(label, warmup_count) \ + ::mean_field::profiling::ScopedTimer MEAN_FIELD_PROFILE_JOIN(mean_field_profile_timer_, __COUNTER__)(label, warmup_count) + +#define MEAN_FIELD_PROFILE_SCOPE(label) \ + MEAN_FIELD_PROFILE_SCOPE_WARMUP(label, 1) + +#define MEAN_FIELD_PROFILE_CALL_WARMUP(label, warmup_count, ...) \ + do { \ + MEAN_FIELD_PROFILE_SCOPE_WARMUP(label, warmup_count); \ + __VA_ARGS__; \ + } while (false) + +#define MEAN_FIELD_PROFILE_CALL(label, ...) \ + MEAN_FIELD_PROFILE_CALL_WARMUP(label, 1, __VA_ARGS__) + +#define MEAN_FIELD_PROFILE_RESET() \ + ::mean_field::profiling::Registry::Get().Reset() + +#define MEAN_FIELD_PROFILE_PRINT(communicator) \ + ::mean_field::profiling::Registry::Get().Print(communicator) \ No newline at end of file diff --git a/libmeanfield/interface/analysis/integral.cppm b/libmeanfield/interface/analysis/integral.cppm index 4006c53..1fd9726 100644 --- a/libmeanfield/interface/analysis/integral.cppm +++ b/libmeanfield/interface/analysis/integral.cppm @@ -12,7 +12,8 @@ export namespace mean_field::analysis { const fem::FEM &fem, const mfem::GridFunction &gf, utils::DOMAINS domain = utils::DOMAINS::ALL, - mapping::COORDINATE_SPACE coord_space = mapping::COORDINATE_SPACE::PHYSICAL + mapping::COORDINATE_SPACE coord_space = + mapping::COORDINATE_SPACE::PHYSICAL ); mfem::Vector get_com( @@ -32,10 +33,9 @@ export namespace mean_field::analysis { ); double get_mesh_volume( - const fem::FEM& fem, - mapping::COORDINATE_SPACE coordinate_space = mapping::COORDINATE_SPACE::PHYSICAL, + const fem::FEM &fem, + mapping::COORDINATE_SPACE coordinate_space = + mapping::COORDINATE_SPACE::PHYSICAL, utils::DOMAINS domain = utils::DOMAINS::STELLAR ); -} - - +} // namespace mean_field::analysis diff --git a/libmeanfield/interface/boundary/context.cppm b/libmeanfield/interface/boundary/context.cppm index d2db63f..c25c6ad 100644 --- a/libmeanfield/interface/boundary/context.cppm +++ b/libmeanfield/interface/boundary/context.cppm @@ -5,20 +5,19 @@ export module mean_field:boundary.contexts; export namespace mean_field::boundary { struct BoundaryContext { - mfem::Array inf_bounds; - mfem::Array stellar_bounds; + mfem::Array inf_bounds; + mfem::Array stellar_bounds; }; - enum class Boundaries : uint8_t { - STELLAR_SURFACE = 1, - INF_SURFACE = 2 - }; + enum class Boundaries : uint8_t { STELLAR_SURFACE = 1, INF_SURFACE = 2 }; int operator-( Boundaries b, const int a ) { - return static_cast(static_cast(b) - static_cast(a)); + return static_cast( + static_cast(b) - static_cast(a) + ); } struct Bounds { @@ -26,9 +25,6 @@ export namespace mean_field::boundary { double r_inf_ref; }; - enum BoundsError : uint8_t { - CANNOT_FIND_VACUUM - }; + enum BoundsError : uint8_t { CANNOT_FIND_VACUUM }; - -} +} // namespace mean_field::boundary diff --git a/libmeanfield/interface/fem.cppm b/libmeanfield/interface/fem.cppm index 9993037..583d800 100644 --- a/libmeanfield/interface/fem.cppm +++ b/libmeanfield/interface/fem.cppm @@ -1,95 +1,183 @@ module; -#include #include +#include + #include +#include export module mean_field:fem; + export import :physics.contexts; export import :boundary.contexts; export import :mapping.domain_mapper; export import :utils.misc; export import :utils.user; export import :quadrature.mfem; +export import :field.mfem; export namespace mean_field::fem { + using GravityField = field::Field; + using DisplacementField = field::Field; + using DensityField = field::Field; + using EnthalpyField = field::Field; + struct FEM { + // ===================================================================== + // Mesh + // ===================================================================== stroid::StroidMesh smesh; std::unique_ptr mesh; - // ===================================== - // 2. Finite Element Collections - // ===================================== - // H1 (Continuous): For Gravitational Potential (Phi) and Velocity (v) - std::unique_ptr H1_fec; + // ===================================================================== + // Compile-time field descriptors + // ===================================================================== - // L2 (Discontinuous): For Density (rho) to fix O-grid boundary scalloping - std::unique_ptr L2_fec; + GravityField gravityField; + DisplacementField displacementField; + DensityField densityField; + EnthalpyField enthalpyField; - // H(div)/RT space for gravitational field - std::unique_ptr RT_fec; + // ===================================================================== + // Gravity field + // + // Collection members are declared before their corresponding spaces so + // that the spaces are destroyed first. + // ===================================================================== + std::unique_ptr gravityPotentialFec; - // ===================================== - // 3. Finite Element Spaces - // ===================================== - std::unique_ptr H1_fes; // Scalar continuous (Gravity) - std::unique_ptr Vec_H1_fes; // Vector continuous (Velocity field) - std::unique_ptr L2_fes; // Scalar discontinuous (Density) - std::unique_ptr RT_fes; // H(div)/RT space for gravitational field + std::unique_ptr gravityPotentialFes; - // Preconditioning for Gravity - std::unique_ptr H1_lor_disc; - const mfem::ParFiniteElementSpace *H1_lor_fes{nullptr}; + std::unique_ptr gravityFluxFec; + + std::unique_ptr gravityFluxFes; + + // ===================================================================== + // Displacement field + // ===================================================================== + + std::unique_ptr displacementFec; + + std::unique_ptr displacementFes; + + std::unique_ptr displacement; + + // ===================================================================== + // Density field + // ===================================================================== + + std::unique_ptr densityFec; + + std::unique_ptr densityFes; + + // ===================================================================== + // Specific-enthalpy field + // ===================================================================== + + std::unique_ptr enthalpyFec; + + std::unique_ptr enthalpyFes; + + // ===================================================================== + // Compactification coordinate + // ===================================================================== + + std::unique_ptr compactificationFec; + + std::unique_ptr compactificationFes; + + std::unique_ptr compactificationCoordinate; + + // ===================================================================== + // Domain mapping + // + // These are declared after displacement so that they are destroyed + // before the displacement grid function to which mapping may refer. + // DomainMapper is retained only for legacy integrators. New operators + // use DomainMapperStateless exclusively. + // ===================================================================== - // ===================================== - // 4. Domain Mapping - // ===================================== std::unique_ptr mapping; - // ===================================== - // 5. Global System Tracking - // ===================================== - // [ Velocity | Density | Mapping Parameters (Surface) ] - mfem::Array block_true_offsets; + std::unique_ptr domainMapperStateless; - mfem::Array gravity_block_true_offsets; + // ===================================================================== + // Block layouts + // + // These arrays are retained only for legacy code. Canonical operator + // layouts are defined by the compile-time forms in :utils.blocks. + // + // Main system: [Displacement | Density] + // Gravity system: [Flux | Potential] + // ===================================================================== - // Essential Boundary Conditions for the fluid (e.g., surface stress-free) - mfem::Array ess_v_tdofs; + mfem::Array blockTrueOffsets; + mfem::Array gravityBlockTrueOffsets; - // Elements entirely in the vacuum domain where fluid equations are not solved - mfem::Array vacuum_tdof_rho; - mfem::Array vacuum_tdof_v; + // ===================================================================== + // Boundary conditions and domain masks + // ===================================================================== + + mfem::Array essentialDisplacementTdofs; + mfem::Array vacuumDensityTdofs; + mfem::Array vacuumEnthalpyTdofs; + mfem::Array vacuumDisplacementTdofs; + + // ===================================================================== + // Global diagnostics + // ===================================================================== - // ===================================== - // 6. Multiphysics State & Integration - // ===================================== mfem::Vector com; mfem::DenseMatrix Q; - int int_order{3}; - std::unique_ptr int_rule; + // ===================================================================== + // Physics and boundary contexts + // ===================================================================== - physics::GravityContext gravity_context; - boundary::BoundaryContext boundary_context; + physics::GravityContext gravityContext; + boundary::BoundaryContext boundaryContext; - std::unique_ptr quadrature_factory; + std::unique_ptr quadratureFactory; + + // ===================================================================== + // Validation + // ===================================================================== - // ===================================== - // 7. Utilities - // ===================================== [[nodiscard]] bool okay() const { - return (mesh != nullptr) && - (H1_fec != nullptr) && (L2_fec != nullptr) && (RT_fec != nullptr) && - (H1_fes != nullptr) && (Vec_H1_fes != nullptr) && (L2_fes != nullptr) && (RT_fes != nullptr); + return mesh != nullptr && + + gravityPotentialFec != nullptr && + gravityPotentialFes != nullptr && + gravityFluxFec != nullptr && gravityFluxFes != nullptr && + + displacementFec != nullptr && displacementFes != nullptr && + displacement != nullptr && + + densityFec != nullptr && densityFes != nullptr && + + enthalpyFec != nullptr && enthalpyFes != nullptr && + + compactificationFec != nullptr && + compactificationFes != nullptr && + compactificationCoordinate != nullptr && + + mapping != nullptr && domainMapperStateless != nullptr && + quadratureFactory != nullptr && + + blockTrueOffsets.Size() == 3 && + gravityBlockTrueOffsets.Size() == 3; } - [[nodiscard]] bool has_mapping() const { return mapping != nullptr; } + [[nodiscard]] bool has_mapping() const { + return mapping != nullptr; + } }; - - FEM setup_fem(const std::string &filename, const utils::Args &args, int extra_refine = 0); -} - + FEM setup_fem( + const std::string &filename, + const utils::Args &args, + int extraRefine = 0 + ); +} // namespace mean_field::fem diff --git a/libmeanfield/interface/field/field_base.cppm b/libmeanfield/interface/field/field_base.cppm new file mode 100644 index 0000000..343b459 --- /dev/null +++ b/libmeanfield/interface/field/field_base.cppm @@ -0,0 +1,356 @@ +module; + +#include +#include +#include +#include + +export module mean_field:field.base; + +export namespace mean_field::field { + template struct TypeList { }; + + template struct TypeListContains; + + template + struct TypeListContains> + : std::bool_constant<(std::same_as || ...)> { }; + + template + inline constexpr bool typeListContains = TypeListContains::value; + + enum class StorageKind { finite_element, global_scalar }; + + inline constexpr int dynamicBlockSize = -1; + + // ------------------------------------------------------------------------- + // Function-space tags + // ------------------------------------------------------------------------- + + struct L2 { + static constexpr std::string_view name = "L2"; + }; + + struct H1 { + static constexpr std::string_view name = "H1"; + }; + + struct RT { + static constexpr std::string_view name = "RT"; + }; + + struct ND { + static constexpr std::string_view name = "ND"; + }; + + template + concept SpaceTag = std::same_as || std::same_as || + std::same_as || std::same_as; + + template + inline constexpr bool spaceSupportsRank = + (std::same_as && (RankV == 0 || RankV == 1)) || + (std::same_as && (RankV == 0 || RankV == 1)) || + (std::same_as && RankV == 1) || + (std::same_as && RankV == 1); + + // ------------------------------------------------------------------------- + // Discretization descriptors + // + // familyOrder is the order passed to the backend's FE collection + // constructor. It is deliberately not called polynomialOrder because those + // values differ for some spaces, notably Raviart-Thomas elements in MFEM. + // ------------------------------------------------------------------------- + + template struct Disc { + using Space = SpaceT; + + static constexpr int familyOrder = FamilyOrderV; + + static_assert( + FamilyOrderV >= 0, + "Finite-element family order must be non-negative." + ); + }; + + template + concept DiscretizationTag = requires { + typename T::Space; + { T::familyOrder } -> std::convertible_to; + } && SpaceTag; + + // ------------------------------------------------------------------------- + // Physical relations between quantities + // ------------------------------------------------------------------------- + + struct FieldRelation { + struct Independent { }; + + template struct Gradient { + using Source = SourceT; + }; + + template struct Divergence { + using Source = SourceT; + }; + + template struct Curl { + using Source = SourceT; + }; + }; + + template struct IsGradient : std::false_type { }; + + template struct IsDivergence : std::false_type { }; + + template struct IsCurl : std::false_type { }; + + template + struct IsGradient> : std::true_type { }; + + template + struct IsDivergence> : std::true_type { + }; + + template + struct IsCurl> : std::true_type { }; + + template + concept ValidRelation = + std::same_as || + IsGradient::value || IsDivergence::value || + IsCurl::value; + + template struct RelationTarget { + using Type = void; + }; + + template + struct RelationTarget> { + using Type = SourceT; + }; + + template + struct RelationTarget> { + using Type = SourceT; + }; + + template + struct RelationTarget> { + using Type = SourceT; + }; + + template + using RelationTargetT = + typename RelationTarget::Type; + + // ------------------------------------------------------------------------- + // Field quantities + // ------------------------------------------------------------------------- + + template + struct Quantity { + using Relation = RelationT; + using Discretization = DiscT; + using Space = typename DiscT::Space; + + static constexpr int rankValue = RankV; + static constexpr int familyOrder = DiscT::familyOrder; + + static constexpr StorageKind storageKind = StorageKind::finite_element; + static constexpr int staticBlockSize = dynamicBlockSize; + + static_assert( + RankV >= 0, + "A field quantity cannot have a negative tensor rank." + ); + + static_assert( + spaceSupportsRank< + Space, + RankV>, + "This function space cannot represent a quantity of this rank." + ); + }; + + template + using ScalarQ = Quantity<0, RelationT, DiscT>; + + template + using VectorQ = Quantity<1, RelationT, DiscT>; + + struct GlobalScalarQ { + using Relation = FieldRelation::Independent; + + static constexpr int rankValue = 0; + static constexpr StorageKind storageKind = StorageKind::global_scalar; + static constexpr int staticBlockSize = 1; + }; + + template + concept FieldQuantity = + requires { + typename T::Relation; + typename T::Discretization; + typename T::Space; + + { T::rankValue } -> std::convertible_to; + { T::familyOrder } -> std::convertible_to; + { T::storageKind } -> std::convertible_to; + { T::staticBlockSize } -> std::convertible_to; + } && SpaceTag && + T::storageKind == StorageKind::finite_element; + + template + concept GlobalScalarQuantity = + requires { + typename T::Relation; + + { T::rankValue } -> std::convertible_to; + { T::storageKind } -> std::convertible_to; + { T::staticBlockSize } -> std::convertible_to; + } && T::rankValue == 0 && + T::storageKind == StorageKind::global_scalar && T::staticBlockSize == 1; + + template + concept RegisteredQuantity = FieldQuantity || GlobalScalarQuantity; + + template + concept DerivedQuantity = FieldQuantity && + (!std::same_as, void>); + + // ------------------------------------------------------------------------- + // Compile-time discretization constraints + // ------------------------------------------------------------------------- + + template + struct RtL2StablePair { + static consteval void validate() { + static_assert( + std::same_as, + "The flux in an RT/L2 pair must use Raviart-Thomas elements." + ); + + static_assert( + std::same_as, + "The potential in an RT/L2 pair must use L2 elements." + ); + + static_assert( + FluxT::rankValue == 1, + "The flux in an RT/L2 pair must be vector-valued." + ); + + static_assert( + PotentialT::rankValue == 0, + "The potential in an RT/L2 pair must be scalar-valued." + ); + + static_assert( + FluxT::familyOrder == PotentialT::familyOrder, + "The MFEM RT and L2 family orders must match." + ); + } + }; + + template + consteval bool validate_constraints(TypeList) { + (ConstraintTs::validate(), ...); + return true; + } + + // ------------------------------------------------------------------------- + // Operations applied to quantities inside weak forms + // + // These describe the mathematics. Backend-specific polynomial-order rules + // are provided by field.mfem. + // ------------------------------------------------------------------------- + + struct FieldOperation { + struct Value { }; + struct Gradient { }; + struct Divergence { }; + struct Curl { }; + struct NormalTrace { }; + }; + + template + concept FieldOperationTag = + std::same_as || + std::same_as || + std::same_as || + std::same_as || + std::same_as; + + template < + RegisteredQuantity QuantityT, + FieldOperationTag OperationT = FieldOperation::Value> + struct Operand { + using Quantity = QuantityT; + using Operation = OperationT; + + static_assert( + FieldQuantity || std::same_as< + OperationT, + FieldOperation::Value>, + "Global scalar quantities support only the value operation." + ); + }; + + template + concept FieldOperand = + requires { + typename T::Quantity; + typename T::Operation; + } && RegisteredQuantity && + FieldOperationTag; + + // ------------------------------------------------------------------------- + // Weak-form descriptions + // + // PolicyKeyV associates the form with a runtime quadrature-policy key. + // + // DynamicOrderCountV is the number of polynomial-order contributions that + // cannot yet be derived from registered quantities. For example, a source + // coefficient supplied at runtime contributes one dynamic order. + // ------------------------------------------------------------------------- + + template < + auto PolicyKeyV, + std::size_t DynamicOrderCountV, + FieldOperand... OperandTs> + struct FormSpec { + static constexpr auto policyKey = PolicyKeyV; + static constexpr std::size_t dynamicOrderCount = DynamicOrderCountV; + + using Operands = TypeList; + }; + + template + concept FieldForm = requires { + typename T::Operands; + + T::policyKey; + + { T::dynamicOrderCount } -> std::convertible_to; + }; + + template + struct IsRegisteredQuantityList : std::false_type { }; + + template + struct IsRegisteredQuantityList> : std::true_type { + }; + + template + inline constexpr bool isRegisteredQuantityList = + IsRegisteredQuantityList::value; + + template struct IsFieldFormList : std::false_type { }; + + template + struct IsFieldFormList> : std::true_type { }; + + template + inline constexpr bool isFieldFormList = IsFieldFormList::value; +} // namespace mean_field::field \ No newline at end of file diff --git a/libmeanfield/interface/field/field_mfem.cppm b/libmeanfield/interface/field/field_mfem.cppm new file mode 100644 index 0000000..06481eb --- /dev/null +++ b/libmeanfield/interface/field/field_mfem.cppm @@ -0,0 +1,380 @@ +module; + +#include +#include +#include +#include +#include + +#include + +export module mean_field:field.mfem; + +export import :field.registry; + +namespace mean_field::field::detail { + template inline constexpr bool alwaysFalse = false; + + // ------------------------------------------------------------------------- + // MFEM finite-element collection construction + // ------------------------------------------------------------------------- + + template struct FecFor; + + template <> struct FecFor { + static std::unique_ptr make( + int familyOrder, + int dimension + ) { + return std::make_unique( + familyOrder, dimension + ); + } + }; + + template <> struct FecFor

{ + static std::unique_ptr make( + int familyOrder, + int dimension + ) { + return std::make_unique( + familyOrder, dimension + ); + } + }; + + template <> struct FecFor { + static std::unique_ptr make( + int familyOrder, + int dimension + ) { + return std::make_unique( + familyOrder, dimension + ); + } + }; + + template <> struct FecFor { + static std::unique_ptr make( + int familyOrder, + int dimension + ) { + return std::make_unique( + familyOrder, dimension + ); + } + }; + + // ------------------------------------------------------------------------- + // MFEM polynomial-order interpretation + // + // familyOrder is the collection constructor argument. + // + // For RT_p: + // value order = p + 1 + // divergence order = p + // normal-trace order = p + // + // This distinction is what allows Disc and Disc to form a + // compatible pair while still giving different value-shape orders. + // ------------------------------------------------------------------------- + + template struct MfemOperandOrder; + + template + struct MfemOperandOrder> { + static constexpr int orderValue = []() consteval { + if constexpr (GlobalScalarQuantity) { + static_assert( + std::same_as, + "Global scalars support only the value operation." + ); + + return 0; + } else { + using Space = typename QuantityT::Space; + constexpr int familyOrder = QuantityT::familyOrder; + + if constexpr (std::same_as) { + if constexpr (std::same_as) { + return familyOrder + 1; + } else { + return familyOrder; + } + } else if constexpr ( + std::same_as + ) { + static_assert( + std::same_as, + "Only RT quantities currently support the divergence " + "polynomial-order rule." + ); + + return familyOrder; + } else if constexpr ( + std::same_as + ) { + static_assert( + std::same_as, + "Only H1 quantities currently support the gradient " + "polynomial-order rule." + ); + + return familyOrder > 0 ? familyOrder - 1 : 0; + } else if constexpr ( + std::same_as + ) { + static_assert( + std::same_as, + "Only ND quantities currently support the curl " + "polynomial-order rule." + ); + + return familyOrder > 0 ? familyOrder - 1 : 0; + } else if constexpr ( + std::same_as + ) { + static_assert( + std::same_as, + "Only RT quantities currently support the normal-trace " + "polynomial-order rule." + ); + + return familyOrder; + } else { + static_assert( + alwaysFalse, + "Unsupported MFEM field operation." + ); + } + } + }(); + }; + + // ------------------------------------------------------------------------- + // Static polynomial-order contribution of an entire form + // ------------------------------------------------------------------------- + + template struct MfemFormOrder; + + template < + auto PolicyKeyV, + std::size_t DynamicOrderCountV, + FieldOperand... OperandTs> + struct MfemFormOrder< + FormSpec> { + static constexpr int staticOrder = + (MfemOperandOrder::orderValue + ... + 0); + }; + + // ------------------------------------------------------------------------- + // MFEM vector-dimension and ordering rules + // + // Vector H1/L2 fields are represented using multiple copies of a scalar + // finite-element space. RT and ND elements are intrinsically vector-valued + // and therefore use vdim = 1. + // ------------------------------------------------------------------------- + + template int get_vdim(int spaceDimension) { + if (spaceDimension <= 0) { + throw std::invalid_argument("Space dimension must be positive."); + } + + if constexpr (QuantityT::rankValue == 0) { + return 1; + } else if constexpr ( + std::same_as || + std::same_as + ) { + return spaceDimension; + } else { + return 1; + } + } + + template + constexpr mfem::Ordering::Type get_ordering() { + if constexpr ( + QuantityT::rankValue == 1 && + (std::same_as || + std::same_as) + ) { + return mfem::Ordering::byVDIM; + } else { + return mfem::Ordering::byNODES; + } + } + + // ------------------------------------------------------------------------- + // Quantity-specific MFEM realization + // + // Backend choices that are part of a field definition live here rather + // than leaking into FEM setup or call sites. + // ------------------------------------------------------------------------- + + template struct MfemQuantityTraits { + static std::unique_ptr + make_fec(int dimension) { + return FecFor::make( + QuantityT::familyOrder, dimension + ); + } + + static constexpr mfem::Ordering::Type ordering = + get_ordering(); + }; + + template <> struct MfemQuantityTraits { + static std::unique_ptr + make_fec(int dimension) { + return std::make_unique( + Gravity::Flux::familyOrder, dimension, + mfem::BasisType::GaussLobatto, mfem::BasisType::IntegratedGLL + ); + } + + static constexpr mfem::Ordering::Type ordering = + mfem::Ordering::byNODES; + }; + + template <> struct MfemQuantityTraits { + static std::unique_ptr + make_fec(int dimension) { + return FecFor

::make( + Displacement::Vector::familyOrder, dimension + ); + } + + static constexpr mfem::Ordering::Type ordering = + mfem::Ordering::byNODES; + }; +} // namespace mean_field::field::detail + +export namespace mean_field::field { + // ------------------------------------------------------------------------- + // User-facing field type + // + // The object itself is currently a zero-cost compile-time descriptor: + // + // Field gravityField; + // + // MFEM construction and typed quadrature-query generation are provided as + // static operations. Runtime ownership can later be added without changing + // Gravity, Displacement, or their form definitions. + // ------------------------------------------------------------------------- + + template class Field { + public: + using Tag = TagT; + + // --------------------------------------------------------------------- + // MFEM finite-element collection construction + // --------------------------------------------------------------------- + + template + requires typeListContains< + QuantityT, + typename TagT::Quantities> + static std::unique_ptr + make_fec(int dimension) { + if (dimension <= 0) { + throw std::invalid_argument("Mesh dimension must be positive."); + } + + return detail::MfemQuantityTraits::make_fec(dimension); + } + + // --------------------------------------------------------------------- + // MFEM parallel finite-element space construction + // + // The finite-element collection must outlive the returned space. + // --------------------------------------------------------------------- + + template + requires typeListContains< + QuantityT, + typename TagT::Quantities> + static std::unique_ptr make_fespace( + mfem::ParMesh &mesh, + mfem::FiniteElementCollection &finiteElementCollection + ) { + return std::make_unique( + &mesh, &finiteElementCollection, + detail::get_vdim(mesh.SpaceDimension()), + detail::MfemQuantityTraits::ordering + ); + } + + // --------------------------------------------------------------------- + // Typed quadrature-query construction + // + // geometryWeightOrder is supplied at runtime because it depends on the + // actual element transformation. + // + // dynamicOrders contains the form-specific polynomial orders that are + // not represented by registered compile-time quantities. + // + // Examples: + // + // Density::Form::CenterOfMass: + // { positionOrder } + // + // Gravity source forms need no dynamic orders because density and + // potential are both registered quantities. + // + // The completed base order is stored in Query::base_order, so Policy + // does not need to understand divergence, RT conventions, or individual + // field layouts. + // --------------------------------------------------------------------- + + template + requires typeListContains< + FormT, + typename TagT::FormList> + static constexpr quadrature::Query make_query( + quadrature::QuadratureRole role, + int geometryWeightOrder, + std::array< + int, + FormT::dynamicOrderCount> dynamicOrders = {}, + utils::DOMAINS domain = utils::DOMAINS::ALL, + quadrature::MappingKind mapping = quadrature::MappingKind::none + ) { + if (geometryWeightOrder < 0) { + throw std::invalid_argument( + "Geometry weight order cannot be negative." + ); + } + + int baseOrder = + detail::MfemFormOrder::staticOrder + geometryWeightOrder; + + for (const int dynamicOrder : dynamicOrders) { + if (dynamicOrder < 0) { + throw std::invalid_argument( + "Dynamic polynomial orders cannot be negative." + ); + } + + baseOrder += dynamicOrder; + } + + return { + .term = FormT::policyKey, + .role = role, + .domain = domain, + .mapping = mapping, + .trial_order = 0, + .test_order = 0, + .coefficient_order = 0, + .geometry_weight_order = geometryWeightOrder, + .base_order = baseOrder + }; + } + }; + + static_assert(FieldTag); + static_assert(FieldTag); + static_assert(FieldTag); + static_assert(FieldTag); +} // namespace mean_field::field diff --git a/libmeanfield/interface/field/field_registry.cppm b/libmeanfield/interface/field/field_registry.cppm new file mode 100644 index 0000000..af36512 --- /dev/null +++ b/libmeanfield/interface/field/field_registry.cppm @@ -0,0 +1,379 @@ +module; + +#include +#include + +export module mean_field:field.registry; + +export import :field.base; +export import :quadrature.policy; + +export namespace mean_field::field { + // ========================================================================= + // Density + // ========================================================================= + + struct Density { + static constexpr std::string_view name = "density"; + static constexpr int scalarOrder = 2; + + struct Scalar final + : ScalarQ> { + static constexpr std::string_view symbol = "ρ"; + }; + + using Quantities = TypeList; + using Constraints = TypeList<>; + + static constexpr bool constraintsAreValid = + validate_constraints(Constraints{}); + + static_assert(constraintsAreValid); + + struct Form { + // Density-space mass matrix: (rho, q). + using ProjectionMass = FormSpec< + quadrature::Term::density_projection, + 0, + Operand, + Operand>; + + // Projection RHS with one runtime coefficient order. + using ProjectionSource = FormSpec< + quadrature::Term::density_projection, + 1, + Operand>; + + // Density-space contribution to the barotropic EOS closure: + // (rho, q_rho). + using EosClosureMass = FormSpec< + quadrature::Term::eos_closure, + 0, + Operand, + Operand>; + + // Integral of density over the physical volume. + using MassConservation = FormSpec< + quadrature::Term::mass_conservation, + 0, + Operand>; + + // The same physical integral used as a nonlinear normalization + // constraint. It has a distinct policy key so solver assembly and + // diagnostics can be overintegrated independently. + using MassNormalization = FormSpec< + quadrature::Term::mass_normalization, + 0, + Operand>; + + // Integral of rho * x. The combined position-coefficient order is + // supplied as one dynamic order. + using CenterOfMass = + FormSpec>; + + // Integral of rho times the quadratic position tensor. The + // combined tensor-coefficient order is supplied dynamically. + using Quadrupole = + FormSpec>; + + using ErrorNorm = FormSpec< + quadrature::Term::error_norm, + 0, + Operand, + Operand>; + }; + + using FormList = TypeList< + Form::ProjectionMass, + Form::ProjectionSource, + Form::EosClosureMass, + Form::MassConservation, + Form::MassNormalization, + Form::CenterOfMass, + Form::Quadrupole, + Form::ErrorNorm>; + }; + + // ========================================================================= + // Gravity + // ========================================================================= + + struct Gravity { + static constexpr std::string_view name = "gravity"; + + static constexpr int potentialOrder = 2; + static constexpr int fluxOrder = 2; + + struct Potential final + : ScalarQ> { + static constexpr std::string_view symbol = "φ"; + }; + + struct Flux final + : VectorQ, Disc> { + static constexpr std::string_view symbol = "∇φ"; + }; + + using Quantities = TypeList; + + using Constraints = TypeList>; + + static constexpr bool constraintsAreValid = + validate_constraints(Constraints{}); + + static_assert(constraintsAreValid); + + struct Form { + using HDivMass = FormSpec< + quadrature::Term::gravity_hdiv_mass, + 0, + Operand, + Operand>; + + using DivergenceCoupling = FormSpec< + quadrature::Term::gravity_divergence, + 0, + Operand, + Operand>; + + using Boundary = FormSpec< + quadrature::Term::gravity_boundary, + 0, + Operand, + Operand>; + + // Density is a registered coefficient field and potential is the + // test field, so the full polynomial order is compile-time data. + using SourceLinear = FormSpec< + quadrature::Term::gravity_source, + 0, + Operand, + Operand>; + + // Mixed density-to-potential projection. Both trial and test + // orders are registered quantities. + using SourceProjection = FormSpec< + quadrature::Term::gravity_source, + 0, + Operand, + Operand>; + + using PotentialErrorNorm = FormSpec< + quadrature::Term::error_norm, + 0, + Operand, + Operand>; + + using FluxErrorNorm = FormSpec< + quadrature::Term::error_norm, + 0, + Operand, + Operand>; + }; + + using FormList = TypeList< + Form::HDivMass, + Form::DivergenceCoupling, + Form::Boundary, + Form::SourceLinear, + Form::SourceProjection, + Form::PotentialErrorNorm, + Form::FluxErrorNorm>; + }; + + // ========================================================================= + // Displacement + // ========================================================================= + + struct Displacement { + static constexpr std::string_view name = "displacement"; + static constexpr int vectorOrder = 3; + + struct Vector final + : VectorQ> { + static constexpr std::string_view symbol = "d"; + }; + + using Quantities = TypeList; + using Constraints = TypeList<>; + + static constexpr bool constraintsAreValid = + validate_constraints(Constraints{}); + + static_assert(constraintsAreValid); + + struct Form { + // Harmonic or pseudoelastic interior mesh extension. For the + // initial Laplacian model this is (grad d, grad w). + using MeshExtension = FormSpec< + quadrature::Term::mesh_extension, + 0, + Operand, + Operand>; + + using ErrorNorm = FormSpec< + quadrature::Term::error_norm, + 0, + Operand, + Operand>; + }; + + using FormList = TypeList; + }; + + struct BarotropicConstant { + static constexpr std::string_view name = "barotropic_constant"; + + struct Scalar final : GlobalScalarQ { + static constexpr std::string_view symbol = "C"; + }; + + using Quantities = TypeList; + using Constraints = TypeList<>; + using FormList = TypeList<>; + + static constexpr bool constraintsAreValid = + validate_constraints(Constraints{}); + + static_assert(constraintsAreValid); + }; + + // ========================================================================= + // Specific enthalpy + // + // Pressure is deliberately not registered as an independent field. For a + // barotrope it is derived from h through the EOS, while h supplies the + // continuous H1 trace used to define the isobaric stellar surface. + // ========================================================================= + + struct Enthalpy { + static constexpr std::string_view name = "specific_enthalpy"; + static constexpr int scalarOrder = 3; + + struct Scalar final + : ScalarQ> { + static constexpr std::string_view symbol = "h"; + }; + + using Quantities = TypeList; + using Constraints = TypeList<>; + + static constexpr bool constraintsAreValid = + validate_constraints(Constraints{}); + + static_assert(constraintsAreValid); + + struct Form { + // EOS source contribution (rho(h), q_rho). The dynamic order is + // the extra polynomial order introduced by the nonlinear EOS + // beyond the registered order of h. For an n=3 polytrope this is + // 2 * hOrder, making rho(h) cubic in h. + using EosClosureSource = FormSpec< + quadrature::Term::eos_closure, + 1, + Operand, + Operand>; + + // (h, q_h) contribution to + // h + phi - Psi_rotation - C = 0. + using EquilibriumEnthalpy = FormSpec< + quadrature::Term::hydrostatic_equilibrium, + 0, + Operand, + Operand>; + + // (phi, q_h) contribution to hydrostatic equilibrium. + using EquilibriumGravity = FormSpec< + quadrature::Term::hydrostatic_equilibrium, + 0, + Operand, + Operand>; + + // (Psi_rotation, q_h). The rotation-potential order is supplied + // dynamically because it belongs to runtime rotation data. + using EquilibriumRotation = FormSpec< + quadrature::Term::hydrostatic_equilibrium, + 1, + Operand>; + + // (C, q_h), where C is spatially constant. + using EquilibriumConstant = FormSpec< + quadrature::Term::hydrostatic_equilibrium, + 0, + Operand, + Operand>; + + // Boundary trace form available for weak enforcement, testing, or + // a future multiplier formulation of h|Gamma_star = 0. + using IsobaricSurface = FormSpec< + quadrature::Term::isobaric_surface, + 0, + Operand, + Operand>; + + // Integral of P(h). The dynamic order is the extra EOS order + // beyond the registered order of h. + using PressureIntegral = FormSpec< + quadrature::Term::pressure_integral, + 1, + Operand>; + + // Weak pressure force in the displacement test space: + // + // -int P(h) I : grad(w) dV + // + // which is equivalent to -int P(h) div(w) dV. The dynamic order + // is the extra EOS order beyond the registered order of h. For an + // n=3 polytrope this is 3 * hOrder, making P(h) quartic in h. + using PressureForce = FormSpec< + quadrature::Term::pressure_force, + 1, + Operand, + Operand>; + + using ErrorNorm = FormSpec< + quadrature::Term::error_norm, + 0, + Operand, + Operand>; + }; + + using FormList = TypeList< + Form::EosClosureSource, + Form::EquilibriumEnthalpy, + Form::EquilibriumGravity, + Form::EquilibriumRotation, + Form::EquilibriumConstant, + Form::IsobaricSurface, + Form::PressureIntegral, + Form::PressureForce, + Form::ErrorNorm>; + }; + + // ========================================================================= + // Field definition concept + // ========================================================================= + + template + concept FieldTag = + requires { + typename T::Quantities; + typename T::Constraints; + typename T::FormList; + + { T::name } -> std::convertible_to; + } && isRegisteredQuantityList && + isFieldFormList; + + static_assert(FieldTag); + static_assert(FieldTag); + static_assert(FieldTag); + static_assert(FieldTag); + static_assert(FieldTag); + + static_assert(DerivedQuantity); + + static_assert(std::same_as< + RelationTargetT, + Gravity::Potential>); +} // namespace mean_field::field diff --git a/libmeanfield/interface/integrators/advection.cppm b/libmeanfield/interface/integrators/advection.cppm index bfed3cb..60d243e 100644 --- a/libmeanfield/interface/integrators/advection.cppm +++ b/libmeanfield/interface/integrators/advection.cppm @@ -25,4 +25,4 @@ export namespace mean_field::integrators { private: const mapping::DomainMapper &m_map; }; -} \ No newline at end of file +} // namespace mean_field::integrators \ No newline at end of file diff --git a/libmeanfield/interface/integrators/centrifugal.cppm b/libmeanfield/interface/integrators/centrifugal.cppm index ae2d4d7..a663250 100644 --- a/libmeanfield/interface/integrators/centrifugal.cppm +++ b/libmeanfield/interface/integrators/centrifugal.cppm @@ -1,14 +1,19 @@ module; #include export module mean_field:integrators.centrifugal; -import :mapping.domain_mapper; +export import :mapping.domain_mapper; export namespace mean_field::integrators { - class CentrifugalForceIntegrator : public mfem::BlockNonlinearFormIntegrator { + class CentrifugalForceIntegrator + : public mfem::BlockNonlinearFormIntegrator { public: - CentrifugalForceIntegrator(const mapping::DomainMapper& map, const mfem::Vector& omega); + CentrifugalForceIntegrator( + const mapping::DomainMapper &map, + const mfem::Vector &omega + ); - void SetOmega(const mfem::Vector& omega); + void SetOmega(const mfem::Vector &omega); + void SetIntegrationRule(const mfem::IntegrationRule &ir); void AssembleElementVector( const mfem::Array &el, @@ -25,8 +30,9 @@ export namespace mean_field::integrators { ) override; private: - const mapping::DomainMapper& m_map; + const mapping::DomainMapper &m_map; mfem::Vector m_omega; + const mfem::IntegrationRule *m_ir = nullptr; }; -} \ No newline at end of file +} // namespace mean_field::integrators \ No newline at end of file diff --git a/libmeanfield/interface/integrators/coriolis.cppm b/libmeanfield/interface/integrators/coriolis.cppm index 7c22a84..e2616ef 100644 --- a/libmeanfield/interface/integrators/coriolis.cppm +++ b/libmeanfield/interface/integrators/coriolis.cppm @@ -3,26 +3,32 @@ module; export module mean_field:integrators.coriolis; import :mapping.domain_mapper; - export namespace mean_field::integrators { class CoriolisIntegrator : public mfem::BlockNonlinearFormIntegrator { public: - CoriolisIntegrator(const mapping::DomainMapper& map, const mfem::Vector& omega); + CoriolisIntegrator( + const mapping::DomainMapper &map, + const mfem::Vector &omega + ); - void AssembleElementVector(const mfem::Array &el, - mfem::ElementTransformation &Tr, - const mfem::Array &elfun, - const mfem::Array &elvec) override; + void AssembleElementVector( + const mfem::Array &el, + mfem::ElementTransformation &Tr, + const mfem::Array &elfun, + const mfem::Array &elvec + ) override; - void AssembleElementGrad(const mfem::Array &el, - mfem::ElementTransformation &Tr, - const mfem::Array &elfun, - const mfem::Array2D &elmats) override; + void AssembleElementGrad( + const mfem::Array &el, + mfem::ElementTransformation &Tr, + const mfem::Array &elfun, + const mfem::Array2D &elmats + ) override; private: - const mapping::DomainMapper& m_map; + const mapping::DomainMapper &m_map; mfem::Vector m_omega; mfem::DenseMatrix m_omega_mat; }; -} \ No newline at end of file +} // namespace mean_field::integrators \ No newline at end of file diff --git a/libmeanfield/interface/integrators/gravity.cppm b/libmeanfield/interface/integrators/gravity.cppm index e4236fb..7a7f1a4 100644 --- a/libmeanfield/interface/integrators/gravity.cppm +++ b/libmeanfield/interface/integrators/gravity.cppm @@ -1,14 +1,29 @@ module; +#include #include export module mean_field:integrators.gravity; import :mapping.domain_mapper; export namespace mean_field::integrators { - class GravityForceIntegrator : public mfem::BlockNonlinearFormIntegrator { - public: - GravityForceIntegrator(const mapping::DomainMapper& map, const mfem::GridFunction& phi); + enum class GravityForceJacobianMode : std::uint8_t { + minimal, + field_coupled, + exact + }; - void SetPotential(const mfem::GridFunction& phi); + class GravityMomentumIntegrator + : public mfem::BlockNonlinearFormIntegrator { + public: + explicit GravityMomentumIntegrator( + const mapping::DomainMapper &map, + GravityForceJacobianMode jacobian_mode = + GravityForceJacobianMode::field_coupled + ); + + void SetJacobianMode(GravityForceJacobianMode jacobian_mode); + void SetIntegrationRule(const mfem::IntegrationRule &integration_rule); + + [[nodiscard]] GravityForceJacobianMode GetJacobianMode() const; void AssembleElementVector( const mfem::Array &el, @@ -16,7 +31,6 @@ export namespace mean_field::integrators { const mfem::Array &elfun, const mfem::Array &elvec ) override; - void AssembleElementGrad( const mfem::Array &el, mfem::ElementTransformation &Tr, @@ -24,9 +38,9 @@ export namespace mean_field::integrators { const mfem::Array2D &elmats ) override; - private: - const mapping::DomainMapper& m_map; - const mfem::GridFunction* m_phi; + const mapping::DomainMapper &m_map; + GravityForceJacobianMode m_jacobian_mode; + const mfem::IntegrationRule *m_integration_rule{nullptr}; }; -} +} // namespace mean_field::integrators \ No newline at end of file diff --git a/libmeanfield/interface/integrators/mass_continuity.cppm b/libmeanfield/interface/integrators/mass_continuity.cppm index fc6d28e..4c2e69f 100644 --- a/libmeanfield/interface/integrators/mass_continuity.cppm +++ b/libmeanfield/interface/integrators/mass_continuity.cppm @@ -4,9 +4,10 @@ export module mean_field:integrators.mass_continuity; import :mapping.domain_mapper; export namespace mean_field::integrators { - class ContinuityVolumeIntegrator : public mfem::BlockNonlinearFormIntegrator { + class ContinuityVolumeIntegrator + : public mfem::BlockNonlinearFormIntegrator { public: - explicit ContinuityVolumeIntegrator(const mapping::DomainMapper& map); + explicit ContinuityVolumeIntegrator(const mapping::DomainMapper &map); void AssembleElementVector( const mfem::Array &el, @@ -21,13 +22,14 @@ export namespace mean_field::integrators { const mfem::Array &elfun, const mfem::Array2D &elmats ) override; + private: - const mapping::DomainMapper& m_map; + const mapping::DomainMapper &m_map; }; class ContinuityFaceIntegrator : public mfem::BlockNonlinearFormIntegrator { public: - explicit ContinuityFaceIntegrator(const mapping::DomainMapper& map); + explicit ContinuityFaceIntegrator(const mapping::DomainMapper &map); void AssembleFaceVector( const mfem::Array &el1, @@ -44,19 +46,20 @@ export namespace mean_field::integrators { const mfem::Array &elfun, const mfem::Array2D &elmats ) override; + private: - static bool skip_face(const mfem::FaceElementTransformations& Tr); + static bool skip_face(const mfem::FaceElementTransformations &Tr); static double compute_u_n( - const mfem::Vector& v_dofs, - const mfem::Vector& shape_v_minus, - const mfem::Vector& n_unit, + const mfem::Vector &v_dofs, + const mfem::Vector &shape_v_minus, + const mfem::Vector &n_unit, int dof_v_minus, int dim ); private: - const mapping::DomainMapper& m_map; + const mapping::DomainMapper &m_map; }; -} +} // namespace mean_field::integrators diff --git a/libmeanfield/interface/integrators/pressure_gradient.cppm b/libmeanfield/interface/integrators/pressure_gradient.cppm index 7ab4dc9..091adbb 100644 --- a/libmeanfield/interface/integrators/pressure_gradient.cppm +++ b/libmeanfield/interface/integrators/pressure_gradient.cppm @@ -1,36 +1,47 @@ module; -#include #include "xad_promote_polyfill.h" #include +#include export module mean_field:integrators.pressure_gradient; import :mapping.domain_mapper; import :utils.misc; export namespace mean_field::integrators { template - class PressureGradientIntegrator : public mfem::BlockNonlinearFormIntegrator { + class PressureGradientIntegrator + : public mfem::BlockNonlinearFormIntegrator { public: - PressureGradientIntegrator(const mapping::DomainMapper& map, utils::EOS_P eos); + PressureGradientIntegrator( + const mapping::DomainMapper &map, + utils::EOS_P eos + ); + void AssembleElementVector( + const mfem::Array &el, + mfem::ElementTransformation &Tr, + const mfem::Array &elfun, + const mfem::Array &elvec + ) override; + void AssembleElementGrad( + const mfem::Array &el, + mfem::ElementTransformation &Tr, + const mfem::Array &elfun, + const mfem::Array2D &elmats + ) override; - void AssembleElementVector(const mfem::Array &el, - mfem::ElementTransformation &Tr, - const mfem::Array &elfun, - const mfem::Array &elvec) override; - void AssembleElementGrad(const mfem::Array &el, - mfem::ElementTransformation &Tr, - const mfem::Array &elfun, - const mfem::Array2D &elmats) override; private: - const mapping::DomainMapper& m_map; + const mapping::DomainMapper &m_map; utils::EOS_P m_eos; }; template PressureGradientIntegrator::PressureGradientIntegrator( - const mapping::DomainMapper& map, + const mapping::DomainMapper &map, utils::EOS_P eos - ) : m_map(map), m_eos(std::move(eos)) {} + ) + : m_map(map), + m_eos(std::move(eos)) { + } template void PressureGradientIntegrator::AssembleElementVector( @@ -43,16 +54,16 @@ export namespace mean_field::integrators { return; } - const mfem::FiniteElement* fe_v = el[0]; - const mfem::FiniteElement* fe_rho = el[1]; + const mfem::FiniteElement *fe_v = el[0]; + const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - const mfem::Vector& rho_dofs = *elfun[1]; + const mfem::Vector &rho_dofs = *elfun[1]; - mfem::Vector& r_v = *elvec[0]; + mfem::Vector &r_v = *elvec[0]; r_v.SetSize(dof_v * dim); r_v = 0.0; if (elvec[1]) { @@ -63,10 +74,11 @@ export namespace mean_field::integrators { mfem::DenseMatrix dshape_v_ref(dof_v, dim), dshape_v_phys(dof_v, dim); mfem::Vector shape_rho(dof_rho); - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); for (int q = 0; q < ir->GetNPoints(); ++q) { - const mfem::IntegrationPoint& ip = ir->IntPoint(q); + const mfem::IntegrationPoint &ip = ir->IntPoint(q); Tr.SetIntPoint(&ip); auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); @@ -76,13 +88,15 @@ export namespace mean_field::integrators { fe_rho->CalcShape(ip, shape_rho); double rho_val = 0.0; - for (int i = 0; i < dof_rho; ++i) rho_val += rho_dofs(i) * shape_rho(i); + for (int i = 0; i < dof_rho; ++i) + rho_val += rho_dofs(i) * shape_rho(i); // Guard against negative density from Newton solver overshoots - if (rho_val < 1e-15) rho_val = 1e-15; + if (rho_val < 1e-15) + rho_val = 1e-15; // Evaluate the exact Equation of State Pressure - EOS_T x_rho = rho_val; + EOS_T x_rho = rho_val; double P_val = m_eos(x_rho, EOS_T(0.0)).value(); for (int i = 0; i < dof_v; ++i) { @@ -95,36 +109,40 @@ export namespace mean_field::integrators { template void PressureGradientIntegrator::AssembleElementGrad( - const mfem::Array &el, + const mfem::Array &el, mfem::ElementTransformation &Tr, const mfem::Array &elfun, const mfem::Array2D &elmats ) { - const mfem::FiniteElement* fe_v = el[0]; - const mfem::FiniteElement* fe_rho = el[1]; + const mfem::FiniteElement *fe_v = el[0]; + const mfem::FiniteElement *fe_rho = el[1]; - const int dof_v = fe_v->GetDof(); - const int dof_rho = fe_rho->GetDof(); - const int dim = Tr.GetSpaceDim(); + const int dof_v = fe_v->GetDof(); + const int dof_rho = fe_rho->GetDof(); + const int dim = Tr.GetSpaceDim(); - const mfem::Vector& rho_dofs = *elfun[1]; + const mfem::Vector &rho_dofs = *elfun[1]; - mfem::DenseMatrix* dv_dv = elmats(0, 0); - mfem::DenseMatrix* dv_drho = elmats(0, 1); + mfem::DenseMatrix *dv_dv = elmats(0, 0); + mfem::DenseMatrix *dv_drho = elmats(0, 1); - if (dv_dv) *dv_dv = 0.0; - if (dv_drho) *dv_drho = 0.0; - if (!dv_drho) return; + if (dv_dv) + *dv_dv = 0.0; + if (dv_drho) + *dv_drho = 0.0; + if (!dv_drho) + return; mfem::DenseMatrix dshape_v_ref(dof_v, dim), dshape_v_phys(dof_v, dim); mfem::Vector shape_rho(dof_rho); - const mfem::IntegrationRule* ir = &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); + const mfem::IntegrationRule *ir = + &mfem::IntRules.Get(fe_v->GetGeomType(), 2 * fe_v->GetOrder()); for (int q = 0; q < ir->GetNPoints(); ++q) { using Scalar = EOS_T::value_type; xad::Tape tape; - const mfem::IntegrationPoint& ip = ir->IntPoint(q); + const mfem::IntegrationPoint &ip = ir->IntPoint(q); Tr.SetIntPoint(&ip); auto [J_inv, detJ, weight] = m_map.GetQuadratureContext(Tr, ip); @@ -140,29 +158,32 @@ export namespace mean_field::integrators { for (int i = 0; i < dof_rho; ++i) { x_rho += rho_dofs(i) * shape_rho(i); } - if (x_rho < 1e-15) x_rho = EOS_T(1e-15); + if (x_rho < 1e-15) + x_rho = EOS_T(1e-15); EOS_T x_P = m_eos(x_rho, EOS_T(0.0)); tape.registerOutput(x_P); x_P.setAdjoint(1.0); tape.computeAdjoints(); - double dP_drho = x_rho.getAdjoint(); + double dP_drho = x_rho.getAdjoint(); - double debug_K = 1.5; - double debug_n = 3.0; - double analytic_dp = debug_K * (1.0 + 1.0 / debug_n) * std::pow(xad::value(x_rho), 1.0 / debug_n); + double debug_K = 1.5; + double debug_n = 3.0; + double analytic_dp = debug_K * (1.0 + 1.0 / debug_n) * + std::pow(xad::value(x_rho), 1.0 / debug_n); - double ad_err = std::abs(dP_drho - analytic_dp); + double ad_err = std::abs(dP_drho - analytic_dp); for (int i = 0; i < dof_v; ++i) { for (int c = 0; c < dim; ++c) { int row = i + c * dof_v; for (int j = 0; j < dof_rho; ++j) { int col = j; - double term = dshape_v_phys(i, c) * dP_drho * shape_rho(j); + double term = + dshape_v_phys(i, c) * dP_drho * shape_rho(j); (*dv_drho)(row, col) -= term * weight; } } } } } -} +} // namespace mean_field::integrators diff --git a/libmeanfield/interface/integrators/viscosity.cppm b/libmeanfield/interface/integrators/viscosity.cppm index 99ebb49..b7b589b 100644 --- a/libmeanfield/interface/integrators/viscosity.cppm +++ b/libmeanfield/interface/integrators/viscosity.cppm @@ -4,9 +4,13 @@ export module mean_field:integrators.viscosity; import :mapping.domain_mapper; export namespace mean_field::integrators { - class ViscosityIntegrator : public mfem::BlockNonlinearFormIntegrator { + class ViscosityIntegrator : public mfem::BlockNonlinearFormIntegrator { public: - ViscosityIntegrator(const mapping::DomainMapper& map, double mu, int quad_boost); + ViscosityIntegrator( + const mapping::DomainMapper &map, + double mu, + int quad_boost + ); void SetMu(const double mu); @@ -23,10 +27,11 @@ export namespace mean_field::integrators { const mfem::Array &elfun, const mfem::Array2D &elmats ) override; + private: - const mapping::DomainMapper& m_map; + const mapping::DomainMapper &m_map; double m_mu; int m_quad_boost; }; -} +} // namespace mean_field::integrators diff --git a/libmeanfield/interface/mapping/coefficients.cppm b/libmeanfield/interface/mapping/coefficients.cppm index b1fc6fc..2df74de 100644 --- a/libmeanfield/interface/mapping/coefficients.cppm +++ b/libmeanfield/interface/mapping/coefficients.cppm @@ -10,7 +10,7 @@ export namespace mean_field::mapping { public: MappedScalarCoefficient( const DomainMapper &map, - mfem::Coefficient &coeff, + Coefficient &coeff, COORDINATE_SPACE coord_space = COORDINATE_SPACE::PHYSICAL ); @@ -21,14 +21,14 @@ export namespace mean_field::mapping { private: static double eval_at_point( - mfem::Coefficient &c, + Coefficient &c, mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip ); private: const DomainMapper &m_map; - mfem::Coefficient &m_coeff; + Coefficient &m_coeff; COORDINATE_SPACE m_coord_space; }; @@ -42,29 +42,37 @@ export namespace mean_field::mapping { MappedDiffusionCoefficient( const DomainMapper &map, - mfem::MatrixCoefficient &sigma + MatrixCoefficient &sigma ); - void Eval(mfem::DenseMatrix &K, mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override; + void Eval( + mfem::DenseMatrix &K, + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) override; private: const DomainMapper &m_map; mfem::Coefficient *m_scalar; - mfem::MatrixCoefficient *m_tensor; + MatrixCoefficient *m_tensor; }; class MappedVectorCoefficient : public mfem::VectorCoefficient { public: MappedVectorCoefficient( const DomainMapper &map, - mfem::VectorCoefficient &coeff + VectorCoefficient &coeff ); - void Eval(mfem::Vector &V, mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override; + void Eval( + mfem::Vector &V, + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) override; private: const DomainMapper &m_map; - mfem::VectorCoefficient &m_coeff; + VectorCoefficient &m_coeff; }; class PhysicalPositionFunctionCoefficient : public mfem::Coefficient { @@ -76,7 +84,10 @@ export namespace mean_field::mapping { Func f ); - double Eval(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override; + double Eval( + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) override; private: Func m_f; @@ -85,11 +96,18 @@ export namespace mean_field::mapping { class MappedHDivMassCoefficient final : public mfem::MatrixCoefficient { public: - MappedHDivMassCoefficient(const DomainMapper& map, const int dim); + MappedHDivMassCoefficient( + const DomainMapper &map, + const int dim + ); + + void Eval( + mfem::DenseMatrix &matrix, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point + ) override; - void Eval(mfem::DenseMatrix& matrix, mfem::ElementTransformation& transformation, const mfem::IntegrationPoint& integration_point) override; private: - const DomainMapper& m_map; - + const DomainMapper &m_map; }; -} +} // namespace mean_field::mapping diff --git a/libmeanfield/interface/mapping/compactification/compactification.cppm b/libmeanfield/interface/mapping/compactification/compactification.cppm new file mode 100644 index 0000000..383056f --- /dev/null +++ b/libmeanfield/interface/mapping/compactification/compactification.cppm @@ -0,0 +1,46 @@ +module; +#include +export module mean_field:mapping.compactification; +export import :mapping.types; + +export namespace mean_field::mapping::compactification { + struct ExteriorMapInput { + const mfem::Vector &reference_position; + const mfem::Vector &displaced_position; + const mfem::DenseMatrix &displacement_jacobian; + double compactification_coordinate; + const mfem::Vector &compactification_coordinate_gradient; + }; + + struct ExteriorMapResult { + mfem::Vector physical_position; + mfem::DenseMatrix mapping_jacobian; + }; + + struct ExteriorMapDirection { + const mfem::Vector &displaced_position_variation; + const mfem::DenseMatrix &displacement_jacobian_variation; + }; + + struct ExteriorMapVariation { + mfem::Vector physical_position_variation; + mfem::DenseMatrix mapping_jacobian_variation; + }; + + class ExteriorDomainMap { + public: + virtual ~ExteriorDomainMap() = default; + + [[nodiscard]] virtual MappingStatus Evaluate( + const ExteriorMapInput &input, + ExteriorMapResult &result + ) const = 0; + [[nodiscard]] virtual MappingStatus EvaluateVariation( + const ExteriorMapInput &input, + const ExteriorMapResult &result, + const ExteriorMapDirection &direction, + ExteriorMapVariation &variation + ) const = 0; + [[nodiscard]] virtual std::string_view GetName() const noexcept = 0; + }; +} // namespace mean_field::mapping::compactification diff --git a/libmeanfield/interface/mapping/compactification/kelvin.cppm b/libmeanfield/interface/mapping/compactification/kelvin.cppm new file mode 100644 index 0000000..6f02290 --- /dev/null +++ b/libmeanfield/interface/mapping/compactification/kelvin.cppm @@ -0,0 +1,50 @@ +module; +#include + +export module mean_field:mapping.kelvin; +export import :mapping.compactification; +export import :mapping.types; +export import :mapping.compactification.options; + +export namespace mean_field::mapping::compactification { + + class KelvinCompactification final : public ExteriorDomainMap { + public: + explicit KelvinCompactification( + options::KelvinCompactificationOptions options + ); + + [[nodiscard]] MappingStatus Evaluate( + const ExteriorMapInput &input, + ExteriorMapResult &result + ) const override; + + [[nodiscard]] MappingStatus EvaluateVariation( + const ExteriorMapInput &input, + const ExteriorMapResult &result, + const ExteriorMapDirection &direction, + ExteriorMapVariation &variation + ) const override; + + [[nodiscard]] std::string_view GetName() const noexcept override; + + [[nodiscard]] double GetReferenceStellarRadius() const noexcept; + [[nodiscard]] double GetReferenceInfinityRadius() const noexcept; + [[nodiscard]] double GetCoordinateTolerance() const noexcept; + + private: + struct RadialFactors { + double coordinate; + double computational_radius; + double scale; + double scale_derivative; + }; + + [[nodiscard]] MappingStatus ComputeRadialFactors( + double compactification_coordinate, + RadialFactors &factors + ) const; + + options::KelvinCompactificationOptions m_options; + }; +} // namespace mean_field::mapping::compactification \ No newline at end of file diff --git a/libmeanfield/interface/mapping/compactification/options.cppm b/libmeanfield/interface/mapping/compactification/options.cppm new file mode 100644 index 0000000..72a2bc8 --- /dev/null +++ b/libmeanfield/interface/mapping/compactification/options.cppm @@ -0,0 +1,9 @@ +export module mean_field:mapping.compactification.options; + +export namespace mean_field::mapping::compactification::options { + struct KelvinCompactificationOptions { + double r_star_ref{1.0}; + double r_inf_ref{2.0}; + double coordinate_tolerance{1.0e-12}; + }; +} // namespace mean_field::mapping::compactification::options diff --git a/libmeanfield/interface/mapping/domain_mapper.cppm b/libmeanfield/interface/mapping/domain_mapper.cppm index a015773..ce221a2 100644 --- a/libmeanfield/interface/mapping/domain_mapper.cppm +++ b/libmeanfield/interface/mapping/domain_mapper.cppm @@ -3,51 +3,302 @@ module; #include "mean_field.h" export module mean_field:mapping.domain_mapper; +export import :mapping.types; +import :mapping.compactification; +import :utils.user; export namespace mean_field::mapping { + enum class FaceElementSide : uint8_t { element_1, element_2 }; + + class ElementDisplacementData { + public: + ElementDisplacementData( + const mfem::FiniteElement &element, + const mfem::Vector &displacement_dofs, + mfem::Ordering::Type ordering = mfem::Ordering::byNODES + ); + + [[nodiscard]] const mfem::FiniteElement &GetElement() const noexcept; + [[nodiscard]] const mfem::DenseMatrix &GetDofMatrix() const noexcept; + [[nodiscard]] int GetDimension() const noexcept; + [[nodiscard]] int GetDofCount() const noexcept; + [[nodiscard]] mfem::Ordering::Type GetOrdering() const noexcept; + + private: + const mfem::FiniteElement *m_element; + mfem::DenseMatrix m_dof_matrix; + int m_dimension; + mfem::Ordering::Type m_ordering; + }; + + struct CompactificationPointData { + double coordinate{0.0}; + mfem::Vector coordinate_gradient; + }; + + [[nodiscard]] ElementDisplacementData + ElementDisplacementDataFromElementVDofs( + const mfem::FiniteElement &element, + const mfem::Vector &displacement_dofs + ); + + class ElementCompactificationData { + public: + ElementCompactificationData( + const mfem::FiniteElement &element, + const mfem::Vector &dofs + ); + + [[nodiscard]] const mfem::FiniteElement &GetElement() const noexcept; + [[nodiscard]] const mfem::Vector &GetDofs() const noexcept; + [[nodiscard]] int GetDofCount() const noexcept; + + private: + const mfem::FiniteElement *m_element; + mfem::Vector m_dofs; + }; + + struct ElementMappingData { + const ElementDisplacementData &displacement; + const ElementCompactificationData &compactification; + }; + + class DomainMapperStateless { + public: + class Workspace { + public: + explicit Workspace(int dimension = 3); + + void SetDimension(int dimension); + + [[nodiscard]] int GetDimension() const noexcept; + + private: + friend class DomainMapperStateless; + + int m_dimension; + + mfem::Vector m_shape; + mfem::DenseMatrix m_mesh_dshape; + mfem::Vector m_field_value; + mfem::DenseMatrix m_field_jacobian; + + mfem::Vector m_compactification_shape; + mfem::DenseMatrix m_compactification_dshape; + CompactificationPointData m_compactification_point; + + mfem::Vector m_reference_normal; + mfem::Vector m_mapped_normal; + mfem::DenseMatrix m_full_element_jacobian; + + mfem::Vector m_vector_temp; + mfem::DenseMatrix m_matrix_temp_1; + mfem::DenseMatrix m_matrix_temp_2; + + compactification::ExteriorMapResult m_exterior_result; + compactification::ExteriorMapVariation m_exterior_variation; + }; + + public: + DomainMapperStateless( + utils::DomainMapperStatelessOptions options, + std::unique_ptr + exterior_map + ); + + DomainMapperStateless(const DomainMapperStateless &) = delete; + DomainMapperStateless & + operator=(const DomainMapperStateless &) = delete; + DomainMapperStateless(DomainMapperStateless &&) = default; + DomainMapperStateless &operator=(DomainMapperStateless &&) = default; + + [[nodiscard]] MappingStatus EvaluatePoint( + const ElementMappingData &element_data, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + Workspace &workspace, + MappingPointContext &context + ) const; + + [[nodiscard]] MappingStatus EvaluateVolume( + const ElementMappingData &element_data, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + Workspace &workspace, + VolumeMappingContext &context + ) const; + + [[nodiscard]] MappingStatus EvaluateFace( + const ElementMappingData &element_data, + mfem::FaceElementTransformations &transformation, + FaceElementSide side, + const mfem::IntegrationPoint &integration_point, + Workspace &workspace, + FaceMappingContext &context + ) const; + + [[nodiscard]] MappingStatus EvaluatePointVariation( + const ElementMappingData &element_data, + const ElementDisplacementData &direction, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + const MappingPointContext &base_context, + Workspace &workspace, + MappingPointVariation &variation + ) const; + + [[nodiscard]] MappingStatus EvaluateVolumeVariation( + const ElementMappingData &element_data, + const ElementDisplacementData &direction, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + const VolumeMappingContext &base_context, + Workspace &workspace, + VolumeMappingVariation &variation + ) const; + + [[nodiscard]] MappingStatus EvaluateFaceVariation( + const ElementMappingData &element_data, + const ElementDisplacementData &direction, + mfem::FaceElementTransformations &transformation, + FaceElementSide side, + const mfem::IntegrationPoint &integration_point, + const FaceMappingContext &base_context, + Workspace &workspace, + FaceMappingVariation &variation + ) const; + + [[nodiscard]] bool IsCompactifiedElement( + const mfem::ElementTransformation &transformation + ) const noexcept; + [[nodiscard]] int GetDimension() const noexcept; + [[nodiscard]] int GetVacuumElementAttribute() const noexcept; + [[nodiscard]] const compactification::ExteriorDomainMap & + GetExteriorMap() const noexcept; + + private: + void ValidateElementData(const ElementMappingData &element_data) const; + + void EvaluateField( + const ElementDisplacementData &field, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + Workspace &workspace, + mfem::Vector &value, + mfem::DenseMatrix &jacobian + ) const; + + [[nodiscard]] MappingStatus EvaluateCompactificationCoordinate( + const ElementCompactificationData &compactification, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + Workspace &workspace, + CompactificationPointData &point_data + ) const; + + [[nodiscard]] static mfem::ElementTransformation & + SelectFaceElementTransformation( + mfem::FaceElementTransformations &transformation, + FaceElementSide side + ); + + [[nodiscard]] static const mfem::IntegrationPoint & + SelectFaceElementIntegrationPoint( + mfem::FaceElementTransformations &transformation, + FaceElementSide side + ); + + utils::DomainMapperStatelessOptions m_options; + std::unique_ptr + m_exterior_map; + }; class DomainMapper { - public: - struct VolumeQuadratureContext { - mfem::DenseMatrix J_inv; - double detJ; - double weight; - }; - - struct FaceQuadratureContext { - mfem::Vector normal; - double ds; - double v_dot_n_scale; - }; public: - explicit DomainMapper(const double r_star_ref, const double r_inf_ref); + explicit DomainMapper( + const double r_star_ref, + const double r_inf_ref + ); - explicit DomainMapper(const mfem::GridFunction &d, const double r_star_ref, const double r_inf_ref); + explicit DomainMapper( + const mfem::GridFunction &d, + const double r_star_ref, + const double r_inf_ref + ); - [[nodiscard]] bool is_vacuum(const mfem::ElementTransformation &T) const; + [[nodiscard]] bool + is_vacuum(const mfem::ElementTransformation &T) const; void SetDisplacement(const mfem::GridFunction &d); - [[nodiscard]] bool IsIdentity() const; + [[nodiscard]] bool HasCompactification() const noexcept; + [[nodiscard]] bool HasDisplacementField() const noexcept; + [[nodiscard]] bool CalcIsIdentity() const; void ResetDisplacement(); - void ComputeJacobian(mfem::ElementTransformation &T, mfem::DenseMatrix &J) const; + void ComputeJacobian( + mfem::ElementTransformation &T, + mfem::DenseMatrix &J + ) const; - double ComputeDetJ(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) const; + double ComputeDetJ( + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) const; - void ComputeMappedDiffusionTensor(mfem::ElementTransformation &T, mfem::DenseMatrix &D) const; + void ComputeMappedDiffusionTensor( + mfem::ElementTransformation &T, + mfem::DenseMatrix &D + ) const; - void ComputeInverseJacobian(mfem::ElementTransformation &T, mfem::DenseMatrix &JInv) const; + void ComputeInverseJacobian( + mfem::ElementTransformation &T, + mfem::DenseMatrix &JInv + ) const; - VolumeQuadratureContext GetQuadratureContext(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) const; + VolumeQuadratureContext GetQuadratureContext( + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip + ) const; - FaceQuadratureContext GetFaceQuadratureContext(mfem::FaceElementTransformations &T, const mfem::IntegrationPoint &ip) const; + FaceQuadratureContext GetFaceQuadratureContext( + mfem::FaceElementTransformations &T, + const mfem::IntegrationPoint &ip + ) const; - void GetPhysicalPoint(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip, mfem::Vector &x_phys) const; + void GetPhysicalPoint( + mfem::ElementTransformation &T, + const mfem::IntegrationPoint &ip, + mfem::Vector &x_phys + ) const; - void GetVectorValue(const int i, const mfem::IntegrationPoint &ip, mfem::Vector &val) const; + void GetVectorValue( + const int i, + const mfem::IntegrationPoint &ip, + mfem::Vector &val + ) const; + void MapHDivFluxToPhysical( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + const mfem::Vector &reference_flux, + mfem::Vector &physical_flux + ) const; + + void MapPhysicalFluxToHDivReference( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + const mfem::Vector &physical_flux, + mfem::Vector &reference_flux + ) const; + + void MapReferenceGradientToPhysical( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + const mfem::Vector &reference_gradient, + mfem::Vector &physical_gradient + ) const; [[nodiscard]] const mfem::GridFunction *GetDisplacement() const; [[nodiscard]] double GetPhysInfRadius() const; @@ -63,9 +314,17 @@ export namespace mean_field::mapping { private: void InitAllScratchSpaces() const; - void ApplyKelvinMapping(const mfem::Vector &x_ref, mfem::Vector &x_phys) const; + void ApplyKelvinMapping( + const mfem::Vector &x_ref, + mfem::Vector &x_phys + ) const; - void ComputeKelvinJacobian(const mfem::Vector &x_ref, const mfem::Vector &x_disp, const mfem::DenseMatrix &J_D, mfem::DenseMatrix &J) const; + void ComputeKelvinJacobian( + const mfem::Vector &x_ref, + const mfem::Vector &x_disp, + const mfem::DenseMatrix &J_D, + mfem::DenseMatrix &J + ) const; void InvalidateCache() const; @@ -98,6 +357,8 @@ export namespace mean_field::mapping { mutable mfem::Vector m_x_ref; mutable mfem::Vector m_x_disp; mutable mfem::Vector m_d_val; + + bool m_displacement_is_identity{true}; }; -} +} // namespace mean_field::mapping diff --git a/libmeanfield/interface/mapping/transformations.cppm b/libmeanfield/interface/mapping/transformations.cppm new file mode 100644 index 0000000..8e66f29 --- /dev/null +++ b/libmeanfield/interface/mapping/transformations.cppm @@ -0,0 +1,87 @@ +module; +#include +export module mean_field:mapping.transformations; +export import :mapping.types; + +export namespace mean_field::mapping { + void MapHDivFluxToPhysical( + const MappingPointContext &context, + const mfem::Vector &reference_flux, + mfem::Vector &physical_flux + ); + void MapPhysicalFluxToHDivReference( + const MappingPointContext &context, + const mfem::Vector &physical_flux, + mfem::Vector &reference_flux + ); + + void MapReferenceGradientToPhysical( + const MappingPointContext &context, + const mfem::Vector &reference_gradient, + mfem::Vector &physical_gradient + ); + void MapPhysicalGradientToReference( + const MappingPointContext &context, + const mfem::Vector &physical_gradient, + mfem::Vector &reference_gradient + ); + + void MapReferenceVectorGradientToPhysical( + const MappingPointContext &context, + const mfem::DenseMatrix &reference_gradient, + mfem::DenseMatrix &physical_gradient + ); + void MapPhysicalVectorGradientToReference( + const MappingPointContext &context, + const mfem::DenseMatrix &physical_gradient, + mfem::DenseMatrix &reference_gradient + ); + + [[nodiscard]] double MapHDivDivergenceToPhysical( + const MappingPointContext &context, + double reference_divergence + ); + + void ComputeHDivMassTensor( + const MappingPointContext &context, + mfem::DenseMatrix &mass_tensor + ); + void ComputeScalarDiffusionTensor( + const MappingPointContext &context, + mfem::DenseMatrix &diffusion_tensor + ); + + void MapHCurlFieldToPhysical( + const MappingPointContext &context, + const mfem::Vector &reference_field, + mfem::Vector &physical_field + ); + void MapPhysicalFieldToHCurlReference( + const MappingPointContext &context, + const mfem::Vector &physical_field, + mfem::Vector &reference_field + ); + void MapHCurlCurlToPhysical( + const MappingPointContext &context, + const mfem::Vector &reference_curl, + mfem::Vector &physical_curl + ); + void MapPhysicalCurlToHCurlReference( + const MappingPointContext &context, + const mfem::Vector &physical_curl, + mfem::Vector &reference_curl + ); + void ComputeHCurlMassTensor( + const MappingPointContext &context, + mfem::DenseMatrix &mass_tensor + ); + void ComputeHCurlCurlTensor( + const MappingPointContext &context, + mfem::DenseMatrix &curl_tensor + ); + void ComputeHDivMassTensorVariation( + const MappingPointContext &context, + const MappingPointVariation &variation, + mfem::DenseMatrix &mass_tensor_variation + ); +} // namespace mean_field::mapping \ No newline at end of file diff --git a/libmeanfield/interface/mapping/types.cppm b/libmeanfield/interface/mapping/types.cppm index 0b27293..440a401 100644 --- a/libmeanfield/interface/mapping/types.cppm +++ b/libmeanfield/interface/mapping/types.cppm @@ -1,10 +1,77 @@ module; #include +#include export module mean_field:mapping.types; -namespace mean_field::mapping { - enum class COORDINATE_SPACE : uint8_t { - PHYSICAL, - REFERENCE +export namespace mean_field::mapping { + enum class COORDINATE_SPACE : uint8_t { PHYSICAL, REFERENCE }; + + enum class MappingStatus : uint8_t { + valid, + invalid_dimension, + non_finite_input, + invalid_reference_radius, + at_compactified_infinity, + outside_reference_domain, + non_finite_result, + non_positive_determinant }; -} \ No newline at end of file + + struct VolumeQuadratureContext { + mfem::DenseMatrix J_inv; + double detJ; + double weight; + }; + + struct FaceQuadratureContext { + mfem::Vector normal; + double ds; + double v_dot_n_scale; + }; + + struct MappingPointContext { + mfem::Vector reference_position; + mfem::Vector displaced_position; + mfem::Vector physical_position; + mfem::DenseMatrix displacement_jacobian; + mfem::DenseMatrix mapping_jacobian; + mfem::DenseMatrix inverse_mapping_jacobian; + double mapping_determinant{0.0}; + bool compactified{false}; + }; + + struct VolumeMappingContext { + MappingPointContext mapping; + VolumeQuadratureContext quadrature; + }; + + struct FaceMappingContext { + MappingPointContext mapping; + FaceQuadratureContext quadrature; + mfem::Vector reference_normal; + double reference_surface_weight{0.0}; + double physical_surface_weight{0.0}; + }; + + struct MappingPointVariation { + mfem::Vector displacement_variation; + mfem::Vector physical_position_variation; + mfem::DenseMatrix displacement_jacobian_variation; + mfem::DenseMatrix mapping_jacobian_variation; + mfem::DenseMatrix inverse_mapping_jacobian_variation; + double mapping_determinant_variation{0.0}; + }; + + struct VolumeMappingVariation { + MappingPointVariation mapping; + mfem::DenseMatrix inverse_element_jacobian_variation; + double weight_variation{0.0}; + }; + + struct FaceMappingVariation { + MappingPointVariation mapping; + mfem::Vector physical_normal_variation; + double physical_surface_weight_variation{0.0}; + double normal_flux_scale_variation{0.0}; + }; +} // namespace mean_field::mapping \ No newline at end of file diff --git a/libmeanfield/interface/mean_field.cppm b/libmeanfield/interface/mean_field.cppm index 7585566..8693e87 100644 --- a/libmeanfield/interface/mean_field.cppm +++ b/libmeanfield/interface/mean_field.cppm @@ -5,11 +5,18 @@ export import :utils.misc; export import :utils.user; export import :utils.domain; export import :physics.gravity; +export import :physics.solid_body; +export import :physics.barotrope; export import :physics.contexts; export import :boundary.contexts; export import :analysis.integral; export import :mapping.domain_mapper; export import :mapping.coefficients; +export import :mapping.compactification; +export import :mapping.kelvin; +export import :mapping.transformations; +export import :mapping.types; +export import :mapping.compactification.options; export import :integrators.advection; export import :integrators.centrifugal; export import :integrators.gravity; @@ -19,3 +26,22 @@ export import :integrators.pressure_gradient; export import :integrators.viscosity; export import :quadrature.policy; export import :quadrature.mfem; +export import :solver.fields; +export import :utils.blocks; +export import :operators.gravity_field; +export import :operators.gravity_field_jacobian; +export import :operators.kernels.gravity_field; +export import :operators.prepared_gravity_source; +export import :operators.prepared_hdiv_mass; +export import :operators.context.gravity_field; +export import :field.base; +export import :field.registry; +export import :field.mfem; +export import :operators.kernels.barotropic_closure; +export import :operators.prepared_barotropic_closure; +export import :operators.context.barotropic_closure_linearization; +export import :physics.rigid_rotation; +export import :operators.kernels.hydrostatic_equilibrium; +export import :operators.context.hydrostatic_equilibrium; +export import :operators.prepared_hydrostatic_equilibrium; +export import :operators.kernels.pressure_force; diff --git a/libmeanfield/interface/operators/contexts/barotropic_closure_linearization_context.cppm b/libmeanfield/interface/operators/contexts/barotropic_closure_linearization_context.cppm new file mode 100644 index 0000000..dac5c2b --- /dev/null +++ b/libmeanfield/interface/operators/contexts/barotropic_closure_linearization_context.cppm @@ -0,0 +1,76 @@ +module; + +#include + +#include + +export module mean_field:operators.context.barotropic_closure_linearization; + +export import :fem; +export import :mapping.domain_mapper; +export import :operators.prepared_barotropic_closure; +export import :physics.barotrope; + +export namespace mean_field::operators::context::barotropic { + struct BarotropicClosureRevisions final { + std::uint64_t density = 0; + std::uint64_t enthalpy = 0; + std::uint64_t displacement = 0; + + [[nodiscard]] bool + operator==(const BarotropicClosureRevisions &) const noexcept = default; + }; + + class BarotropicClosureLinearizationContext final { + public: + BarotropicClosureLinearizationContext( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope + ); + + void Prepare( + const mfem::Vector &baseDensityTrue, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &displacementTrue, + const BarotropicClosureRevisions &revisions + ); + + [[nodiscard]] bool IsPrepared() const noexcept; + + [[nodiscard]] bool MatchesRevisions( + const BarotropicClosureRevisions &revisions + ) const noexcept; + + [[nodiscard]] std::uint64_t GetPreparationCount() const noexcept; + + [[nodiscard]] const BarotropicClosureRevisions &GetRevisions() const; + + [[nodiscard]] const mfem::Vector &GetBaseDensityTrue() const; + + [[nodiscard]] const mfem::Vector &GetBaseEnthalpyTrue() const; + + [[nodiscard]] const mfem::Vector &GetDisplacementTrue() const; + + [[nodiscard]] + const PreparedBarotropicClosureOperator &GetOperator() const noexcept; + + void BuildResidual(mfem::Vector &residual) const; + + private: + void VerifyPrepared() const; + + const fem::FEM &m_f; + + PreparedBarotropicClosureOperator m_operator; + + mfem::Vector m_baseDensityTrue; + mfem::Vector m_baseEnthalpyTrue; + mfem::Vector m_displacementTrue; + + BarotropicClosureRevisions m_revisions; + + std::uint64_t m_preparationCount = 0; + bool m_isPrepared = false; + }; +} // namespace mean_field::operators::context::barotropic \ No newline at end of file diff --git a/libmeanfield/interface/operators/contexts/gravity_field_context.cppm b/libmeanfield/interface/operators/contexts/gravity_field_context.cppm new file mode 100644 index 0000000..ca48092 --- /dev/null +++ b/libmeanfield/interface/operators/contexts/gravity_field_context.cppm @@ -0,0 +1,157 @@ +module; +#include +#include +#include +#include + +export module mean_field:operators.context.gravity_field; +export import :fem; +export import :mapping.domain_mapper; +export import :operators.prepared_gravity_source; +export import :operators.prepared_hdiv_mass; + +export namespace mean_field::operators::context::gravity_field { + template struct Revision { + std::uint64_t value{0}; + + constexpr auto operator<=>(const Revision &) const = default; + }; + + struct DiscretizationRevisionTag { }; + struct DisplacementRevisionTag { }; + struct DensityRevisionTag { }; + struct GravityGradientRevisionTag { }; + struct GravityPotentialRevisionTag { }; + + using DiscretizationRevision = Revision; + using DisplacementRevision = Revision; + using DensityRevision = Revision; + using GravityGradientRevision = Revision; + using GravityPotentialRevision = Revision; + + struct GravityFieldRevisions { + DiscretizationRevision discretization; + DisplacementRevision displacement; + DensityRevision density; + GravityGradientRevision gravity_gradient; + GravityPotentialRevision gravity_potential; + }; + + struct GravityFieldStateView { + const mfem::Vector &density; + const mfem::Vector &displacement; + const mfem::Vector &gravity_gradient; + const mfem::Vector &gravity_potential; + }; + + struct GravityFieldGeometryPreparation { + bool reconstructed_operators{false}; + bool rebuilt_mass_operator{false}; + bool rebuilt_source_operator{false}; + bool refreshed_variation_state{false}; + + [[nodiscard]] bool DidAnyWork() const noexcept { + return reconstructed_operators || rebuilt_mass_operator || + rebuilt_source_operator || refreshed_variation_state; + } + }; + + class GravityFieldGeometryContext { + public: + GravityFieldGeometryContext( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper + ); + + GravityFieldGeometryContext(const GravityFieldGeometryContext &) = + delete; + GravityFieldGeometryContext & + operator=(const GravityFieldGeometryContext &) = delete; + GravityFieldGeometryContext(GravityFieldGeometryContext &&) = delete; + GravityFieldGeometryContext & + operator=(GravityFieldGeometryContext &&) = delete; + + GravityFieldGeometryPreparation Prepare( + const mfem::Vector &displacement_true, + DiscretizationRevision discretization_revision, + DisplacementRevision displacement_revision + ); + + [[nodiscard]] const PreparedMappedHDivMassOperator & + GetMassOperator() const; + [[nodiscard]] const PreparedMappedGravitySourceOperator & + GetSourceOperator() const; + [[nodiscard]] const mfem::Vector &GetDisplacement() const; + [[nodiscard]] DiscretizationRevision + GetDiscretizationRevision() const noexcept; + [[nodiscard]] DisplacementRevision + GetDisplacementRevision() const noexcept; + [[nodiscard]] bool IsPrepared() const noexcept; + + private: + const fem::FEM &m_fem; + const mapping::DomainMapperStateless &m_domain_mapper; + + std::unique_ptr m_mass_operator; + std::unique_ptr m_source_operator; + + mfem::Vector m_displacement_true; + + DiscretizationRevision m_discretization_revision; + DisplacementRevision m_displacement_revision; + + bool m_is_prepared{false}; + }; + + struct GravityFieldPreparationReport { + GravityFieldGeometryPreparation geometry; + bool updated_density{false}; + bool updated_gravity_gradient{false}; + + [[nodiscard]] bool DidAnyWork() const noexcept { + return geometry.DidAnyWork() || updated_density || + updated_gravity_gradient; + } + }; + + class GravityFieldLinearizationContext { + public: + GravityFieldLinearizationContext( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper + ); + + GravityFieldLinearizationContext( + const GravityFieldLinearizationContext & + ) = delete; + GravityFieldLinearizationContext & + operator=(const GravityFieldLinearizationContext &) = delete; + GravityFieldLinearizationContext(GravityFieldLinearizationContext &&) = + delete; + GravityFieldLinearizationContext & + operator=(GravityFieldLinearizationContext &&) = delete; + + GravityFieldPreparationReport Prepare( + const GravityFieldStateView &state, + const GravityFieldRevisions &revisions + ); + + [[nodiscard]] const GravityFieldGeometryContext & + GetGeometryContext() const; + [[nodiscard]] const mfem::Vector &GetDensity() const; + [[nodiscard]] const mfem::Vector &GetGravityGradient() const; + [[nodiscard]] const GravityFieldRevisions &GetRevisions() const; + [[nodiscard]] bool IsPrepared() const noexcept; + + private: + const fem::FEM &m_fem; + + GravityFieldGeometryContext m_geometry_context; + + mfem::Vector m_density_true; + mfem::Vector m_gravity_gradient_true; + + GravityFieldRevisions m_revisions; + bool m_is_prepared{false}; + }; +} // namespace mean_field::operators::context::gravity_field \ No newline at end of file diff --git a/libmeanfield/interface/operators/contexts/hydrostatic_equilibrium_context.cppm b/libmeanfield/interface/operators/contexts/hydrostatic_equilibrium_context.cppm new file mode 100644 index 0000000..f83b9da --- /dev/null +++ b/libmeanfield/interface/operators/contexts/hydrostatic_equilibrium_context.cppm @@ -0,0 +1,154 @@ +module; + +#include +#include + +#include + +export module mean_field:operators.context.hydrostatic_equilibrium; + +export import :fem; +export import :mapping.domain_mapper; + +export namespace mean_field::operators::context::hydrostatic { + template struct DependencyStamp { + std::uint64_t identity{0}; + std::uint64_t revision{0}; + + [[nodiscard]] constexpr bool + CanFollow(const DependencyStamp &prepared) const noexcept { + return identity != prepared.identity || + revision >= prepared.revision; + } + + constexpr auto operator<=>(const DependencyStamp &) const = default; + }; + + struct DiscretizationDependencyTag { }; + struct EnthalpyDependencyTag { }; + struct GravityPotentialDependencyTag { }; + struct DisplacementDependencyTag { }; + struct RotationDependencyTag { }; + struct BernoulliConstantDependencyTag { }; + + using DiscretizationDependency = + DependencyStamp; + + using EnthalpyDependency = DependencyStamp; + + using GravityPotentialDependency = + DependencyStamp; + + using DisplacementDependency = DependencyStamp; + + using RotationDependency = DependencyStamp; + + using BernoulliConstantDependency = + DependencyStamp; + + struct HydrostaticEquilibriumDependencies { + DiscretizationDependency discretization; + EnthalpyDependency enthalpy; + GravityPotentialDependency gravityPotential; + DisplacementDependency displacement; + RotationDependency rotation; + BernoulliConstantDependency bernoulliConstant; + + constexpr auto + operator<=>(const HydrostaticEquilibriumDependencies &) const = default; + }; + + struct HydrostaticEquilibriumStateView { + const mfem::Vector &enthalpy; + const mfem::Vector &gravityPotential; + const mfem::Vector &displacement; + double bernoulliConstant{0.0}; + }; + + struct HydrostaticPreparationReport { + bool preparedStaticDependencies{false}; + bool preparedGeometryState{false}; + bool preparedRotationDependencies{false}; + bool preparedBaseState{false}; + + bool updatedEnthalpy{false}; + bool updatedGravityPotential{false}; + bool updatedDisplacement{false}; + bool updatedBernoulliConstant{false}; + + [[nodiscard]] bool DidAnyWork() const noexcept { + return preparedStaticDependencies || preparedGeometryState || + preparedRotationDependencies || preparedBaseState; + } + }; + + struct HydrostaticPreparationStatistics { + std::uint64_t staticPreparations{0}; + std::uint64_t geometryPreparations{0}; + std::uint64_t rotationPreparations{0}; + std::uint64_t baseStatePreparations{0}; + + constexpr auto + operator<=>(const HydrostaticPreparationStatistics &) const = default; + }; + + class HydrostaticEquilibriumContext { + public: + HydrostaticEquilibriumContext( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper + ); + + HydrostaticEquilibriumContext(const HydrostaticEquilibriumContext &) = + delete; + + HydrostaticEquilibriumContext & + operator=(const HydrostaticEquilibriumContext &) = delete; + + HydrostaticEquilibriumContext(HydrostaticEquilibriumContext &&) = + delete; + + HydrostaticEquilibriumContext & + operator=(HydrostaticEquilibriumContext &&) = delete; + + HydrostaticPreparationReport Prepare( + const HydrostaticEquilibriumStateView &state, + const HydrostaticEquilibriumDependencies &dependencies + ); + + [[nodiscard]] bool IsPrepared() const noexcept; + + [[nodiscard]] bool MatchesDependencies( + const HydrostaticEquilibriumDependencies &dependencies + ) const noexcept; + + [[nodiscard]] const HydrostaticEquilibriumDependencies & + GetDependencies() const; + + [[nodiscard]] const HydrostaticPreparationStatistics & + GetPreparationStatistics() const noexcept; + + [[nodiscard]] const mfem::Vector &GetBaseEnthalpyTrue() const; + + [[nodiscard]] const mfem::Vector &GetBaseGravityPotentialTrue() const; + + [[nodiscard]] const mfem::Vector &GetDisplacementTrue() const; + + [[nodiscard]] double GetBernoulliConstant() const; + + private: + void VerifyPrepared() const; + + const fem::FEM &m_f; + const mapping::DomainMapperStateless &m_domainMapper; + + mfem::Vector m_baseEnthalpyTrue; + mfem::Vector m_baseGravityPotentialTrue; + mfem::Vector m_displacementTrue; + double m_bernoulliConstant{0.0}; + + HydrostaticEquilibriumDependencies m_dependencies; + HydrostaticPreparationStatistics m_statistics; + bool m_isPrepared{false}; + }; +} // namespace mean_field::operators::context::hydrostatic diff --git a/libmeanfield/interface/operators/gravity_field.cppm b/libmeanfield/interface/operators/gravity_field.cppm new file mode 100644 index 0000000..09a44d6 --- /dev/null +++ b/libmeanfield/interface/operators/gravity_field.cppm @@ -0,0 +1,147 @@ +module; +#include +#include +#include + +export module mean_field:operators.gravity_field; +export import :fem; +export import :mapping.domain_mapper; +export import :operators.gravity_field_jacobian; +export import :operators.context.gravity_field; + +export namespace mean_field::operators { + enum class GravityResidualBlock : std::uint8_t { + gradient_equation = 0, + poisson_equation = 1, + count = 2 + }; + + constexpr int + gravity_residual_block_index(const GravityResidualBlock block) noexcept { + return static_cast(block); + } + + inline constexpr int gravity_residual_block_count = + gravity_residual_block_index(GravityResidualBlock::count); + + class GravityFieldOperator final : public mfem::Operator { + public: + GravityFieldOperator( + fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + context::gravity_field::GravityFieldLinearizationContext + &linearization_context, + const mfem::Array &state_true_offsets, + GravityFieldJacobianOperator &jacobian + ); + + context::gravity_field::GravityFieldPreparationReport Prepare( + const mfem::Vector &state, + const context::gravity_field::GravityFieldRevisions &revisions + ); + + void Mult( + const mfem::Vector &state, + mfem::Vector &residual + ) const override; + + Operator &GetGradient(const mfem::Vector &state) const override; + + [[nodiscard]] const mfem::Array & + GetStateTrueOffsets() const noexcept; + + [[nodiscard]] const mfem::Array & + GetResidualTrueOffsets() const noexcept; + + [[nodiscard]] context::gravity_field::GravityFieldLinearizationContext & + GetLinearizationContext() noexcept; + + [[nodiscard]] const context::gravity_field:: + GravityFieldLinearizationContext & + GetLinearizationContext() const noexcept; + + void ApplyGravityUnknowns( + const mfem::Vector &gravity_gradient, + const mfem::Vector &gravity_potential, + const context::gravity_field::GravityFieldGeometryContext + &geometry_context, + mfem::Vector &action + ) const; + + void ApplyDensitySource( + const mfem::Vector &density, + const context::gravity_field::GravityFieldGeometryContext + &geometry_context, + mfem::Vector &action + ) const; + + private: + fem::FEM &m_fem; + const mapping::DomainMapperStateless &m_domain_mapper; + context::gravity_field::GravityFieldLinearizationContext + &m_linearization_context; + mfem::Array m_state_true_offsets; + mfem::Array m_residual_true_offsets; + GravityFieldJacobianOperator &m_jacobian; + }; + + class ReducedGravityFieldOperator final : public mfem::Operator { + public: + ReducedGravityFieldOperator( + GravityFieldOperator &gravity_field_operator, + context::gravity_field::GravityFieldGeometryContext + &gravity_field_geometry_context, + const mfem::Vector &displacement + ); + + ReducedGravityFieldOperator(const ReducedGravityFieldOperator &) = + delete; + ReducedGravityFieldOperator & + operator=(const ReducedGravityFieldOperator &) = delete; + ReducedGravityFieldOperator(ReducedGravityFieldOperator &&) = delete; + ReducedGravityFieldOperator & + operator=(ReducedGravityFieldOperator &&) = delete; + + void SetDisplacement(const mfem::Vector &displacement); + + [[nodiscard]] const mfem::Vector &GetDisplacement() const; + + void BuildRightHandSide( + const mfem::Vector &density, + mfem::Vector &right_hand_side + ) const; + + void Mult( + const mfem::Vector &gravity_state, + mfem::Vector &action + ) const override; + + [[nodiscard]] GravityFieldOperator &GetGravityFieldOperator() noexcept; + + [[nodiscard]] const GravityFieldOperator & + GetGravityFieldOperator() const noexcept; + + [[nodiscard]] context::gravity_field::GravityFieldGeometryContext & + GetGeometryContext() noexcept; + + [[nodiscard]] const context::gravity_field:: + GravityFieldGeometryContext & + GetGeometryContext() const noexcept; + + [[nodiscard]] const mfem::Array & + GetGravityTrueOffsets() const noexcept; + + private: + void ValidateDisplacement(const mfem::Vector &displacement) const; + + void ValidateDensity(const mfem::Vector &density) const; + + void ValidateGravityState(const mfem::Vector &gravity_state) const; + + private: + GravityFieldOperator &m_gravity_field_operator; + mfem::Array m_gravity_true_offsets; + context::gravity_field::GravityFieldGeometryContext + &m_gravity_field_geometry_context; + }; +} // namespace mean_field::operators \ No newline at end of file diff --git a/libmeanfield/interface/operators/gravity_field_jacobian.cppm b/libmeanfield/interface/operators/gravity_field_jacobian.cppm new file mode 100644 index 0000000..0bda980 --- /dev/null +++ b/libmeanfield/interface/operators/gravity_field_jacobian.cppm @@ -0,0 +1,38 @@ +module; +#include + +export module mean_field:operators.gravity_field_jacobian; +export import :fem; +export import :mapping.domain_mapper; +export import :operators.context.gravity_field; + +export namespace mean_field::operators { + class GravityFieldJacobianOperator final : public mfem::Operator { + public: + GravityFieldJacobianOperator( + fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const context::gravity_field::GravityFieldLinearizationContext + &linearization_context, + const mfem::Array &state_true_offsets, + const mfem::Array &residual_true_offsets + ); + + void Mult( + const mfem::Vector &direction, + mfem::Vector &action + ) const override; + + [[nodiscard]] const context::gravity_field:: + GravityFieldLinearizationContext & + GetLinearizationContext() const noexcept; + + private: + fem::FEM &m_fem; + const mapping::DomainMapperStateless &m_domain_mapper; + const context::gravity_field::GravityFieldLinearizationContext + &m_linearization_context; + mfem::Array m_state_true_offsets; + mfem::Array m_residual_true_offsets; + }; +} // namespace mean_field::operators \ No newline at end of file diff --git a/libmeanfield/interface/operators/kernels/barotropic_closure_kernels.cppm b/libmeanfield/interface/operators/kernels/barotropic_closure_kernels.cppm new file mode 100644 index 0000000..722ea82 --- /dev/null +++ b/libmeanfield/interface/operators/kernels/barotropic_closure_kernels.cppm @@ -0,0 +1,51 @@ +module; + +#include + +export module mean_field:operators.kernels.barotropic_closure; + +export import :fem; +export import :mapping.domain_mapper; +export import :physics.barotrope; + +export namespace mean_field::operators::kernels { + void apply_barotropic_closure( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope, + const mfem::Vector &densityTrue, + const mfem::Vector &enthalpyTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &residual + ); + + void apply_barotropic_closure_density_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope, + const mfem::Vector &densityVariationTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &action + ); + + void apply_barotropic_closure_enthalpy_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &enthalpyVariationTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &action + ); + + void apply_barotropic_closure_displacement_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope, + const mfem::Vector &baseDensityTrue, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &displacementTrue, + const mfem::Vector &displacementVariationTrue, + mfem::Vector &action + ); +} // namespace mean_field::operators::kernels \ No newline at end of file diff --git a/libmeanfield/interface/operators/kernels/gravity_kernels.cppm b/libmeanfield/interface/operators/kernels/gravity_kernels.cppm new file mode 100644 index 0000000..538dcba --- /dev/null +++ b/libmeanfield/interface/operators/kernels/gravity_kernels.cppm @@ -0,0 +1,42 @@ +module; +#include +export module mean_field:operators.kernels.gravity_field; +export import :mapping.domain_mapper; +export import :fem; + +export namespace mean_field::operators::kernels { + + void apply_mapped_hdiv_mass( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &gravity_gradient_true, + const mfem::Vector &displacement_true, + mfem::Vector &action + ); + + void apply_mapped_source( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &density_true, + const mfem::Vector &displacement_true, + mfem::Vector &action + ); + + void apply_mapped_hdiv_mass_variation( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &gravity_gradient_true, + const mfem::Vector &displacement_true, + const mfem::Vector &displacement_variation_true, + mfem::Vector &action + ); + + void apply_mapped_source_variation( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &density_true, + const mfem::Vector &displacement_true, + const mfem::Vector &displacement_variation_true, + mfem::Vector &action_variation + ); +} // namespace mean_field::operators::kernels diff --git a/libmeanfield/interface/operators/kernels/hydrostatic_equilibrium_kernels.cppm b/libmeanfield/interface/operators/kernels/hydrostatic_equilibrium_kernels.cppm new file mode 100644 index 0000000..f97f606 --- /dev/null +++ b/libmeanfield/interface/operators/kernels/hydrostatic_equilibrium_kernels.cppm @@ -0,0 +1,73 @@ +module; + +#include + +export module mean_field:operators.kernels.hydrostatic_equilibrium; + +export import :fem; +export import :mapping.domain_mapper; +export import :physics.rigid_rotation; + +export namespace mean_field::operators::kernels { + void apply_hydrostatic_equilibrium( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::RigidRotation &rotation, + const mfem::Vector &enthalpyTrue, + const mfem::Vector &potentialTrue, + const mfem::Vector &displacementTrue, + double bernoulliConstant, + mfem::Vector &residual + ); + + void apply_hydrostatic_equilibrium_enthalpy_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const mfem::Vector &enthalpyVariationTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &action + ); + + void apply_hydrostatic_equilibrium_potential_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const mfem::Vector &potentialVariationTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &action + ); + + void apply_hydrostatic_equilibrium_constant_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + double constantVariation, + const mfem::Vector &displacementTrue, + mfem::Vector &action + ); + + void apply_hydrostatic_equilibrium_displacement_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::RigidRotation &rotation, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &basePotentialTrue, + const mfem::Vector &baseDisplacementTrue, + double baseBernoulliConstant, + const mfem::Vector &displacementVariationTrue, + mfem::Vector &action + ); + + void apply_hydrostatic_equilibrium_action( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::RigidRotation &rotation, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &basePotentialTrue, + const mfem::Vector &baseDisplacementTrue, + double baseBernoulliConstant, + const mfem::Vector &enthalpyVariationTrue, + const mfem::Vector &potentialVariationTrue, + double constantVariation, + const mfem::Vector &displacementVariationTrue, + mfem::Vector &action + ); +} // namespace mean_field::operators::kernels \ No newline at end of file diff --git a/libmeanfield/interface/operators/kernels/pressure_force_kernels.cppm b/libmeanfield/interface/operators/kernels/pressure_force_kernels.cppm new file mode 100644 index 0000000..7288fa2 --- /dev/null +++ b/libmeanfield/interface/operators/kernels/pressure_force_kernels.cppm @@ -0,0 +1,20 @@ +module; + +#include + +export module mean_field:operators.kernels.pressure_force; + +export import :fem; +export import :mapping.domain_mapper; +export import :physics.barotrope; + +export namespace mean_field::operators::kernels { + void apply_pressure_force_residual( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope, + const mfem::Vector &enthalpyTrue, + const mfem::Vector &displacementTrue, + mfem::Vector &residualTrue + ); +} // namespace mean_field::operators::kernels \ No newline at end of file diff --git a/libmeanfield/interface/operators/prepared_barotropic_closure_operator.cppm b/libmeanfield/interface/operators/prepared_barotropic_closure_operator.cppm new file mode 100644 index 0000000..f53abcf --- /dev/null +++ b/libmeanfield/interface/operators/prepared_barotropic_closure_operator.cppm @@ -0,0 +1,90 @@ +module; + +#include +#include +#include + +export module mean_field:operators.prepared_barotropic_closure; + +export import :fem; +export import :mapping.domain_mapper; +export import :physics.barotrope; + +export namespace mean_field::operators { + class PreparedBarotropicClosureOperator final : public mfem::Operator { + public: + PreparedBarotropicClosureOperator( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper, + const physics::PolytropicBarotrope &barotrope + ); + + void Prepare( + const mfem::Vector &baseDensityTrue, + const mfem::Vector &baseEnthalpyTrue, + const mfem::Vector &displacementTrue + ); + + void Mult( + const mfem::Vector &densityVariationTrue, + const mfem::Vector &enthalpyVariationTrue, + const mfem::Vector &displacementVariationTrue, + mfem::Vector &action + ) const; + + void Mult( + const mfem::Vector &combinedVariation, + mfem::Vector &action + ) const override; + + void BuildResidual(mfem::Vector &residual) const; + + [[nodiscard]] bool IsPrepared() const noexcept; + + [[nodiscard]] std::uint64_t GetPreparationCount() const noexcept; + + [[nodiscard]] int GetDensitySize() const noexcept; + + [[nodiscard]] int GetEnthalpySize() const noexcept; + + private: + void VerifyPrepared() const; + + void Mult( + const mfem::Vector &densityVariationTrue, + const mfem::Vector &enthalpyVariationTrue, + mfem::Vector &action + ) const; + + struct ElementPAData { + mfem::Array densityDofs; + mfem::Array enthalpyDofs; + + mfem::DofTransformation *densityDofTransformation{nullptr}; + mfem::DofTransformation *enthalpyDofTransformation{nullptr}; + + mfem::DenseMatrix densityBasis; + mfem::DenseMatrix enthalpyBasis; + + mfem::Vector weightedResidual; + mfem::Vector quadratureWeights; + mfem::Vector weightedEnthalpyDerivative; + }; + + const fem::FEM &m_fem; + const mapping::DomainMapperStateless &m_domainMapper; + const physics::PolytropicBarotrope &m_barotrope; + + std::vector m_elements; + + mfem::Vector m_baseDensityTrue; + mfem::Vector m_baseEnthalpyTrue; + mfem::Vector m_baseDisplacementTrue; + + int m_densitySize{0}; + int m_enthalpySize{0}; + + std::uint64_t m_preparationCount{0}; + bool m_isPrepared{false}; + }; +} // namespace mean_field::operators diff --git a/libmeanfield/interface/operators/prepared_gravity_source.cppm b/libmeanfield/interface/operators/prepared_gravity_source.cppm new file mode 100644 index 0000000..6cc29f0 --- /dev/null +++ b/libmeanfield/interface/operators/prepared_gravity_source.cppm @@ -0,0 +1,61 @@ +module; +#include +#include +#include +#include + +export module mean_field:operators.prepared_gravity_source; +export import :fem; +export import :mapping.domain_mapper; + +export namespace mean_field::operators { + class PreparedMappedGravitySourceOperator final : public mfem::Operator { + public: + PreparedMappedGravitySourceOperator( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper + ); + + void Prepare(const mfem::Vector &displacement_true); + void Mult( + const mfem::Vector &density_true, + mfem::Vector &action + ) const override; + + [[nodiscard]] bool IsPrepared() const noexcept; + [[nodiscard]] std::uint64_t GetPreparationCount() const noexcept; + + void MultTranspose( + const mfem::Vector &potential_true, + mfem::Vector &action + ) const override; + + private: + struct ElementPAData { + int element_id{-1}; + + mfem::Array density_dofs; + mfem::Array potential_dofs; + + mfem::DofTransformation *density_dof_transformation{nullptr}; + mfem::DofTransformation *potential_dof_transformation{nullptr}; + + // Rows are quadrature points; columns are element DOFs. + mfem::DenseMatrix density_basis; + mfem::DenseMatrix potential_basis; + + // Contains quadrature weight, mesh Jacobian, mapped Jacobian, + // and 4*pi*G. + mfem::Vector quadrature_data; + }; + + const fem::FEM &m_fem; + const mapping::DomainMapperStateless &m_domain_mapper; + + mfem::Array m_stellar_marker; + std::vector m_elements; + + std::uint64_t m_preparation_count{0}; + bool m_is_prepared{false}; + }; +} // namespace mean_field::operators diff --git a/libmeanfield/interface/operators/prepared_hdiv_mass.cppm b/libmeanfield/interface/operators/prepared_hdiv_mass.cppm new file mode 100644 index 0000000..e4f2285 --- /dev/null +++ b/libmeanfield/interface/operators/prepared_hdiv_mass.cppm @@ -0,0 +1,40 @@ +module; +#include +#include +#include + +export module mean_field:operators.prepared_hdiv_mass; +export import :fem; +export import :mapping.domain_mapper; + +export namespace mean_field::operators { + class PreparedMappedHDivMassOperator final : public mfem::Operator { + public: + PreparedMappedHDivMassOperator( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper + ); + + void Prepare(const mfem::Vector &displacement_true); + void Mult( + const mfem::Vector &gravity_gradient_true, + mfem::Vector &action + ) const override; + + [[nodiscard]] bool IsPrepared() const noexcept; + [[nodiscard]] std::uint64_t GetPreparationCount() const noexcept; + + private: + const fem::FEM &m_fem; + const mapping::DomainMapperStateless &m_domain_mapper; + + mfem::Array m_stellar_marker; + mfem::Array m_vacuum_marker; + + std::unique_ptr m_stellar_mass_coefficient; + std::unique_ptr m_vacuum_mass_coefficient; + std::unique_ptr m_mass_form; + std::uint64_t m_preparation_count{0}; + bool m_is_prepared{false}; + }; +} // namespace mean_field::operators \ No newline at end of file diff --git a/libmeanfield/interface/operators/prepared_hydrostatic_equilibrium_operator.cppm b/libmeanfield/interface/operators/prepared_hydrostatic_equilibrium_operator.cppm new file mode 100644 index 0000000..8d27969 --- /dev/null +++ b/libmeanfield/interface/operators/prepared_hydrostatic_equilibrium_operator.cppm @@ -0,0 +1,278 @@ +module; + +#include +#include +#include +#include +#include + +#include + +export module mean_field:operators.prepared_hydrostatic_equilibrium; + +export import :fem; +export import :mapping.domain_mapper; +export import :operators.context.hydrostatic_equilibrium; +export import :physics.rigid_rotation; + +export namespace mean_field::operators { + struct PreparedHydrostaticEquilibriumReport { + context::hydrostatic::HydrostaticPreparationReport contextReport; + + bool updatedRotation{false}; + bool preparedAlgebraicJacobianBlocks{false}; + bool preparedDisplacementJacobianData{false}; + bool preparedResidual{false}; + + [[nodiscard]] bool DidAnyWork() const noexcept { + return contextReport.DidAnyWork() || updatedRotation || + preparedAlgebraicJacobianBlocks || + preparedDisplacementJacobianData || preparedResidual; + } + }; + + struct PreparedHydrostaticAlgebraicJacobianStatistics { + std::uint64_t preparations{0}; + std::uint64_t enthalpyApplications{0}; + std::uint64_t gravityPotentialApplications{0}; + std::uint64_t bernoulliConstantApplications{0}; + std::uint64_t combinedApplications{0}; + + constexpr auto operator<=>( + const PreparedHydrostaticAlgebraicJacobianStatistics & + ) const = default; + }; + + struct PreparedHydrostaticDisplacementJacobianStatistics { + std::uint64_t preparations{0}; + std::uint64_t applications{0}; + + constexpr auto operator<=>( + const PreparedHydrostaticDisplacementJacobianStatistics & + ) const = default; + }; + + struct PreparedHydrostaticCompleteJacobianStatistics { + std::uint64_t applications{0}; + + constexpr auto operator<=>( + const PreparedHydrostaticCompleteJacobianStatistics & + ) const = default; + }; + + enum class HydrostaticJacobianInputBlock : int { + enthalpy = 0, + gravityPotential = 1, + bernoulliConstant = 2, + displacement = 3 + }; + + class HydrostaticJacobianBlockLayout final { + public: + explicit HydrostaticJacobianBlockLayout(const fem::FEM &f); + + [[nodiscard]] int Offset(HydrostaticJacobianInputBlock block) const; + + [[nodiscard]] int Size(HydrostaticJacobianInputBlock block) const; + + [[nodiscard]] int GetTotalSize() const noexcept; + + [[nodiscard]] int GetResidualSize() const noexcept; + + private: + int m_enthalpySize{0}; + int m_gravityPotentialSize{0}; + int m_displacementSize{0}; + int m_totalSize{0}; + int m_residualSize{0}; + }; + + class PreparedHydrostaticEquilibriumOperator final { + public: + PreparedHydrostaticEquilibriumOperator( + const fem::FEM &f, + const mapping::DomainMapperStateless &domainMapper + ); + + PreparedHydrostaticEquilibriumOperator( + const PreparedHydrostaticEquilibriumOperator & + ) = delete; + + PreparedHydrostaticEquilibriumOperator & + operator=(const PreparedHydrostaticEquilibriumOperator &) = delete; + + PreparedHydrostaticEquilibriumOperator( + PreparedHydrostaticEquilibriumOperator && + ) = delete; + + PreparedHydrostaticEquilibriumOperator & + operator=(PreparedHydrostaticEquilibriumOperator &&) = delete; + + PreparedHydrostaticEquilibriumReport Prepare( + const context::hydrostatic::HydrostaticEquilibriumStateView &state, + const context::hydrostatic::HydrostaticEquilibriumDependencies + &dependencies, + const physics::RigidRotation &rotation + ); + + void BuildResidual(mfem::Vector &residual) const; + + void ApplyEnthalpyJacobianAction( + const mfem::Vector &enthalpyVariation, + mfem::Vector &action + ) const; + + void ApplyGravityPotentialJacobianAction( + const mfem::Vector &gravityPotentialVariation, + mfem::Vector &action + ) const; + + void ApplyBernoulliConstantJacobianAction( + double bernoulliConstantVariation, + mfem::Vector &action + ) const; + + void ApplyAlgebraicJacobianAction( + const mfem::Vector &enthalpyVariation, + const mfem::Vector &gravityPotentialVariation, + double bernoulliConstantVariation, + mfem::Vector &action + ) const; + + void ApplyDisplacementJacobianAction( + const mfem::Vector &displacementVariation, + mfem::Vector &action + ) const; + + void ApplyCompleteJacobianAction( + const mfem::Vector &enthalpyVariation, + const mfem::Vector &gravityPotentialVariation, + double bernoulliConstantVariation, + const mfem::Vector &displacementVariation, + mfem::Vector &action + ) const; + + [[nodiscard]] bool IsPrepared() const noexcept; + + [[nodiscard]] const context::hydrostatic:: + HydrostaticPreparationStatistics & + GetContextPreparationStatistics() const noexcept; + + [[nodiscard]] std::uint64_t + GetResidualPreparationCount() const noexcept; + + [[nodiscard]] std::uint64_t + GetResidualApplicationCount() const noexcept; + + [[nodiscard]] const PreparedHydrostaticAlgebraicJacobianStatistics & + GetAlgebraicJacobianStatistics() const noexcept; + + [[nodiscard]] const PreparedHydrostaticDisplacementJacobianStatistics & + GetDisplacementJacobianStatistics() const noexcept; + + [[nodiscard]] const PreparedHydrostaticCompleteJacobianStatistics & + GetCompleteJacobianStatistics() const noexcept; + + [[nodiscard]] std::size_t GetStellarElementCount() const noexcept; + + [[nodiscard]] const fem::FEM &GetFEM() const noexcept; + + private: + struct ElementPAData { + int elementId{-1}; + + mfem::Array enthalpyDofs; + mfem::Array gravityPotentialDofs; + mfem::Array displacementDofs; + + mfem::DofTransformation *enthalpyDofTransformation{nullptr}; + + mfem::DofTransformation *gravityPotentialDofTransformation{nullptr}; + + mfem::DofTransformation *displacementDofTransformation{nullptr}; + + const mfem::IntegrationRule *integrationRule{nullptr}; + + // Rows are quadrature points and columns are element DOFs. + mfem::DenseMatrix enthalpyBasis; + mfem::DenseMatrix gravityPotentialBasis; + + // Rows are quadrature points and columns are physical components. + mfem::DenseMatrix physicalPositions; + + mfem::Vector quadratureWeights; + std::vector baseMappingContexts; + + std::optional + baseDisplacementData; + + std::optional + compactificationData; + + mfem::Vector rotationPotential; + mfem::DenseMatrix rotationGradient; + mfem::Vector hydrostaticImbalance; + mfem::Vector weightedResidual; + + // Geometry-dependent algebraic Jacobian blocks. + mfem::DenseMatrix enthalpyJacobian; + mfem::DenseMatrix gravityPotentialJacobian; + mfem::Vector bernoulliConstantJacobian; + }; + + void PrepareStaticPlan(); + void PrepareGeometry(); + void PrepareAlgebraicJacobianBlocks(); + void PrepareRotation(); + void PrepareBaseState(); + void FinalizeDisplacementJacobianPreparation(); + void AssembleCachedResidual(); + void VerifyPrepared() const; + + const fem::FEM &m_fem; + const mapping::DomainMapperStateless &m_domainMapper; + + context::hydrostatic::HydrostaticEquilibriumContext m_context; + + std::optional m_rotation; + std::vector m_elements; + mfem::Vector m_cachedResidual; + + std::uint64_t m_residualPreparationCount{0}; + + mutable std::uint64_t m_residualApplicationCount{0}; + + mutable PreparedHydrostaticAlgebraicJacobianStatistics + m_algebraicJacobianStatistics; + + mutable PreparedHydrostaticDisplacementJacobianStatistics + m_displacementJacobianStatistics; + + mutable PreparedHydrostaticCompleteJacobianStatistics + m_completeJacobianStatistics; + + bool m_isPrepared{false}; + }; + + class PreparedHydrostaticEquilibriumJacobianOperator final + : public mfem::Operator { + public: + PreparedHydrostaticEquilibriumJacobianOperator( + const fem::FEM &f, + const PreparedHydrostaticEquilibriumOperator &preparedOperator + ); + + void Mult( + const mfem::Vector &direction, + mfem::Vector &action + ) const override; + + [[nodiscard]] const HydrostaticJacobianBlockLayout & + GetLayout() const noexcept; + + private: + HydrostaticJacobianBlockLayout m_layout; + + const PreparedHydrostaticEquilibriumOperator &m_preparedOperator; + }; +} // namespace mean_field::operators diff --git a/libmeanfield/interface/physics/barotrope.cppm b/libmeanfield/interface/physics/barotrope.cppm new file mode 100644 index 0000000..9958aca --- /dev/null +++ b/libmeanfield/interface/physics/barotrope.cppm @@ -0,0 +1,173 @@ +module; + +#include +#include +#include + +export module mean_field:physics.barotrope; + +export namespace mean_field::physics { + class PolytropicBarotrope final { + public: + PolytropicBarotrope( + const double polytropic_index, + const double polytropic_constant + ) + : m_polytropic_index(polytropic_index), + m_polytropic_constant(polytropic_constant), + m_enthalpy_scale((polytropic_index + 1.0) * polytropic_constant) { + if (!std::isfinite(polytropic_index) || polytropic_index < 1.0) { + throw std::invalid_argument( + std::format( + "The differentiable polytropic closure requires a " + "finite polytropic index greater than or equal to one. " + "Instead a value of {} has been provided", + polytropic_index + ) + ); + } + + if (!std::isfinite(polytropic_constant) || + polytropic_constant <= 0.0) { + throw std::invalid_argument( + std::format( + "The polytropic constant must be finite and positive. " + "Instead a value of {} has been provided", + polytropic_constant + ) + ); + } + }; + + [[nodiscard]] double polytropic_index() const noexcept { + return m_polytropic_index; + } + + [[nodiscard]] double polytropic_constant() const noexcept { + return m_polytropic_constant; + } + + [[nodiscard]] double enthalpy_scale() const noexcept { + return m_enthalpy_scale; + } + + [[nodiscard]] double pressure_from_density(const double density) const { + validate_nonnegativity(density, "density"); + if (density == 0.0) { + return 0.0; + } + + return m_polytropic_constant * + std::pow(density, 1.0 + 1.0 / m_polytropic_index); + } + + [[nodiscard]] double enthalpy_from_density(const double density) const { + validate_nonnegativity(density, "density"); + if (density == 0.0) { + return 0.0; + } + + return m_enthalpy_scale * + std::pow(density, 1.0 / m_polytropic_index); + } + + [[nodiscard]] double + density_from_enthalpy(const double enthalpy) const { + validate_finite(enthalpy, "enthalpy"); + + if (enthalpy <= 0.0) { + return 0.0; + } + + return std::pow(enthalpy / m_enthalpy_scale, m_polytropic_index); + } + + [[nodiscard]] double + pressure_from_enthalpy(const double enthalpy) const { + validate_finite(enthalpy, "enthalpy"); + + if (enthalpy <= 0.0) { + return 0.0; + } + + return density_from_enthalpy(enthalpy) * enthalpy / + (m_polytropic_index + 1.0); + } + + [[nodiscard]] double + density_derivative_from_enthalpy(const double enthalpy) const { + validate_finite(enthalpy, "enthalpy"); + if (enthalpy < 0.0) { + return 0.0; + } + + if (enthalpy == 0.0) { + return m_polytropic_index == 1.0 ? 1.0 / m_enthalpy_scale : 0.0; + } + + return m_polytropic_index / m_enthalpy_scale * + std::pow( + enthalpy / m_enthalpy_scale, m_polytropic_index - 1.0 + ); + } + + [[nodiscard]] double + pressure_derivative_from_enthalpy(const double enthalpy) const { + validate_finite(enthalpy, "enthalpy"); + + if (enthalpy <= 0.0) { + return 0.0; + } + + return density_from_enthalpy(enthalpy); + } + + [[nodiscard]] double + pressure_derivative_from_density(const double density) const { + validate_nonnegativity(density, "density"); + if (density == 0.0) { + return 0.0; + } + + return m_polytropic_constant * (1.0 + 1.0 / m_polytropic_index) * + std::pow(density, 1.0 / m_polytropic_index); + } + + private: + static void validate_finite( + const double value, + const char *quantity + ) { + if (!std::isfinite(value)) { + throw std::domain_error( + std::format( + "The {} must be finite. Instead a value of {} has been " + "provided", + quantity, value + ) + ); + } + } + + static void validate_nonnegativity( + const double value, + const char *quantity + ) { + validate_finite(value, quantity); + if (value < 0.0) { + throw std::domain_error( + std::format( + "The {} must be non-negative. Instead a value of {} " + "has been " + "provided", + quantity, value + ) + ); + } + } + + double m_polytropic_index; + double m_polytropic_constant; + double m_enthalpy_scale; + }; +} // namespace mean_field::physics \ No newline at end of file diff --git a/libmeanfield/interface/physics/context.cppm b/libmeanfield/interface/physics/context.cppm index 7ca3517..80e405d 100644 --- a/libmeanfield/interface/physics/context.cppm +++ b/libmeanfield/interface/physics/context.cppm @@ -1,4 +1,5 @@ module; +#include #include export module mean_field:physics.contexts; @@ -23,6 +24,6 @@ export namespace mean_field::physics { std::unique_ptr Schur; std::unique_ptr mapped_hdiv_mass_coeff; - + std::unique_ptr source_form; }; -} +} // namespace mean_field::physics diff --git a/libmeanfield/interface/physics/gravity.cppm b/libmeanfield/interface/physics/gravity.cppm index a030615..6fa5f90 100644 --- a/libmeanfield/interface/physics/gravity.cppm +++ b/libmeanfield/interface/physics/gravity.cppm @@ -10,7 +10,10 @@ export namespace mean_field::physics { mfem::ParGridFunction gradPhi; mfem::ParGridFunction phi; - explicit GravitySolution(fem::FEM& fem): gradPhi(fem.RT_fes.get()), phi(fem.L2_fes.get()) {} + explicit GravitySolution(fem::FEM &fem) + : gradPhi(fem.gravityFluxFes.get()), + phi(fem.gravityPotentialFes.get()) { + } }; GravitySolution grav_potential( @@ -20,6 +23,13 @@ export namespace mean_field::physics { bool phi_warm = false ); + GravitySolution grav_potential_new( + fem::FEM &f, + const utils::Args &args, + const mfem::GridFunction &rho, + const mfem::GridFunction &displacement + ); + mfem::GridFunction get_potential( fem::FEM &fem, const utils::Args &args, @@ -40,6 +50,4 @@ export namespace mean_field::physics { ); void update_stiffness_matrix(fem::FEM &fem); -} - - +} // namespace mean_field::physics diff --git a/libmeanfield/interface/physics/rigid_rotation.cppm b/libmeanfield/interface/physics/rigid_rotation.cppm new file mode 100644 index 0000000..9d7c25b --- /dev/null +++ b/libmeanfield/interface/physics/rigid_rotation.cppm @@ -0,0 +1,127 @@ +module; + +#include +#include + +export module mean_field:physics.rigid_rotation; + +export namespace mean_field::physics { + class RigidRotation final { + public: + RigidRotation( + const mfem::Vector &angularVelocity, + const mfem::Vector ¢er + ) + : m_angularVelocity(angularVelocity), + m_center(center) { + MFEM_VERIFY( + m_angularVelocity.Size() == 3, + "RigidRotation requires a three-dimensional " + "angular-velocity vector." + ); + + MFEM_VERIFY( + m_center.Size() == 3, + "RigidRotation requires a three-dimensional center." + ); + + for (int component = 0; component < 3; ++component) { + MFEM_VERIFY( + std::isfinite(m_angularVelocity(component)), + "RigidRotation received a non-finite " + "angular-velocity component." + ); + + MFEM_VERIFY( + std::isfinite(m_center(component)), + "RigidRotation received a non-finite center component." + ); + } + } + + [[nodiscard]] double + potential(const mfem::Vector &physicalPosition) const { + MFEM_VERIFY( + physicalPosition.Size() == 3, + "RigidRotation::potential requires a " + "three-dimensional position." + ); + + const double relativeX = physicalPosition(0) - m_center(0); + + const double relativeY = physicalPosition(1) - m_center(1); + + const double relativeZ = physicalPosition(2) - m_center(2); + + const double crossX = m_angularVelocity(1) * relativeZ - + m_angularVelocity(2) * relativeY; + + const double crossY = m_angularVelocity(2) * relativeX - + m_angularVelocity(0) * relativeZ; + + const double crossZ = m_angularVelocity(0) * relativeY - + m_angularVelocity(1) * relativeX; + + return 0.5 * (crossX * crossX + crossY * crossY + crossZ * crossZ); + } + + [[nodiscard]] double potential_directional_derivative( + const mfem::Vector &physicalPosition, + const mfem::Vector &physicalPositionVariation + ) const { + MFEM_VERIFY( + physicalPosition.Size() == 3, + "RigidRotation derivative requires a " + "three-dimensional position." + ); + + MFEM_VERIFY( + physicalPositionVariation.Size() == 3, + "RigidRotation derivative requires a " + "three-dimensional direction." + ); + + double angularVelocitySquared = 0.0; + double angularVelocityDotPosition = 0.0; + + for (int component = 0; component < 3; ++component) { + const double relativePosition = + physicalPosition(component) - m_center(component); + + angularVelocitySquared += + m_angularVelocity(component) * m_angularVelocity(component); + + angularVelocityDotPosition += + m_angularVelocity(component) * relativePosition; + } + + double derivative = 0.0; + + for (int component = 0; component < 3; ++component) { + const double relativePosition = + physicalPosition(component) - m_center(component); + + const double gradientComponent = + angularVelocitySquared * relativePosition - + angularVelocityDotPosition * m_angularVelocity(component); + + derivative += + gradientComponent * physicalPositionVariation(component); + } + + return derivative; + } + + [[nodiscard]] const mfem::Vector &angular_velocity() const noexcept { + return m_angularVelocity; + } + + [[nodiscard]] const mfem::Vector ¢er() const noexcept { + return m_center; + } + + private: + mfem::Vector m_angularVelocity; + mfem::Vector m_center; + }; +} // namespace mean_field::physics \ No newline at end of file diff --git a/libmeanfield/interface/physics/solid.cppm b/libmeanfield/interface/physics/solid.cppm index 369fcea..5d5d2be 100644 --- a/libmeanfield/interface/physics/solid.cppm +++ b/libmeanfield/interface/physics/solid.cppm @@ -5,5 +5,8 @@ export module mean_field:physics.solid_body; export import :fem; export namespace mean_field::physics { - double compute_moment_of_inertia(const fem::FEM &fem, const mfem::GridFunction &rho_ref); + double compute_moment_of_inertia( + const fem::FEM &fem, + const mfem::GridFunction &rho_ref + ); } \ No newline at end of file diff --git a/libmeanfield/interface/quadrature/mfem.cppm b/libmeanfield/interface/quadrature/mfem.cppm index 28ce5f0..c86587d 100644 --- a/libmeanfield/interface/quadrature/mfem.cppm +++ b/libmeanfield/interface/quadrature/mfem.cppm @@ -4,93 +4,116 @@ module; export module mean_field:quadrature.mfem; export import :quadrature.policy; +export import :integrators.centrifugal; +import :field.mfem; export namespace mean_field::quadrature { struct MfemRule { Resolution resolution; - const mfem::IntegrationRule* integration_rule; + const mfem::IntegrationRule *integration_rule; }; class RuleFactory { public: - explicit RuleFactory( - Policy policy - ); - MfemRule get( - const Query& query, - mfem::Geometry::Type geometry - ) const; - MfemRule get( - Term term, + explicit RuleFactory(Policy policy); + MfemRule + get(const Query &query, + mfem::Geometry::Type geometry) const; + MfemRule + get(Term term, QuadratureRole role, mfem::Geometry::Type geometry, int base_order, utils::DOMAINS domain = utils::DOMAINS::ALL, - MappingKind mapping = MappingKind::none - ) const; + MappingKind mapping = MappingKind::none) const; Resolution configure_gravity_hdiv_mass( - mfem::VectorFEMassIntegrator& integrator, + mfem::VectorFEMassIntegrator &integrator, QuadratureRole role, - const mfem::FiniteElement& element, - const mfem::ElementTransformation& transformation, + const mfem::FiniteElement &element, + const mfem::ElementTransformation &transformation, utils::DOMAINS domain = utils::DOMAINS::ALL, - MappingKind mapping = MappingKind::none + MappingKind mapping = MappingKind::none ) const; Resolution configure_gravity_divergence( - mfem::VectorFEDivergenceIntegrator& integrator, + mfem::VectorFEDivergenceIntegrator &integrator, QuadratureRole role, - const mfem::FiniteElement& trial_element, - const mfem::FiniteElement& test_element, - const mfem::ElementTransformation& transformation, + const mfem::FiniteElement &trial_element, + const mfem::FiniteElement &test_element, + const mfem::ElementTransformation &transformation, utils::DOMAINS domain = utils::DOMAINS::ALL, - MappingKind mapping = MappingKind::none + MappingKind mapping = MappingKind::none ) const; Resolution configure_gravity_boundary( - mfem::VectorFEBoundaryFluxLFIntegrator& integrator, + mfem::VectorFEBoundaryFluxLFIntegrator &integrator, QuadratureRole role, - const mfem::FiniteElement& boundary_element, + const mfem::FiniteElement &boundary_element, utils::DOMAINS domain = utils::DOMAINS::VACUUM, - MappingKind mapping = MappingKind::none + MappingKind mapping = MappingKind::none ) const; Resolution configure_gravity_source( - mfem::DomainLFIntegrator& integrator, + mfem::DomainLFIntegrator &integrator, QuadratureRole role, - const mfem::FiniteElement& test_element, - const mfem::ElementTransformation& transformation, + const mfem::FiniteElement &test_element, + const mfem::ElementTransformation &transformation, int coefficient_order, utils::DOMAINS domain = utils::DOMAINS::STELLAR, - MappingKind mapping = MappingKind::none + MappingKind mapping = MappingKind::none ) const; - template + Resolution configure_gravity_source( + mfem::MixedScalarMassIntegrator &integrator, + QuadratureRole role, + const mfem::FiniteElement &trial_element, + const mfem::FiniteElement &test_element, + const mfem::ElementTransformation &transformation, + int coefficient_order, + utils::DOMAINS domain = utils::DOMAINS::STELLAR, + MappingKind mapping = MappingKind::none + ) const; + + Resolution configure_centrifugal( + integrators::CentrifugalForceIntegrator &integrator, + QuadratureRole role, + const mfem::FiniteElement &density_element, + const mfem::FiniteElement &velocity_element, + const mfem::ElementTransformation &transformation, + int position_order, + utils::DOMAINS domain = utils::DOMAINS::STELLAR, + MappingKind mapping = MappingKind::none + ) const; + + template Resolution configure( - IntegratorType& integrator, + IntegratorType &integrator, Term term, QuadratureRole role, mfem::Geometry::Type geometry, int base_order, utils::DOMAINS domain = utils::DOMAINS::ALL, - MappingKind mapping = MappingKind::none + MappingKind mapping = MappingKind::none ) const; - private: Policy policy; }; - RuleFactory::RuleFactory(Policy policy) : policy(std::move(policy)) {} + RuleFactory::RuleFactory(Policy policy) : policy(std::move(policy)) { + } MfemRule RuleFactory::get( - const Query& query, + const Query &query, const mfem::Geometry::Type geometry ) const { const Resolution resolution = policy.resolve(query); - const mfem::IntegrationRule& integration_rule = mfem::IntRules.Get(geometry, resolution.order); - return {.resolution = resolution, .integration_rule = &integration_rule}; + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(geometry, resolution.order); + return { + .resolution = resolution, .integration_rule = &integration_rule + }; } MfemRule RuleFactory::get( @@ -102,87 +125,197 @@ export namespace mean_field::quadrature { const MappingKind mapping ) const { Query query{.term = term}; - query.domain = domain; - query.mapping = mapping; - query.role = role; + query.domain = domain; + query.mapping = mapping; + query.role = role; query.base_order = base_order; return get(query, geometry); } Resolution RuleFactory::configure_gravity_hdiv_mass( - mfem::VectorFEMassIntegrator& integrator, + mfem::VectorFEMassIntegrator &integrator, const QuadratureRole role, - const mfem::FiniteElement& element, - const mfem::ElementTransformation& transformation, + const mfem::FiniteElement &element, + const mfem::ElementTransformation &transformation, const utils::DOMAINS domain, const MappingKind mapping ) const { - const int base_order = 2 * element.GetOrder() + transformation.OrderW(); - return configure(integrator, Term::gravity_hdiv_mass, role, element.GetGeomType(), base_order, domain, mapping); + using GravityField = field::Field; + MFEM_VERIFY( + element.GetOrder() == field::Gravity::Flux::familyOrder + 1, + "The H(div) element order does not match the registered gravity " + "flux." + ); + const Query query = + GravityField::make_query( + role, transformation.OrderW(), {}, domain, mapping + ); + const auto [resolution, integration_rule] = + get(query, element.GetGeomType()); + integrator.SetIntegrationRule(*integration_rule); + return resolution; } Resolution RuleFactory::configure_gravity_divergence( - mfem::VectorFEDivergenceIntegrator& integrator, + mfem::VectorFEDivergenceIntegrator &integrator, const QuadratureRole role, - const mfem::FiniteElement& trial_element, - const mfem::FiniteElement& test_element, - const mfem::ElementTransformation& transformation, + const mfem::FiniteElement &trial_element, + const mfem::FiniteElement &test_element, + const mfem::ElementTransformation &transformation, const utils::DOMAINS domain, const MappingKind mapping ) const { - const Query query = { - .term = Term::gravity_divergence, - .role = role, - .domain = domain, - .mapping = mapping, - .trial_order = trial_element.GetOrder(), - .test_order = test_element.GetOrder(), - .geometry_weight_order = transformation.OrderW() - }; + using GravityField = field::Field; + MFEM_VERIFY( + trial_element.GetOrder() == field::Gravity::Flux::familyOrder + 1, + "The divergence trial element does not match the registered " + "gravity flux." + ); + MFEM_VERIFY( + test_element.GetOrder() == field::Gravity::Potential::familyOrder, + "The divergence test element does not match the registered " + "gravity potential." + ); + const Query query = + GravityField::make_query( + role, transformation.OrderW(), {}, domain, mapping + ); - const auto [resolution, integration_rule] = get(query, trial_element.GetGeomType()); + const auto [resolution, integration_rule] = + get(query, trial_element.GetGeomType()); integrator.SetIntegrationRule(*integration_rule); return resolution; } Resolution RuleFactory::configure_gravity_boundary( - mfem::VectorFEBoundaryFluxLFIntegrator& integrator, + mfem::VectorFEBoundaryFluxLFIntegrator &integrator, const QuadratureRole role, - const mfem::FiniteElement& boundary_element, + const mfem::FiniteElement &boundary_element, const utils::DOMAINS domain, const MappingKind mapping ) const { - const int base_order = 2 * boundary_element.GetOrder(); - return configure(integrator, Term::gravity_boundary, role, boundary_element.GetGeomType(), base_order, domain, mapping); - } - - Resolution RuleFactory::configure_gravity_source( - mfem::DomainLFIntegrator& integrator, - const QuadratureRole role, - const mfem::FiniteElement& test_element, - const mfem::ElementTransformation& transformation, - const int coefficient_order, - const utils::DOMAINS domain, - const MappingKind mapping - ) const { - const Query query = { - .term = Term::gravity_source, - .role = role, - .domain = domain, - .mapping = mapping, - .test_order = test_element.GetOrder(), - .coefficient_order = coefficient_order, - .geometry_weight_order = transformation.OrderW() - }; - - const auto [resolution, integration_rule] = get(query, test_element.GetGeomType()); + using GravityField = field::Field; + MFEM_VERIFY( + boundary_element.GetOrder() == field::Gravity::Flux::familyOrder, + "The boundary element does not match the registered gravity-flux " + "normal trace." + ); + const Query query = + GravityField::make_query( + role, 0, {}, domain, mapping + ); + const auto [resolution, integration_rule] = + get(query, boundary_element.GetGeomType()); integrator.SetIntegrationRule(*integration_rule); return resolution; } - template + Resolution RuleFactory::configure_gravity_source( + mfem::DomainLFIntegrator &integrator, + const QuadratureRole role, + const mfem::FiniteElement &test_element, + const mfem::ElementTransformation &transformation, + const int coefficient_order, + const utils::DOMAINS domain, + const MappingKind mapping + ) const { + using GravityField = field::Field; + MFEM_VERIFY( + test_element.GetOrder() == field::Gravity::Potential::familyOrder, + "The gravity-source test element does not match the registered " + "gravity potential." + ); + MFEM_VERIFY( + coefficient_order == field::Density::Scalar::familyOrder, + "The gravity-source coefficient order does not match the " + "registered density field." + ); + const Query query = + GravityField::make_query( + role, transformation.OrderW(), {}, domain, mapping + ); + + const auto [resolution, integration_rule] = + get(query, test_element.GetGeomType()); + integrator.SetIntegrationRule(*integration_rule); + return resolution; + } + Resolution RuleFactory::configure_gravity_source( + mfem::MixedScalarMassIntegrator &integrator, + QuadratureRole role, + const mfem::FiniteElement &trial_element, + const mfem::FiniteElement &test_element, + const mfem::ElementTransformation &transformation, + int coefficient_order, + utils::DOMAINS domain, + MappingKind mapping + ) const { + MFEM_VERIFY( + trial_element.GetGeomType() == test_element.GetGeomType(), + "Gravity source trial and test elements must use the same geometry." + ); + MFEM_VERIFY( + trial_element.GetGeomType() == transformation.GetGeometryType(), + "Gravity source element and transformation geometries must agree." + ); + + using GravityField = field::Field; + MFEM_VERIFY( + trial_element.GetOrder() == field::Density::Scalar::familyOrder, + "The gravity-source trial element does not match the registered " + "density field." + ); + MFEM_VERIFY( + test_element.GetOrder() == field::Gravity::Potential::familyOrder, + "The gravity-source test element does not match the registered " + "gravity potential." + ); + MFEM_VERIFY( + coefficient_order == 0, + "The mapped gravity-source coefficient order must be zero; " + "density order is supplied by the registered trial field." + ); + const Query query = + GravityField::make_query( + role, transformation.OrderW(), {}, domain, mapping + ); + + const auto [resolution, integration_rule] = + get(query, transformation.GetGeometryType()); + integrator.SetIntRule(integration_rule); + return resolution; + } + + Resolution RuleFactory::configure_centrifugal( + integrators::CentrifugalForceIntegrator &integrator, + const QuadratureRole role, + const mfem::FiniteElement &density_element, + const mfem::FiniteElement &velocity_element, + const mfem::ElementTransformation &transformation, + const int position_order, + const utils::DOMAINS domain, + const MappingKind mapping + ) const { + const Query query = { + .term = Term::centrifugal, + .role = role, + .domain = domain, + .mapping = mapping, + .trial_order = density_element.GetOrder(), + .test_order = velocity_element.GetOrder(), + .coefficient_order = position_order, + .geometry_weight_order = transformation.OrderW() + }; + + const auto [resolution, integration_rule] = + get(query, velocity_element.GetGeomType()); + integrator.SetIntegrationRule(*integration_rule); + return resolution; + } + + template Resolution RuleFactory::configure( - IntegratorType& integrator, + IntegratorType &integrator, const Term term, const QuadratureRole role, const mfem::Geometry::Type geometry, @@ -190,9 +323,10 @@ export namespace mean_field::quadrature { const utils::DOMAINS domain, const MappingKind mapping ) const { - const auto [resolution, integration_rule] = get(term, role, geometry, base_order, domain, mapping); + const auto [resolution, integration_rule] = + get(term, role, geometry, base_order, domain, mapping); integrator.SetIntegrationRule(*integration_rule); return resolution; } -} +} // namespace mean_field::quadrature diff --git a/libmeanfield/interface/quadrature/policy.cppm b/libmeanfield/interface/quadrature/policy.cppm index d0a1d12..d2d529d 100644 --- a/libmeanfield/interface/quadrature/policy.cppm +++ b/libmeanfield/interface/quadrature/policy.cppm @@ -2,7 +2,9 @@ module; #include #include #include +#include #include +#include export module mean_field:quadrature.policy; export import :utils.misc; @@ -13,11 +15,19 @@ export namespace mean_field::quadrature { gravity_divergence, gravity_source, gravity_boundary, + centrifugal, density_projection, + eos_closure, + hydrostatic_equilibrium, + isobaric_surface, + mesh_extension, mass_conservation, + mass_normalization, center_of_mass, quadrupole, gravitational_energy, + pressure_integral, + pressure_force, virial, error_norm }; @@ -29,19 +39,9 @@ export namespace mean_field::quadrature { projection }; - enum class MappingKind { - none, - affine, - general, - kelvin - }; + enum class MappingKind { none, affine, general, kelvin }; - enum class Mode { - fast, - production, - reference, - convergence - }; + enum class Mode { fast, production, reference, convergence }; struct RuleControl { std::optional fixed_order; @@ -55,17 +55,24 @@ export namespace mean_field::quadrature { RuleControl projection; }; - struct RuleSet { RuleControl gravity_hdiv_mass; RuleControl gravity_divergence; RuleControl gravity_source; RuleControl gravity_boundary; + RuleControl centrifugal; RuleControl density_projection; + RuleControl eos_closure; + RuleControl hydrostatic_equilibrium; + RuleControl isobaric_surface; + RuleControl mesh_extension; RuleControl mass_conservation; + RuleControl mass_normalization; RuleControl center_of_mass; RuleControl quadrupole; RuleControl gravitational_energy; + RuleControl pressure_integral; + RuleControl pressure_force; RuleControl virial; RuleControl error_norm; RoleControls roles; @@ -74,12 +81,12 @@ export namespace mean_field::quadrature { struct Query { Term term; - QuadratureRole role = QuadratureRole::discretization; - utils::DOMAINS domain = utils::DOMAINS::ALL; - MappingKind mapping = MappingKind::none; - int trial_order = 0; - int test_order = 0; - int coefficient_order = 0; + QuadratureRole role = QuadratureRole::discretization; + utils::DOMAINS domain = utils::DOMAINS::ALL; + MappingKind mapping = MappingKind::none; + int trial_order = 0; + int test_order = 0; + int coefficient_order = 0; int geometry_weight_order = 0; std::optional base_order; }; @@ -96,16 +103,16 @@ export namespace mean_field::quadrature { }; struct QuadratureManifestOptions { - bool enabled = false; + bool enabled = false; bool include_repeated_queries = false; std::optional output_file; }; struct QuadratureValidationOptions { bool require_explicit_base_order = false; - bool require_explicit_mfem_rule = false; - bool reject_negative_boosts = true; - bool report_unused_overrides = true; + bool require_explicit_mfem_rule = false; + bool reject_negative_boosts = true; + bool report_unused_overrides = true; }; struct QuadratureRoleOptions { @@ -116,7 +123,7 @@ export namespace mean_field::quadrature { }; struct QuadratureOptions { - Mode mode = Mode::production; + Mode mode = Mode::production; int global_boost = 0; std::optional fallback_fixed_order; @@ -124,11 +131,19 @@ export namespace mean_field::quadrature { QuadratureTermOptions gravity_divergence; QuadratureTermOptions gravity_source; QuadratureTermOptions gravity_boundary; + QuadratureTermOptions centrifugal; QuadratureTermOptions density_projection; + QuadratureTermOptions eos_closure; + QuadratureTermOptions hydrostatic_equilibrium; + QuadratureTermOptions isobaric_surface; + QuadratureTermOptions mesh_extension; QuadratureTermOptions mass_conservation; + QuadratureTermOptions mass_normalization; QuadratureTermOptions center_of_mass; QuadratureTermOptions quadrupole; QuadratureTermOptions gravitational_energy; + QuadratureTermOptions pressure_integral; + QuadratureTermOptions pressure_force; QuadratureTermOptions virial; QuadratureTermOptions error_norm; @@ -139,44 +154,51 @@ export namespace mean_field::quadrature { QuadratureValidationOptions validation; }; - RuleSet make_rule_set(Mode mode, int global_boost = 0); + RuleSet make_rule_set( + Mode mode, + int global_boost = 0 + ); class Policy { public: explicit Policy(RuleSet rule_set); - Resolution resolve(const Query& query) const; + Resolution resolve(const Query &query) const; private: - const RuleControl& get_control(Term term) const; - static int compute_base_order(const Query& query) ; - const RuleControl& get_role_control(QuadratureRole role) const; + const RuleControl &get_control(Term term) const; + static int compute_base_order(const Query &query); + const RuleControl &get_role_control(QuadratureRole role) const; RuleSet rule_set; }; - RuleSet make_rule_set(const Mode mode, const int global_boost) { + RuleSet make_rule_set( + const Mode mode, + const int global_boost + ) { RuleSet rule_set; switch (mode) { - case Mode::fast: - case Mode::production: - case Mode::convergence: - rule_set.fallback.boost = global_boost; - break; - case Mode::reference: - rule_set.fallback.boost = global_boost + 8; - break; + case Mode::fast: + case Mode::production: + case Mode::convergence: + rule_set.fallback.boost = global_boost; + break; + case Mode::reference: + rule_set.fallback.boost = global_boost + 8; + break; } return rule_set; } - Policy::Policy(RuleSet rule_set) : rule_set(std::move(rule_set)) {} + Policy::Policy(RuleSet rule_set) : rule_set(std::move(rule_set)) { + } - Resolution Policy::resolve(const Query& query) const { - const int base_order = compute_base_order(query); - const RuleControl& term_control = get_control(query.term); - const RuleControl& role_control = get_role_control(query.role); + Resolution Policy::resolve(const Query &query) const { + const int base_order = compute_base_order(query); + const RuleControl &term_control = get_control(query.term); + const RuleControl &role_control = get_role_control(query.role); std::optional fixed_order; if (term_control.fixed_order.has_value()) { @@ -189,49 +211,96 @@ export namespace mean_field::quadrature { if (fixed_order.has_value()) { if (*fixed_order < 0) { - throw std::invalid_argument("Quadrature fixed order cannot be negative."); + throw std::invalid_argument( + "Quadrature fixed order cannot be negative." + ); } - return {.base_order = base_order, .boost = 0, .order = *fixed_order, .used_fixed_order = true}; + return { + .base_order = base_order, + .boost = 0, + .order = *fixed_order, + .used_fixed_order = true + }; } - const int boost = rule_set.fallback.boost + role_control.boost + term_control.boost; + const int boost = + rule_set.fallback.boost + role_control.boost + term_control.boost; const int order = base_order + boost; if (order < 0) { - throw std::invalid_argument("Resolved quadrature order cannot be negative."); + throw std::invalid_argument( + "Resolved quadrature order cannot be negative." + ); } - return {.base_order = base_order, .boost = boost, .order = order, .used_fixed_order = false}; + return { + .base_order = base_order, + .boost = boost, + .order = order, + .used_fixed_order = false + }; } - const RuleControl& Policy::get_control(const Term term) const { + const RuleControl &Policy::get_control(const Term term) const { switch (term) { - case Term::gravity_hdiv_mass: return rule_set.gravity_hdiv_mass; - case Term::gravity_divergence: return rule_set.gravity_divergence; - case Term::gravity_source: return rule_set.gravity_source; - case Term::gravity_boundary: return rule_set.gravity_boundary; - case Term::density_projection: return rule_set.density_projection; - case Term::mass_conservation: return rule_set.mass_conservation; - case Term::center_of_mass: return rule_set.center_of_mass; - case Term::quadrupole: return rule_set.quadrupole; - case Term::gravitational_energy: return rule_set.gravitational_energy; - case Term::virial: return rule_set.virial; - case Term::error_norm: return rule_set.error_norm; + case Term::gravity_hdiv_mass: + return rule_set.gravity_hdiv_mass; + case Term::gravity_divergence: + return rule_set.gravity_divergence; + case Term::gravity_source: + return rule_set.gravity_source; + case Term::gravity_boundary: + return rule_set.gravity_boundary; + case Term::centrifugal: + return rule_set.centrifugal; + case Term::density_projection: + return rule_set.density_projection; + case Term::eos_closure: + return rule_set.eos_closure; + case Term::hydrostatic_equilibrium: + return rule_set.hydrostatic_equilibrium; + case Term::isobaric_surface: + return rule_set.isobaric_surface; + case Term::mesh_extension: + return rule_set.mesh_extension; + case Term::mass_conservation: + return rule_set.mass_conservation; + case Term::mass_normalization: + return rule_set.mass_normalization; + case Term::center_of_mass: + return rule_set.center_of_mass; + case Term::quadrupole: + return rule_set.quadrupole; + case Term::gravitational_energy: + return rule_set.gravitational_energy; + case Term::pressure_integral: + return rule_set.pressure_integral; + case Term::pressure_force: + return rule_set.pressure_force; + case Term::virial: + return rule_set.virial; + case Term::error_norm: + return rule_set.error_norm; } throw std::logic_error("Unknown quadrature term."); } - int Policy::compute_base_order(const Query& query) { + int Policy::compute_base_order(const Query &query) { if (query.base_order.has_value()) { if (*query.base_order < 0) { - throw std::invalid_argument("Quadrature base order cannot be negative."); + throw std::invalid_argument( + "Quadrature base order cannot be negative." + ); } return *query.base_order; } - if (query.trial_order < 0 || query.test_order < 0 || query.coefficient_order < 0 || query.geometry_weight_order < 0) { - throw std::invalid_argument("Quadrature query orders cannot be negative."); + if (query.trial_order < 0 || query.test_order < 0 || + query.coefficient_order < 0 || query.geometry_weight_order < 0) { + throw std::invalid_argument( + "Quadrature query orders cannot be negative." + ); } int trial_order = query.trial_order; @@ -239,18 +308,24 @@ export namespace mean_field::quadrature { trial_order = std::max(0, trial_order - 1); } - return trial_order + query.test_order + query.coefficient_order + query.geometry_weight_order; + return trial_order + query.test_order + query.coefficient_order + + query.geometry_weight_order; } - const RuleControl& Policy::get_role_control(const QuadratureRole role) const { + const RuleControl & + Policy::get_role_control(const QuadratureRole role) const { switch (role) { - case QuadratureRole::discretization: return rule_set.roles.discretization; - case QuadratureRole::preconditioner: return rule_set.roles.preconditioner; - case QuadratureRole::diagnostic: return rule_set.roles.diagnostic; - case QuadratureRole::projection: return rule_set.roles.projection; + case QuadratureRole::discretization: + return rule_set.roles.discretization; + case QuadratureRole::preconditioner: + return rule_set.roles.preconditioner; + case QuadratureRole::diagnostic: + return rule_set.roles.diagnostic; + case QuadratureRole::projection: + return rule_set.roles.projection; } throw std::logic_error("Unknown quadrature role."); } -} +} // namespace mean_field::quadrature diff --git a/libmeanfield/interface/solver/fields.cppm b/libmeanfield/interface/solver/fields.cppm new file mode 100644 index 0000000..bd54dbe --- /dev/null +++ b/libmeanfield/interface/solver/fields.cppm @@ -0,0 +1,29 @@ +module; + +#include + +export module mean_field:solver.fields; + +export namespace mean_field::solver { + enum class FieldBlock : std::uint8_t { + velocity = 0, + density = 1, + gravity_gradient = 2, + gravity_potential = 3, + displacement = 4, + count = 5 + }; + + [[nodiscard]] constexpr int block_index(const FieldBlock field) noexcept { + return static_cast(field); + } + + inline constexpr int field_block_count = block_index(FieldBlock::count); + + static_assert(block_index(FieldBlock::velocity) == 0); + static_assert(block_index(FieldBlock::density) == 1); + static_assert(block_index(FieldBlock::gravity_gradient) == 2); + static_assert(block_index(FieldBlock::gravity_potential) == 3); + static_assert(block_index(FieldBlock::displacement) == 4); + static_assert(field_block_count == 5); +} // namespace mean_field::solver \ No newline at end of file diff --git a/libmeanfield/interface/utils/blocks.cppm b/libmeanfield/interface/utils/blocks.cppm new file mode 100644 index 0000000..0321f64 --- /dev/null +++ b/libmeanfield/interface/utils/blocks.cppm @@ -0,0 +1,493 @@ +module; +#include +#include +#include +#include +#include +export module mean_field:utils.blocks; + +export namespace mean_field::utils::blocks { + inline constexpr int dynamic_block_size = -1; + + struct block { }; + + struct residual_block_base : block { + static constexpr int static_block_size = dynamic_block_size; + }; + + struct value_block_base : block { + static constexpr int static_block_size = dynamic_block_size; + }; + + struct term { }; + struct field { }; + + template struct block_row { }; + template + struct residual_block final : residual_block_base { + static constexpr int index = index_value; + + // ReSharper disable once CppNonExplicitConversionOperator + constexpr operator int() const noexcept { + return index; + } + }; + + template struct value_block final : value_block_base { + static constexpr int index = index_value; + + // ReSharper disable once CppNonExplicitConversionOperator + constexpr operator int() const noexcept { + return index; + } + }; + + struct density final : field { + struct mass final : term { + struct value final : value_block_base { }; + struct residual final : residual_block_base { }; + }; + + static inline constexpr mass mass_term{}; + }; + + struct displacement final : field { + struct geometry final : term { + struct value final : value_block_base { }; + struct residual final : residual_block_base { }; + }; + + static inline constexpr geometry geometry_term{}; + }; + + struct gravity final : field { + struct gradient final : term { + struct value final : value_block_base { }; + struct residual final : residual_block_base { }; + }; + + struct poisson final : term { + struct value final : value_block_base { }; + struct residual final : residual_block_base { }; + }; + + static inline constexpr gradient gradient_term{}; + static inline constexpr poisson poisson_term{}; + }; + + struct enthalpy final : field { + struct specific final : term { + struct value final : value_block_base { }; + struct residual final : residual_block_base { }; + }; + + static inline constexpr specific specific_term{}; + }; + + struct barotropic_constant final : field { + struct mass_normalization final : term { + struct value final : value_block_base { + static constexpr int static_block_size = 1; + }; + + struct residual final : residual_block_base { + static constexpr int static_block_size = 1; + }; + }; + + static inline constexpr mass_normalization mass_normalization_term{}; + }; + + inline constexpr density density_field{}; + inline constexpr displacement displacement_field{}; + inline constexpr gravity gravity_field{}; + inline constexpr enthalpy enthalpy_field{}; + inline constexpr barotropic_constant barotropic_constant_field{}; + + template struct type_list { + static constexpr int size = sizeof...(Types); + }; + + template struct contains_type; + + template + struct contains_type> : std::false_type { }; + + template + struct contains_type> + : std::conditional_t< + std::is_same_v, + std::true_type, + contains_type>> { }; + + template + inline constexpr bool contains_type_v = contains_type::value; + + template struct type_count; + + template + struct type_count> : std::integral_constant { }; + + template + struct type_count> + : std::integral_constant< + int, + (std::is_same_v ? 1 : 0) + + type_count>::value> { }; + + template + inline constexpr int type_count_v = type_count::value; + + template struct types_are_unique; + + template + struct types_are_unique> + : std::bool_constant< + ((type_count_v> == 1) && ...)> { }; + + template + inline constexpr bool types_are_unique_v = types_are_unique::value; + + template struct block_row_traits { + using residual = void; + using values = type_list<>; + + static constexpr int value_count = 0; + static constexpr bool is_block_row = false; + }; + + template + struct block_row_traits> { + using residual = Residual; + using values = type_list; + + static constexpr int value_count = sizeof...(Values); + static constexpr bool is_block_row = true; + }; + + template struct type_index; + + template + struct type_index> { + static constexpr int value = 0; + }; + + template + struct type_index> { + static constexpr int value = + 1 + type_index>::value; + }; + + template + inline constexpr int type_index_v = type_index::value; + + template struct block_form { + using value_blocks = ValueBlocks; + using residual_blocks = ResidualBlocks; + + static constexpr int value_block_count = ValueBlocks::size; + static constexpr int residual_block_count = ResidualBlocks::size; + }; + + template struct block_form_is_valid : std::false_type { }; + + template + struct block_form_is_valid< + block_form, type_list>> + : std::bool_constant< + (std::is_base_of_v && ...) && + (std::is_base_of_v && ...) && + types_are_unique_v> && + types_are_unique_v>> { }; + + template + inline constexpr bool block_form_is_valid_v = + block_form_is_valid::value; + + template + struct block_row_is_valid : std::false_type { }; + + template < + typename Residual, + typename... Values, + typename ValueBlocks, + typename ResidualBlocks> + struct block_row_is_valid< + block_row, + ValueBlocks, + ResidualBlocks> + : std::bool_constant< + std::is_base_of_v && + contains_type_v && + ((std::is_base_of_v && + contains_type_v) && + ...) && + types_are_unique_v>> { }; + + template struct row_residual_list; + + template struct row_residual_list> { + using type = type_list::residual...>; + }; + + template + using row_residual_list_t = typename row_residual_list::type; + + template + struct jacobian_form_is_valid : std::false_type { }; + + template + struct jacobian_form_is_valid< + block_form, type_list>, + type_list> { + using form_type = + block_form, type_list>; + + using value_blocks = type_list; + using residual_blocks = type_list; + using rows = type_list; + + static constexpr bool value = + block_form_is_valid_v && + (block_row_is_valid::value && + ...) && + std::is_same_v, residual_blocks>; + }; + + template + inline constexpr bool jacobian_form_is_valid_v = + jacobian_form_is_valid::value; + + template + concept valid_jacobian_form = jacobian_form_is_valid_v; + + template + struct has_jacobian_coupling; + + template + struct has_jacobian_coupling> + : std::false_type { }; + + template < + typename Residual, + typename Value, + typename RowResidual, + typename... RowValues, + typename... RemainingRows> + struct has_jacobian_coupling< + Residual, + Value, + type_list, RemainingRows...>> + : std::conditional_t< + std::is_same_v, + std::bool_constant<(std::is_same_v || ...)>, + has_jacobian_coupling< + Residual, + Value, + type_list>> { }; + + template + inline constexpr bool has_jacobian_coupling_v = + has_jacobian_coupling::value; + + template < + typename Form, + typename Term> + consteval auto get_value_block(const Term &) { + using value_type = typename Term::value; + constexpr int index = + type_index_v; + return value_block{}; + } + + template < + typename Form, + typename Term> + consteval auto get_residual_block(const Term &) { + using residual_type = typename Term::residual; + constexpr int index = + type_index_v; + return residual_block{}; + } + + template class form_layout { + public: + form_layout( + const std::array< + int, + Form::value_block_count> &value_sizes, + const std::array< + int, + Form::residual_block_count> &residual_sizes + ) { + build_offsets( + m_value_offsets, value_sizes, typename Form::value_blocks{} + ); + + build_offsets( + m_residual_offsets, residual_sizes, + typename Form::residual_blocks{} + ); + } + + template [[nodiscard]] int size(value_block) const { + return m_value_offsets[index + 1] - m_value_offsets[index]; + } + + template + [[nodiscard]] int size(residual_block) const { + return m_residual_offsets[index + 1] - m_residual_offsets[index]; + } + + template + [[nodiscard]] int offset(value_block) const { + return m_value_offsets[index]; + } + + template + [[nodiscard]] int offset(residual_block) const { + return m_residual_offsets[index]; + } + + [[nodiscard]] + const mfem::Array &value_offsets() const noexcept { + return m_value_offsets; + } + + [[nodiscard]] + const mfem::Array &residual_offsets() const noexcept { + return m_residual_offsets; + } + + private: + template + [[nodiscard]] + static int resolve_block_size(const int requested_size) { + if constexpr (BlockType::static_block_size == dynamic_block_size) { + return requested_size; + } else { + if (requested_size != BlockType::static_block_size) { + throw std::invalid_argument( + "A statically sized block was given an " + "incompatible runtime size." + ); + } + + return BlockType::static_block_size; + } + } + + template + static void build_offsets( + mfem::Array &offsets, + const std::array< + int, + sizeof...(BlockTypes)> &requested_sizes, + type_list + ) { + offsets.SetSize(sizeof...(BlockTypes) + 1); + offsets[0] = 0; + + int block_index = 0; + + ((offsets[block_index + 1] = + offsets[block_index] + + resolve_block_size(requested_sizes[block_index]), + ++block_index), + ...); + } + + mfem::Array m_value_offsets; + mfem::Array m_residual_offsets; + }; + using gravity_field_form = block_form< + type_list< + density::mass::value, + displacement::geometry::value, + gravity::gradient::value, + gravity::poisson::value>, + type_list>; + + using gravity_jacobian_form = type_list< + block_row< + gravity::gradient::residual, + gravity::gradient::value, + gravity::poisson::value, + displacement::geometry::value>, + block_row< + gravity::poisson::residual, + gravity::gradient::value, + density::mass::value, + displacement::geometry::value>>; + + // Columns: + // [rho, d, g, Phi, h, C] + // + // Rows: + // [R_g, R_Phi, R_rho, R_d, R_h, R_M] + using barotropic_equilibrium_form = block_form< + type_list< + density::mass::value, + displacement::geometry::value, + gravity::gradient::value, + gravity::poisson::value, + enthalpy::specific::value, + barotropic_constant::mass_normalization::value>, + type_list< + gravity::gradient::residual, + gravity::poisson::residual, + density::mass::residual, + displacement::geometry::residual, + enthalpy::specific::residual, + barotropic_constant::mass_normalization::residual>>; + + using barotropic_equilibrium_jacobian_form = type_list< + // R_g(g, Phi, d) + block_row< + gravity::gradient::residual, + gravity::gradient::value, + gravity::poisson::value, + displacement::geometry::value>, + + // R_Phi(g, rho, d) + block_row< + gravity::poisson::residual, + gravity::gradient::value, + density::mass::value, + displacement::geometry::value>, + + // R_rho(rho, h, d) + block_row< + density::mass::residual, + density::mass::value, + enthalpy::specific::value, + displacement::geometry::value>, + + // R_d(d, h) + block_row< + displacement::geometry::residual, + displacement::geometry::value, + enthalpy::specific::value>, + + // R_h(h, Phi, d, C) + block_row< + enthalpy::specific::residual, + enthalpy::specific::value, + gravity::poisson::value, + displacement::geometry::value, + barotropic_constant::mass_normalization::value>, + + // R_M(rho, d) + block_row< + barotropic_constant::mass_normalization::residual, + density::mass::value, + displacement::geometry::value>>; + + static_assert(valid_jacobian_form< + gravity_field_form, + gravity_jacobian_form>); + + static_assert(valid_jacobian_form< + barotropic_equilibrium_form, + barotropic_equilibrium_jacobian_form>); +} // namespace mean_field::utils::blocks diff --git a/libmeanfield/interface/utils/domain.cppm b/libmeanfield/interface/utils/domain.cppm index ab286f9..b481213 100644 --- a/libmeanfield/interface/utils/domain.cppm +++ b/libmeanfield/interface/utils/domain.cppm @@ -21,4 +21,4 @@ export namespace mean_field::utils { mapping::COORDINATE_SPACE vspace = mapping::COORDINATE_SPACE::REFERENCE, mapping::COORDINATE_SPACE rspace = mapping::COORDINATE_SPACE::PHYSICAL ); -} \ No newline at end of file +} // namespace mean_field::utils \ No newline at end of file diff --git a/libmeanfield/interface/utils/misc.cppm b/libmeanfield/interface/utils/misc.cppm index 0d7f2b8..e958c12 100644 --- a/libmeanfield/interface/utils/misc.cppm +++ b/libmeanfield/interface/utils/misc.cppm @@ -1,7 +1,7 @@ module; -#include -#include #include +#include +#include #include @@ -14,8 +14,10 @@ import :boundary.contexts; export namespace mean_field::utils { constexpr double APPROX_MAX_ACCEPTABLE_POTENTIAL_ERROR_SI_BURNING = 1e-4; - - bool is_vacuum(const mfem::ElementTransformation &Tr, mfem::Array elvec) { + bool is_vacuum( + const mfem::ElementTransformation &Tr, + mfem::Array elvec + ) { if (Tr.Attribute == 3) { const int size_elvec = elvec.Size(); for (int i = 0; i < size_elvec; i++) { @@ -28,45 +30,60 @@ export namespace mean_field::utils { return false; } - constexpr std::string_view ANSI_GREEN = "\033[32m"; - constexpr std::string_view ANSI_RED = "\033[31m"; - constexpr std::string_view ANSI_YELLOW = "\033[33m"; - constexpr std::string_view ANSI_BLUE = "\033[34m"; - constexpr std::string_view ANSI_MAGENTA = "\033[35m"; - constexpr std::string_view ANSI_CYAN = "\033[36m"; - constexpr std::string_view ANSI_RESET = "\033[0m"; - constexpr std::string_view ANSI_BCYAN = "\033[1;36m"; + bool is_vacuum( + const mfem::ElementTransformation &Tr, + const mfem::Array2D &elmats + ) { + if (Tr.Attribute == 3) { + const int cols = elmats.NumCols(); + const int rows = elmats.NumRows(); + for (int rowID = 0; rowID < rows; rowID++) { + for (int colID = 0; colID < cols; colID++) { + if (elmats(rowID, colID)) { + *elmats(rowID, colID) = 0.0; + } + } + } + return true; + } + return false; + } + constexpr std::string_view ANSI_GREEN = "\033[32m"; + constexpr std::string_view ANSI_RED = "\033[31m"; + constexpr std::string_view ANSI_YELLOW = "\033[33m"; + constexpr std::string_view ANSI_BLUE = "\033[34m"; + constexpr std::string_view ANSI_MAGENTA = "\033[35m"; + constexpr std::string_view ANSI_CYAN = "\033[36m"; + constexpr std::string_view ANSI_RESET = "\033[0m"; + constexpr std::string_view ANSI_BCYAN = "\033[1;36m"; - constexpr double G = 1.0; - constexpr double MASS = 1.0; - constexpr double RADIUS = 1.0; + constexpr double G = 1.0; + constexpr double MASS = 1.0; + constexpr double RADIUS = 1.0; [[maybe_unused]] constexpr char HOST[10] = "localhost"; - [[maybe_unused]] constexpr int PORT = 19916; + [[maybe_unused]] constexpr int PORT = 19916; + template + concept is_xad = std::is_same_v> || + std::is_same_v> || + std::is_same_v>; - template - concept is_xad = - std::is_same_v > - || std::is_same_v > - || std::is_same_v >; - - template + template concept is_real = std::is_floating_point_v || is_xad; - template - using EOS_P = std::function; + template + using EOS_P = std::function; enum class DOMAINS : uint8_t { - CORE = 1 << 0, + CORE = 1 << 0, ENVELOPE = 1 << 1, - VACUUM = 1 << 2, - STELLAR = CORE | ENVELOPE, - ALL = CORE | ENVELOPE | VACUUM + VACUUM = 1 << 2, + STELLAR = CORE | ENVELOPE, + ALL = CORE | ENVELOPE | VACUUM }; - DOMAINS operator|( DOMAINS lhs, DOMAINS rhs @@ -78,7 +95,7 @@ export namespace mean_field::utils { ); void populate_element_mask( - const mfem::Mesh* mesh, + const mfem::Mesh *mesh, DOMAINS domain, mfem::Array &mask ); @@ -89,13 +106,14 @@ export namespace mean_field::utils { mfem::Array &ess_tdof ); - std::expected discover_bounds( + std::expected< + boundary::Bounds, + boundary::BoundsError> + discover_bounds( const mfem::Mesh *mesh, int vacuum_attr ); - int get_mesh_order( - const mfem::Mesh &mesh - ); + int get_mesh_order(const mfem::Mesh &mesh); -} +} // namespace mean_field::utils diff --git a/libmeanfield/interface/utils/user.cppm b/libmeanfield/interface/utils/user.cppm index def4e4e..53ab587 100644 --- a/libmeanfield/interface/utils/user.cppm +++ b/libmeanfield/interface/utils/user.cppm @@ -3,6 +3,8 @@ module; export module mean_field:utils.user; export import :quadrature.policy; +export import :mapping.compactification.options; + export namespace mean_field::utils { struct potential { double rtol; @@ -16,6 +18,11 @@ export namespace mean_field::utils { double L; }; + struct DomainMapperStatelessOptions { + int dimension{3}; + int vacuum_element_attribute{3}; + }; + struct Args { std::string mesh_file; potential p{}; @@ -24,13 +31,13 @@ export namespace mean_field::utils { double index{}; double mass{}; double c{}; - - int quad_boost{0}; - + DomainMapperStatelessOptions domain_mapper_options{}; + mapping::compactification::options::KelvinCompactificationOptions + kelvin_options{}; int max_iters{}; double tol{}; quadrature::QuadratureOptions quadrature{}; }; -} \ No newline at end of file +} // namespace mean_field::utils diff --git a/sandbox.smesh b/sandbox.smesh index 41e4a96..6b1ddea 100644 --- a/sandbox.smesh +++ b/sandbox.smesh @@ -4,6 +4,7 @@ # - Type : Serial or Parallel (S for Serial, P for Parallel) # - mesh : the primary computational domain which can be of n order and be h-refined # - reference mesh : a reference, linear order mesh, used to ensure that the primary mesh remains well formed +# - exterior coordinate : a scalar material coordinate which is zero at the stellar surface and one at infinity # - config : The configuration options initially used to generate the mesh # - refinement-levels : the total number of refinement levels the primary mesh has been subjected too # NOTE: EACH BLOCK OF DATA IS STORED BETWEEN "BEGIN BLOCK \n ... \nEND BLOCK @@ -12,7 +13,7 @@ BEGIN BLOCK HEADER MESH_TYPE:S REFINEMENT_LEVELS:2 - DATE_CREATED:2026-07-14 + DATE_CREATED:2026-07-30 COMMENT: STROID_VERSION:0.4.0 END BLOCK HEADER @@ -1074,82 +1075,82 @@ FiniteElementCollection: H1_3D_P4 VDim: 3 Ordering: 0 --0.14433757 -0.14433757 --0.14433757 -0.14433757 --0.14433757 -0.14433757 --0.14433757 -0.14433757 --0.57735027 -0.57735027 --0.57735027 -0.57735027 --0.57735027 -0.57735027 --0.57735027 -0.57735027 --3.4641016 -3.4641016 --3.4641016 -3.4641016 --3.4641016 -3.4641016 --3.4641016 -3.4641016 +-0.14433756729740643 +0.14433756729740643 +-0.14433756729740643 +0.14433756729740643 +-0.14433756729740643 +0.14433756729740643 +-0.14433756729740643 +0.14433756729740643 +-0.57735026918962573 +0.57735026918962573 +-0.57735026918962573 +0.57735026918962573 +-0.57735026918962573 +0.57735026918962573 +-0.57735026918962573 +0.57735026918962573 +-3.4641016151377544 +3.4641016151377544 +-3.4641016151377544 +3.4641016151377544 +-3.4641016151377544 +3.4641016151377544 +-3.4641016151377544 +3.4641016151377544 0 -0.1767767 +0.17677669529663689 0 --0.1767767 +-0.17677669529663689 0 -0.1767767 +0.17677669529663689 0 --0.1767767 --0.1767767 -0.1767767 -0.1767767 --0.1767767 +-0.17677669529663689 +-0.17677669529663689 +0.17677669529663689 +0.17677669529663689 +-0.17677669529663689 0 -0.70710678 +0.70710678118654757 0 --0.70710678 --0.36084392 -0.36084392 -0.36084392 --0.36084392 +-0.70710678118654757 +-0.36084391824351608 +0.36084391824351608 +0.36084391824351608 +-0.36084391824351608 0 -0.70710678 +0.70710678118654757 0 --0.70710678 --0.36084392 -0.36084392 -0.36084392 --0.36084392 -0.70710678 --0.70710678 -0.70710678 --0.70710678 +-0.70710678118654757 +-0.36084391824351608 +0.36084391824351608 +0.36084391824351608 +-0.36084391824351608 +0.70710678118654757 +-0.70710678118654757 +0.70710678118654757 +-0.70710678118654757 0 -4.2426407 +4.2426406871192857 0 --4.2426407 --2.0207259 -2.0207259 -2.0207259 --2.0207259 -4.2426407 -4.2426407 -4.2426407 -2.0207259 -2.0207259 +-4.2426406871192857 +-2.0207259421636898 +2.0207259421636898 +2.0207259421636898 +-2.0207259421636898 +4.2426406871192857 +4.2426406871192857 +4.2426406871192857 +2.0207259421636898 +2.0207259421636898 0 --4.2426407 +-4.2426406871192857 0 --2.0207259 --2.0207259 --4.2426407 --4.2426407 +-2.0207259421636898 +-2.0207259421636898 +-4.2426406871192857 +-4.2426406871192857 0 0 0.25 @@ -1158,37 +1159,37 @@ Ordering: 0 0 0 0 -0.44194174 +0.44194173824159222 0 --0.44194174 +-0.44194173824159222 0 -0.44194174 +0.44194173824159222 0 --0.44194174 +-0.44194173824159222 0 -0.44194174 --0.44194174 +0.44194173824159222 +-0.44194173824159222 0 0 -0.44194174 --0.44194174 +0.44194173824159222 +-0.44194173824159222 1 -1 0 -2.4748737 +2.4748737341529163 0 --2.4748737 +-2.4748737341529163 0 -2.4748737 -2.4748737 -2.4748737 +2.4748737341529163 +2.4748737341529163 +2.4748737341529163 6 0 --2.4748737 +-2.4748737341529163 0 0 --2.4748737 --2.4748737 +-2.4748737341529163 +-2.4748737341529163 -6 0 0 @@ -1205,916 +1206,916 @@ Ordering: 0 -3.5 0 0 --0.072168784 +-0.072168783648703216 0 --0.088388348 --0.1692508 --0.088388348 +-0.088388347648318447 +-0.1692508000965825 +-0.088388347648318447 0 -0.125 --0.23385359 --0.1692508 +-0.23385358667337133 +-0.1692508000965825 0 0 --0.23385359 -0.072168784 -0.1692508 -0.088388348 -0.088388348 -0.23385359 +-0.23385358667337133 +0.072168783648703216 +0.1692508000965825 +0.088388347648318447 +0.088388347648318447 +0.23385358667337133 0.125 -0.1692508 -0.23385359 -0.1692508 -0.072168784 +0.1692508000965825 +0.23385358667337133 +0.1692508000965825 +0.072168783648703216 0 -0.23385359 -0.088388348 +0.23385358667337133 +0.088388347648318447 0 -0.1692508 +0.1692508000965825 0 --0.072168784 --0.1692508 --0.088388348 --0.23385359 --0.1692508 --0.072168784 +-0.072168783648703216 +-0.1692508000965825 +-0.088388347648318447 +-0.23385358667337133 +-0.1692508000965825 +-0.072168783648703216 0 --0.088388348 --0.1692508 --0.1692508 +-0.088388347648318447 +-0.1692508000965825 +-0.1692508000965825 0 0 --0.23385359 -0.072168784 -0.1692508 -0.088388348 -0.1692508 -0.23385359 -0.1692508 -0.072168784 +-0.23385358667337133 +0.072168783648703216 +0.1692508000965825 +0.088388347648318447 +0.1692508000965825 +0.23385358667337133 +0.1692508000965825 +0.072168783648703216 0 -0.1692508 +0.1692508000965825 0 --0.072168784 --0.1692508 --0.1692508 --0.28867513 +-0.072168783648703216 +-0.1692508000965825 +-0.1692508000965825 +-0.28867513459481287 0 --0.35355339 --0.6770032 --0.18042196 +-0.35355339059327379 +-0.67700320038633 +-0.18042195912175804 0 --0.22097087 --0.423127 --0.46909709 +-0.22097086912079611 +-0.42312700024145622 +-0.46909709371657093 0 0 --0.57452426 -0.28867513 -0.6770032 -0.35355339 -0.18042196 -0.423127 -0.22097087 -0.46909709 -0.57452426 -0.6770032 -0.28867513 +-0.57452425971406995 +0.28867513459481287 +0.67700320038633 +0.35355339059327379 +0.18042195912175804 +0.42312700024145622 +0.22097086912079611 +0.46909709371657093 +0.57452425971406995 +0.67700320038633 +0.28867513459481287 0 -0.423127 -0.18042196 +0.42312700024145622 +0.18042195912175804 0 -0.46909709 +0.46909709371657093 0 --0.28867513 --0.6770032 --0.18042196 --0.423127 --0.46909709 --0.25259074 +-0.28867513459481287 +-0.67700320038633 +-0.18042195912175804 +-0.42312700024145622 +-0.46909709371657093 +-0.25259074277046123 0 0 --0.30935922 -0.25259074 -0.30935922 -0.25259074 +-0.30935921676911454 +0.25259074277046123 +0.30935921676911454 +0.25259074277046123 0 --0.25259074 --0.18042196 +-0.25259074277046123 +-0.18042195912175804 0 --0.22097087 --0.423127 --0.25259074 +-0.22097086912079611 +-0.42312700024145622 +-0.25259074277046123 0 0 --0.30935922 -0.18042196 -0.423127 -0.22097087 -0.25259074 -0.30935922 -0.423127 -0.18042196 +-0.30935921676911454 +0.18042195912175804 +0.42312700024145622 +0.22097086912079611 +0.25259074277046123 +0.30935921676911454 +0.42312700024145622 +0.18042195912175804 0 -0.25259074 +0.25259074277046123 0 --0.18042196 --0.423127 --0.25259074 --0.28867513 +-0.18042195912175804 +-0.42312700024145622 +-0.25259074277046123 +-0.28867513459481287 0 --0.35355339 --0.6770032 --0.46909709 +-0.35355339059327379 +-0.67700320038633 +-0.46909709371657093 0 0 --0.57452426 -0.28867513 -0.6770032 -0.35355339 -0.46909709 -0.57452426 -0.6770032 -0.28867513 +-0.57452425971406995 +0.28867513459481287 +0.67700320038633 +0.35355339059327379 +0.46909709371657093 +0.57452425971406995 +0.67700320038633 +0.28867513459481287 0 -0.46909709 +0.46909709371657093 0 --0.28867513 --0.6770032 --0.46909709 +-0.28867513459481287 +-0.67700320038633 +-0.46909709371657093 0 --0.22097087 --0.423127 +-0.22097086912079611 +-0.42312700024145622 0 --0.30935922 -0.423127 -0.22097087 -0.30935922 -0.423127 +-0.30935921676911454 +0.42312700024145622 +0.22097086912079611 +0.30935921676911454 +0.42312700024145622 0 --0.423127 +-0.42312700024145622 0 --0.35355339 --0.6770032 +-0.35355339059327379 +-0.67700320038633 0 --0.57452426 -0.6770032 -0.35355339 -0.57452426 -0.6770032 +-0.57452425971406995 +0.67700320038633 +0.35355339059327379 +0.57452425971406995 +0.67700320038633 0 --0.6770032 +-0.67700320038633 0 --0.35355339 --0.6770032 +-0.35355339059327379 +-0.67700320038633 0 --0.22097087 --0.423127 +-0.22097086912079611 +-0.42312700024145622 0 --0.57452426 -0.6770032 -0.35355339 -0.423127 -0.22097087 -0.57452426 -0.6770032 +-0.57452425971406995 +0.67700320038633 +0.35355339059327379 +0.42312700024145622 +0.22097086912079611 +0.57452425971406995 +0.67700320038633 0 -0.423127 +0.42312700024145622 0 --0.6770032 --0.423127 +-0.67700320038633 +-0.42312700024145622 0 --0.30935922 -0.30935922 -0.58463397 -0.58463397 +-0.30935921676911454 +0.30935921676911454 +0.58463396668342837 +0.58463396668342837 0.4375 -0.58463397 -0.58463397 -0.93541435 -0.93541435 +0.58463396668342837 +0.58463396668342837 +0.93541434669348533 +0.93541434669348533 0.8125 -0.93541435 -0.93541435 --0.58463397 --0.58463397 +0.93541434669348533 +0.93541434669348533 +-0.58463396668342837 +-0.58463396668342837 -0.4375 --0.58463397 --0.58463397 --0.93541435 --0.93541435 +-0.58463396668342837 +-0.58463396668342837 +-0.93541434669348533 +-0.93541434669348533 -0.8125 --0.93541435 --0.93541435 --1.010363 +-0.93541434669348533 +-0.93541434669348533 +-1.0103629710818449 0 --1.2374369 --2.3695112 --1.2990381 +-1.2374368670764582 +-2.3695112013521551 +-1.299038105676658 0 0 --1.5909903 -1.010363 -2.3695112 -1.2374369 -1.2990381 -1.5909903 -2.3695112 -1.010363 +-1.5909902576697321 +1.0103629710818449 +2.3695112013521551 +1.2374368670764582 +1.299038105676658 +1.5909902576697321 +2.3695112013521551 +1.0103629710818449 0 -1.2990381 +1.299038105676658 0 --1.010363 --2.3695112 --1.2990381 --1.7320508 +-1.0103629710818449 +-2.3695112013521551 +-1.299038105676658 +-1.7320508075688772 0 --2.1213203 --4.0620192 --2.7424138 +-2.1213203435596428 +-4.0620192023179804 +-2.7424137786507221 0 0 --3.3587572 -1.7320508 -4.0620192 -2.1213203 -2.7424138 -3.3587572 -4.0620192 -1.7320508 +-3.3587572106361008 +1.7320508075688772 +4.0620192023179804 +2.1213203435596428 +2.7424137786507221 +3.3587572106361008 +4.0620192023179804 +1.7320508075688772 0 -2.7424138 +2.7424137786507221 0 --1.7320508 --4.0620192 --2.7424138 -2.3695112 -3.2739502 -3.2739502 -1.5909903 +-1.7320508075688772 +-4.0620192023179804 +-2.7424137786507221 +2.3695112013521551 +3.2739502134271987 +3.2739502134271987 +1.5909902576697321 2.25 -2.3695112 -2.3695112 -3.2739502 -1.2990381 -1.5909903 -2.3695112 -2.3695112 -3.2739502 -1.2990381 -1.5909903 -2.3695112 -4.0620192 -5.6124861 -5.6124861 -3.3587572 +2.3695112013521551 +2.3695112013521551 +3.2739502134271987 +1.299038105676658 +1.5909902576697321 +2.3695112013521551 +2.3695112013521551 +3.2739502134271987 +1.299038105676658 +1.5909902576697321 +2.3695112013521551 +4.0620192023179804 +5.6124860801609122 +5.6124860801609122 +3.3587572106361008 4.75 -4.0620192 -4.0620192 -5.6124861 -2.7424138 -3.3587572 -4.0620192 -4.0620192 -5.6124861 -2.7424138 -3.3587572 -4.0620192 -1.010363 +4.0620192023179804 +4.0620192023179804 +5.6124860801609122 +2.7424137786507221 +3.3587572106361008 +4.0620192023179804 +4.0620192023179804 +5.6124860801609122 +2.7424137786507221 +3.3587572106361008 +4.0620192023179804 +1.0103629710818449 0 -1.2374369 +1.2374368670764582 0 0 --1.010363 --2.3695112 --1.2374369 --1.2990381 --1.5909903 --2.3695112 --1.010363 +-1.0103629710818449 +-2.3695112013521551 +-1.2374368670764582 +-1.299038105676658 +-1.5909902576697321 +-2.3695112013521551 +-1.0103629710818449 0 --1.2990381 +-1.299038105676658 0 -1.010363 -1.7320508 +1.0103629710818449 +1.7320508075688772 0 -2.1213203 +2.1213203435596428 0 0 --1.7320508 --4.0620192 --2.1213203 --2.7424138 --3.3587572 --4.0620192 --1.7320508 +-1.7320508075688772 +-4.0620192023179804 +-2.1213203435596428 +-2.7424137786507221 +-3.3587572106361008 +-4.0620192023179804 +-1.7320508075688772 0 --2.7424138 +-2.7424137786507221 0 -1.7320508 --2.3695112 --3.2739502 --3.2739502 --1.5909903 +1.7320508075688772 +-2.3695112013521551 +-3.2739502134271987 +-3.2739502134271987 +-1.5909902576697321 -2.25 --2.3695112 --3.2739502 --2.3695112 --3.2739502 --1.5909903 --2.3695112 --4.0620192 --5.6124861 --5.6124861 --3.3587572 +-2.3695112013521551 +-3.2739502134271987 +-2.3695112013521551 +-3.2739502134271987 +-1.5909902576697321 +-2.3695112013521551 +-4.0620192023179804 +-5.6124860801609122 +-5.6124860801609122 +-3.3587572106361008 -4.75 --4.0620192 --5.6124861 --4.0620192 --5.6124861 --3.3587572 --4.0620192 -0 --1.2374369 -0 -1.2374369 -0 -0 --2.1213203 -0 -2.1213203 -0 -0 --1.2374369 -0 -1.2374369 -0 -0 --2.1213203 -0 -2.1213203 -0 --0.0846254 --0.0846254 -0 --0.11692679 --0.21949279 --0.11692679 -0.0846254 -0.0846254 -0.21949279 -0.11692679 -0.11692679 -0.0846254 -0.21949279 -0.0846254 -0 -0.11692679 --0.0846254 --0.0846254 --0.21949279 --0.11692679 --0.0846254 -0 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--2.835333 --1.9580625 --2.5046141 --3.0511657 --2.9831024 --3.1651153 --3.3040635 --3.2288939 --3.4259037 --3.5763005 --3.4746854 --3.6866922 --3.8485375 --3.0716364 --2.5214179 --1.9711994 --3.3247227 --2.7291692 --2.1336156 --3.577809 --2.9369204 --2.2960318 --2.1133603 --2.70326 --3.2931597 --2.2423063 --2.8681985 --3.4940907 --2.3407432 --2.994112 --3.6474808 --3.4097669 --3.4746108 --3.5070151 --3.6907132 --3.7609 --3.7959743 --3.9716596 --4.0471891 --4.0849334 --3.2082196 --2.6335351 --2.0588506 --3.4725596 --2.8505242 --2.2284888 --3.7368996 --3.0675133 --2.398127 --1.7535076 --1.7373054 --1.7048834 --1.8979871 --1.88045 --1.8453566 --2.0424667 --2.0235946 --1.9858298 --2.4156281 --3.0898995 --3.7641708 --2.4615664 --3.1486604 --3.8357545 --2.4845231 --3.178025 --3.8715269 --1.4525295 --0.87784504 --0.30316056 --1.5722101 --0.95017474 --0.32813936 --1.6918907 --1.0225044 --0.35311815 --0.35569515 --1.0299665 --1.7042378 --0.36245944 --1.0495535 --1.7366475 --0.36583975 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--2.1477066 --2.118774 --2.1800655 --2.2104785 --2.1477066 --2.2104785 --2.2416195 --1.1064189 --1.0307797 --0.928038 --1.4787542 --1.3776608 --1.2403441 --1.8510895 --1.7245418 --1.5526502 --1.6605336 --1.8351999 --1.9642842 --1.6968504 --1.8814343 --2.0175074 --1.7149616 --1.9044368 --2.0439512 --1.4812912 --1.5716717 --1.6406679 --1.7270828 --1.8324601 --1.9129049 --1.9728743 --2.0932486 --2.1851419 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --2.1093453 --1.9736361 --1.7903684 --2.4593502 --2.3011228 --2.0874453 --2.8093551 --2.6286094 --2.3845222 --2.2066813 --2.3683416 --2.4906074 --2.3683416 --2.5790245 --2.7365332 --2.4906074 --2.7365332 --2.9191065 --1.693156 --1.725355 --1.7414457 --1.9741024 --2.0116442 --2.0304048 --2.2550488 --2.2979333 --2.319364 --1.8821488 --2.0905188 --2.2439221 --2.1944549 --2.4373998 --2.6162574 --2.506761 --2.7842809 --2.9885928 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --2.5830523 --2.639545 --2.6677181 --2.8547554 --2.9266755 --2.9624572 --3.0555531 --3.1383448 --3.1794797 --2.357996 --2.4270069 --2.4612421 --2.7492597 --2.8297216 --2.8696374 --3.1405234 --3.2324363 --3.2780328 --2.4612421 --2.4270069 --2.357996 --2.8696374 --2.8297216 --2.7492597 --3.2780328 --3.2324363 --3.1405234 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --3.2052108 --3.2958707 --3.3408769 --3.2958707 --3.391213 --3.4385221 --3.3408769 --3.4385221 --3.4869636 --2.2439221 --2.0905188 --1.8821488 --2.6162574 --2.4373998 --2.1944549 --2.9885928 --2.7842809 --2.506761 --2.5830523 --2.8547554 --3.0555531 --2.639545 --2.9266755 --3.1383448 --2.6677181 --2.9624572 --3.1794797 --0.858661 --0.85072708 --0.83485064 --1.1476201 --1.1370163 --1.115797 --1.4365793 --1.4233054 --1.3967434 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --1.0899943 --1.1202634 --1.1352953 --1.4568024 --1.4972577 --1.5173482 --1.8236105 --1.874252 --1.8994011 --1.7149616 --1.6968504 --1.6605336 --1.9044368 --1.8814343 --1.8351999 --2.0439512 --2.0175074 --1.9642842 --0.80897011 --0.77494991 --0.73038568 --1.0812071 --1.0357383 --0.97617722 --1.3534441 --1.2965268 --1.2219688 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --1.6011047 --1.5225053 --1.4185809 --1.7591999 --1.6579443 --1.5225053 --1.8765684 --1.7591999 --1.6011047 --0.928038 --1.0307797 --1.1064189 --1.2403441 --1.3776608 --1.4787542 --1.5526502 --1.7245418 --1.8510895 --1.1352953 --1.1202634 --1.0899943 --1.5173482 --1.4972577 --1.4568024 --1.8994011 --1.874252 --1.8236105 --1.9642842 --1.8351999 --1.6605336 --2.0175074 --1.8814343 --1.6968504 --2.0439512 --1.9044368 --1.7149616 --1.1626657 --1.1966931 --1.2135736 --1.5539294 --1.5994078 --1.621969 --1.9451931 --2.0021225 --2.0303643 --2.1477066 --2.118774 --2.0604927 --2.2104785 --2.1800655 --2.118774 --2.2416195 --2.2104785 --2.1477066 --1.7414457 --1.725355 --1.693156 --2.0304048 --2.0116442 --1.9741024 --2.319364 --2.2979333 --2.2550488 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --2.2106115 --2.2720001 --2.3024862 --2.5774196 --2.6489944 --2.6845391 --2.9442277 --3.0259887 --3.066592 --2.6677181 --2.639545 --2.5830523 --2.9624572 --2.9266755 --2.8547554 --3.1794797 --3.1383448 --3.0555531 --1.6406679 --1.5716717 --1.4812912 --1.9129049 --1.8324601 --1.7270828 --2.1851419 --2.0932486 --1.9728743 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --2.4906074 --2.3683416 --2.2066813 --2.7365332 --2.5790245 --2.3683416 --2.9191065 --2.7365332 --2.4906074 --1.8821488 --2.0905188 --2.2439221 --2.1944549 --2.4373998 --2.6162574 --2.506761 --2.7842809 --2.9885928 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --3.0555531 --2.8547554 --2.5830523 --3.1383448 --2.9266755 --2.639545 --3.1794797 --2.9624572 --2.6677181 --2.357996 --2.4270069 --2.4612421 --2.7492597 --2.8297216 --2.8696374 --3.1405234 --3.2324363 --3.2780328 --3.3408769 --3.2958707 --3.2052108 --3.4385221 --3.391213 --3.2958707 --3.4869636 --3.4385221 --3.3408769 --1.1352953 --1.1202634 --1.0899943 --1.5173482 --1.4972577 --1.4568024 --1.8994011 --1.874252 --1.8236105 --1.0899943 --1.1202634 --1.1352953 --1.4568024 --1.4972577 --1.5173482 --1.8236105 --1.874252 --1.8994011 --1.1626657 --1.1966931 --1.2135736 --1.5539294 --1.5994078 --1.621969 --1.9451931 --2.0021225 --2.0303643 --2.2416195 --2.2104785 --2.1477066 --2.2104785 --2.1800655 --2.118774 --2.1477066 --2.118774 --2.0604927 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --2.0439512 --1.9044368 --1.7149616 --2.0175074 --1.8814343 --1.6968504 --1.9642842 --1.8351999 --1.6605336 --0.73038568 --0.77494991 --0.80897011 --0.97617722 --1.0357383 --1.0812071 --1.2219688 --1.2965268 --1.3534441 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --1.8765684 --1.7591999 --1.6011047 --1.7591999 --1.6579443 --1.5225053 --1.6011047 --1.5225053 --1.4185809 --0.83485064 --0.85072708 --0.858661 --1.115797 --1.1370163 --1.1476201 --1.3967434 --1.4233054 --1.4365793 --0.928038 --1.0307797 --1.1064189 --1.2403441 --1.3776608 --1.4787542 --1.5526502 --1.7245418 --1.8510895 --2.0439512 --2.0175074 --1.9642842 --1.9044368 --1.8814343 --1.8351999 --1.7149616 --1.6968504 --1.6605336 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --2.2106115 --2.2720001 --2.3024862 --2.5774196 --2.6489944 --2.6845391 --2.9442277 --3.0259887 --3.066592 --2.357996 --2.4270069 --2.4612421 --2.7492597 --2.8297216 --2.8696374 --3.1405234 --3.2324363 --3.2780328 --3.4869636 --3.4385221 --3.3408769 --3.4385221 --3.391213 --3.2958707 --3.3408769 --3.2958707 --3.2052108 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --3.1794797 --2.9624572 --2.6677181 --3.1383448 --2.9266755 --2.639545 --3.0555531 --2.8547554 --2.5830523 --1.4812912 --1.5716717 --1.6406679 --1.7270828 --1.8324601 --1.9129049 --1.9728743 --2.0932486 --2.1851419 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --2.9191065 --2.7365332 --2.4906074 --2.7365332 --2.5790245 --2.3683416 --2.4906074 --2.3683416 --2.2066813 --1.693156 --1.725355 --1.7414457 --1.9741024 --2.0116442 --2.0304048 --2.2550488 --2.2979333 --2.319364 --1.8821488 --2.0905188 --2.2439221 --2.1944549 --2.4373998 --2.6162574 --2.506761 --2.7842809 --2.9885928 --3.1794797 --3.1383448 --3.0555531 --2.9624572 --2.9266755 --2.8547554 --2.6677181 --2.639545 --2.5830523 --1.1352953 --1.1202634 --1.0899943 --1.5173482 --1.4972577 --1.4568024 --1.8994011 --1.874252 --1.8236105 --1.0400626 --0.97314799 --0.8827835 --1.3900675 --1.3006346 --1.1798604 --1.7400724 --1.6281212 --1.4769373 --1.7149616 --1.9044368 --2.0439512 --1.6968504 --1.8814343 --2.0175074 --1.6605336 --1.8351999 --1.9642842 --1.1352953 --1.1202634 --1.0899943 --1.5173482 --1.4972577 --1.4568024 --1.8994011 --1.874252 --1.8236105 --2.1477066 --2.2104785 --2.2416195 --2.118774 --2.1800655 --2.2104785 --2.0604927 --2.118774 --2.1477066 --0.858661 --0.85072708 --0.83485064 --1.1476201 --1.1370163 --1.115797 --1.4365793 --1.4233054 --1.3967434 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --1.9642842 --2.0175074 --2.0439512 --1.8351999 --1.8814343 --1.9044368 --1.6605336 --1.6968504 --1.7149616 --0.80897011 --0.77494991 --0.73038568 --1.0812071 --1.0357383 --0.97617722 --1.3534441 --1.2965268 --1.2219688 --1.6011047 --1.7591999 --1.8765684 --1.5225053 --1.6579443 --1.7591999 --1.4185809 --1.5225053 --1.6011047 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --2.1093453 --1.9736361 --1.7903684 --2.4593502 --2.3011228 --2.0874453 --2.8093551 --2.6286094 --2.3845222 --2.6677181 --2.9624572 --3.1794797 --2.639545 --2.9266755 --3.1383448 --2.5830523 --2.8547554 --3.0555531 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --3.3408769 --3.4385221 --3.4869636 --3.2958707 --3.391213 --3.4385221 --3.2052108 --3.2958707 --3.3408769 --1.7414457 --1.725355 --1.693156 --2.0304048 --2.0116442 --1.9741024 --2.319364 --2.2979333 --2.2550488 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --3.0555531 --3.1383448 --3.1794797 --2.8547554 --2.9266755 --2.9624572 --2.5830523 --2.639545 --2.6677181 --1.6406679 --1.5716717 --1.4812912 --1.9129049 --1.8324601 --1.7270828 --2.1851419 --2.0932486 --1.9728743 --2.4906074 --2.7365332 --2.9191065 --2.3683416 --2.5790245 --2.7365332 --2.2066813 --2.3683416 --2.4906074 --2.2321968 --2.3683935 --2.4723657 --2.4779883 --2.6291819 --2.7446027 --2.7237799 --2.8899704 --3.0168397 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --3.178628 --2.9741243 --2.6979533 --3.5286329 --3.3016109 --2.9950302 --3.8786378 --3.6290976 --3.2921071 --2.9947818 --3.2141779 --3.38011 --3.2141779 --3.5001046 --3.7138665 --3.38011 --3.7138665 --3.9616445 --2.5514614 --2.5999829 --2.6242304 --2.8324078 --2.8862721 --2.9131896 --3.1133542 --3.1725612 --3.2021487 --2.8362596 --3.1502579 --3.3814253 --3.1485657 --3.4971389 --3.7537607 --3.4608718 --3.8440199 --4.126096 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --3.505571 --3.5822397 --3.6204746 --3.874311 --3.9719168 --4.0204776 --4.1468221 --4.2591823 --4.3150081 --3.5533263 --3.6573206 --3.7089105 --3.94459 --4.0600353 --4.1173059 --4.3358537 --4.46275 --4.5257012 --3.7089105 --3.6573206 --3.5533263 --4.1173059 --4.0600353 --3.94459 --4.5257012 --4.46275 --4.3358537 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --4.349929 --4.4729674 --4.5340472 --4.4729674 --4.6023605 --4.6665657 --4.5340472 --4.6665657 --4.7323078 --3.3814253 --3.1502579 --2.8362596 --3.7537607 --3.4971389 --3.1485657 --4.126096 --3.8440199 --3.4608718 --3.505571 --3.874311 --4.1468221 --3.5822397 --3.9719168 --4.2591823 --3.6204746 --4.0204776 --4.3150081 --2.9831024 --3.1651153 --3.3040635 --3.2288939 --3.4259037 --3.5763005 --3.4746854 --3.6866922 --3.8485375 --3.6055383 --3.9746125 --4.2479107 --3.9026152 --4.3020991 --4.5979156 --4.1996921 --4.6295857 --4.9479206 --4.2479107 --3.9746125 --3.6055383 --4.5979156 --4.3020991 --3.9026152 --4.9479206 --4.6295857 --4.1996921 --3.7828823 --4.0600142 --4.2696126 --4.0600142 --4.4211848 --4.6911998 --4.2696126 --4.6911998 --5.0041825 --3.4097669 --3.4746108 --3.5070151 --3.6907132 --3.7609 --3.7959743 --3.9716596 --4.0471891 --4.0849334 --3.7903705 --4.2099969 --4.5189286 --4.1026766 --4.556878 --4.8912639 --4.4149826 --4.903759 --5.2635992 --4.636868 --4.5754734 --4.4518459 --5.0189209 --4.9524678 --4.818654 --5.4009738 --5.3294621 --5.1854621 --4.4280896 --4.5249343 --4.5732311 --4.8938665 --5.0171581 --5.078498 --5.2380911 --5.3800197 --5.4505366 --4.7486566 --4.8876343 --4.956579 --5.1399203 --5.290349 --5.3649743 --5.5311839 --5.6930637 --5.7733697 --4.956579 --4.8876343 --4.7486566 --5.3649743 --5.290349 --5.1399203 --5.7733697 --5.6930637 --5.5311839 --4.636868 --4.5754734 --4.4518459 --5.0189209 --4.9524678 --4.818654 --5.4009738 --5.3294621 --5.1854621 --5.4946471 --5.6500641 --5.7272175 --5.6500641 --5.813508 --5.8946093 --5.7272175 --5.8946093 --5.9776519 --4.5189286 --4.2099969 --3.7903705 --4.8912639 --4.556878 --4.1026766 --5.2635992 --4.903759 --4.4149826 --4.4280896 --4.8938665 --5.2380911 --4.5249343 --5.0171581 --5.3800197 --4.5732311 --5.078498 --5.4505366 --2.6242304 --2.5999829 --2.5514614 --2.9131896 --2.8862721 --2.8324078 --3.2021487 --3.1725612 --3.1133542 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --3.3312287 --3.4237367 --3.4696771 --3.6980368 --3.8007311 --3.85173 --4.0648449 --4.1777254 --4.2337829 --3.6204746 --3.5822397 --3.505571 --4.0204776 --3.9719168 --3.874311 --4.3150081 --4.2591823 --4.1468221 --2.4723657 --2.3683935 --2.2321968 --2.7446027 --2.6291819 --2.4779883 --3.0168397 --2.8899704 --2.7237799 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --3.38011 --3.2141779 --2.9947818 --3.7138665 --3.5001046 --3.2141779 --3.9616445 --3.7138665 --3.38011 --2.8362596 --3.1502579 --3.3814253 --3.1485657 --3.4971389 --3.7537607 --3.4608718 --3.8440199 --4.126096 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --4.1468221 --3.874311 --3.505571 --4.2591823 --3.9719168 --3.5822397 --4.3150081 --4.0204776 --3.6204746 --3.5533263 --3.6573206 --3.7089105 --3.94459 --4.0600353 --4.1173059 --4.3358537 --4.46275 --4.5257012 --4.5340472 --4.4729674 --4.349929 --4.6665657 --4.6023605 --4.4729674 --4.7323078 --4.6665657 --4.5340472 --3.5070151 --3.4746108 --3.4097669 --3.7959743 --3.7609 --3.6907132 --4.0849334 --4.0471891 --3.9716596 --3.6055383 --3.9746125 --4.2479107 --3.9026152 --4.3020991 --4.5979156 --4.1996921 --4.6295857 --4.9479206 --4.4518459 --4.5754734 --4.636868 --4.818654 --4.9524678 --5.0189209 --5.1854621 --5.3294621 --5.4009738 --4.5732311 --4.5249343 --4.4280896 --5.078498 --5.0171581 --4.8938665 --5.4505366 --5.3800197 --5.2380911 --3.3040635 --3.1651153 --2.9831024 --3.5763005 --3.4259037 --3.2288939 --3.8485375 --3.6866922 --3.4746854 --3.6055383 --3.9746125 --4.2479107 --3.9026152 --4.3020991 --4.5979156 --4.1996921 --4.6295857 --4.9479206 --4.2696126 --4.0600142 --3.7828823 --4.6911998 --4.4211848 --4.0600142 --5.0041825 --4.6911998 --4.2696126 --3.7903705 --4.2099969 --4.5189286 --4.1026766 --4.556878 --4.8912639 --4.4149826 --4.903759 --5.2635992 --4.636868 --4.5754734 --4.4518459 --5.0189209 --4.9524678 --4.818654 --5.4009738 --5.3294621 --5.1854621 --5.2380911 --4.8938665 --4.4280896 --5.3800197 --5.0171581 --4.5249343 --5.4505366 --5.078498 --4.5732311 --4.7486566 --4.8876343 --4.956579 --5.1399203 --5.290349 --5.3649743 --5.5311839 --5.6930637 --5.7733697 --5.7272175 --5.6500641 --5.4946471 --5.8946093 --5.813508 --5.6500641 --5.9776519 --5.8946093 --5.7272175 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --3.3312287 --3.4237367 --3.4696771 --3.6980368 --3.8007311 --3.85173 --4.0648449 --4.1777254 --4.2337829 --3.5533263 --3.6573206 --3.7089105 --3.94459 --4.0600353 --4.1173059 --4.3358537 --4.46275 --4.5257012 --4.7323078 --4.6665657 --4.5340472 --4.6665657 --4.6023605 --4.4729674 --4.5340472 --4.4729674 --4.349929 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --4.3150081 --4.0204776 --3.6204746 --4.2591823 --3.9719168 --3.5822397 --4.1468221 --3.874311 --3.505571 --2.2321968 --2.3683935 --2.4723657 --2.4779883 --2.6291819 --2.7446027 --2.7237799 --2.8899704 --3.0168397 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --3.9616445 --3.7138665 --3.38011 --3.7138665 --3.5001046 --3.2141779 --3.38011 --3.2141779 --2.9947818 --2.5514614 --2.5999829 --2.6242304 --2.8324078 --2.8862721 --2.9131896 --3.1133542 --3.1725612 --3.2021487 --2.8362596 --3.1502579 --3.3814253 --3.1485657 --3.4971389 --3.7537607 --3.4608718 --3.8440199 --4.126096 --4.3150081 --4.2591823 --4.1468221 --4.0204776 --3.9719168 --3.874311 --3.6204746 --3.5822397 --3.505571 --4.636868 --4.5754734 --4.4518459 --5.0189209 --4.9524678 --4.818654 --5.4009738 --5.3294621 --5.1854621 --4.4518459 --4.5754734 --4.636868 --4.818654 --4.9524678 --5.0189209 --5.1854621 --5.3294621 --5.4009738 --4.7486566 --4.8876343 --4.956579 --5.1399203 --5.290349 --5.3649743 --5.5311839 --5.6930637 --5.7733697 --5.9776519 --5.8946093 --5.7272175 --5.8946093 --5.813508 --5.6500641 --5.7272175 --5.6500641 --5.4946471 --3.6055383 --3.9746125 --4.2479107 --3.9026152 --4.3020991 --4.5979156 --4.1996921 --4.6295857 --4.9479206 --5.4505366 --5.078498 --4.5732311 --5.3800197 --5.0171581 --4.5249343 --5.2380911 --4.8938665 --4.4280896 --2.9831024 --3.1651153 --3.3040635 --3.2288939 --3.4259037 --3.5763005 --3.4746854 --3.6866922 --3.8485375 --3.6055383 --3.9746125 --4.2479107 --3.9026152 --4.3020991 --4.5979156 --4.1996921 --4.6295857 --4.9479206 --5.0041825 --4.6911998 --4.2696126 --4.6911998 --4.4211848 --4.0600142 --4.2696126 --4.0600142 --3.7828823 --3.4097669 --3.4746108 --3.5070151 --3.6907132 --3.7609 --3.7959743 --3.9716596 --4.0471891 --4.0849334 --3.7903705 --4.2099969 --4.5189286 --4.1026766 --4.556878 --4.8912639 --4.4149826 --4.903759 --5.2635992 --5.4505366 --5.3800197 --5.2380911 --5.078498 --5.0171581 --4.8938665 --4.5732311 --4.5249343 --4.4280896 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --3.178628 --2.9741243 --2.6979533 --3.5286329 --3.3016109 --2.9950302 --3.8786378 --3.6290976 --3.2921071 --3.6204746 --4.0204776 --4.3150081 --3.5822397 --3.9719168 --4.2591823 --3.505571 --3.874311 --4.1468221 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --4.5340472 --4.6665657 --4.7323078 --4.4729674 --4.6023605 --4.6665657 --4.349929 --4.4729674 --4.5340472 --2.6242304 --2.5999829 --2.5514614 --2.9131896 --2.8862721 --2.8324078 --3.2021487 --3.1725612 --3.1133542 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --4.1468221 --4.2591823 --4.3150081 --3.874311 --3.9719168 --4.0204776 --3.505571 --3.5822397 --3.6204746 --2.4723657 --2.3683935 --2.2321968 --2.7446027 --2.6291819 --2.4779883 --3.0168397 --2.8899704 --2.7237799 --3.38011 --3.7138665 --3.9616445 --3.2141779 --3.5001046 --3.7138665 --2.9947818 --3.2141779 --3.38011 --4.636868 --4.5754734 --4.4518459 --5.0189209 --4.9524678 --4.818654 --5.4009738 --5.3294621 --5.1854621 --4.2479107 --3.9746125 --3.6055383 --4.5979156 --4.3020991 --3.9026152 --4.9479206 --4.6295857 --4.1996921 --4.5732311 --5.078498 --5.4505366 --4.5249343 --5.0171581 --5.3800197 --4.4280896 --4.8938665 --5.2380911 --4.636868 --4.5754734 --4.4518459 --5.0189209 --4.9524678 --4.818654 --5.4009738 --5.3294621 --5.1854621 --5.7272175 --5.8946093 --5.9776519 --5.6500641 --5.813508 --5.8946093 --5.4946471 --5.6500641 --5.7272175 --3.5070151 --3.4746108 --3.4097669 --3.7959743 --3.7609 --3.6907132 --4.0849334 --4.0471891 --3.9716596 --3.6055383 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-3.5162679 -2.8864031 -2.2565383 -3.3683958 -2.7650191 -2.1616425 -3.174693 -2.6060141 -2.0373352 --0.76656418 --0.82272227 --0.86519534 --0.82272227 --0.89590996 --0.95062587 --0.86519534 --0.95062587 --1.0140488 --1.0245306 --1.0995872 --1.1563534 --1.0995872 --1.1974042 --1.2705333 --1.1563534 --1.2705333 --1.3552994 --1.2824971 --1.3764521 --1.4475115 --1.3764521 --1.4988985 --1.5904407 --1.4475115 --1.5904407 --1.6965501 --0.89730916 --0.91693379 --0.92672065 --0.99169429 --1.0166781 --1.0291081 --1.0614481 --1.0902085 --1.104498 --1.1992743 --1.225503 --1.2385834 --1.3254222 --1.3588136 --1.3754266 --1.4186497 --1.4570887 --1.476187 --1.5012394 --1.5340723 --1.5504462 --1.65915 --1.7009492 --1.721745 --1.7758513 --1.8239689 --1.8478759 --1.1134366 --1.1449304 --1.1605647 --1.1449304 --1.1780507 --1.1944851 --1.1605647 --1.1944851 --1.2113128 --1.4881336 --1.5302257 --1.5511214 --1.5302257 --1.5744917 --1.5964567 --1.5511214 --1.5964567 --1.6189474 --1.8628306 --1.915521 --1.9416781 --1.915521 --1.9709328 --1.9984283 --1.9416781 --1.9984283 --2.026582 --0.89730916 --0.99169429 --1.0614481 --0.91693379 --1.0166781 --1.0902085 --0.92672065 --1.0291081 --1.104498 --1.1992743 --1.3254222 --1.4186497 --1.225503 --1.3588136 --1.4570887 --1.2385834 --1.3754266 --1.476187 --1.5012394 --1.65915 --1.7758513 --1.5340723 --1.7009492 --1.8239689 --1.5504462 --1.721745 --1.8478759 --1.5546647 --1.6685586 --1.754698 --1.6685586 --1.8169901 --1.9279592 --1.754698 --1.9279592 --2.0565868 --1.8126311 --1.9454235 --2.045856 --1.9454235 --2.1184844 --2.2478666 --2.045856 --2.2478666 --2.3978374 --2.0705975 --2.2222884 --2.3370141 --2.2222884 --2.4199786 --2.567774 --2.3370141 --2.567774 --2.7390881 --1.8198278 --1.8596284 --1.8794771 --2.0112498 --2.0619194 --2.0871285 --2.152717 --2.2110459 --2.2400265 --2.1217929 --2.1681977 --2.1913399 --2.3449777 --2.4040549 --2.433447 --2.5099187 --2.5779261 --2.6117154 --2.4237581 --2.4767669 --2.5032026 --2.6787056 --2.7461904 --2.7797655 --2.8671203 --2.9448063 --2.9834044 --2.2581548 --2.3220271 --2.3537351 --2.3220271 --2.3891982 --2.4225286 --2.3537351 --2.4225286 --2.456657 --2.6328517 --2.7073224 --2.7442917 --2.7073224 --2.7856392 --2.8245003 --2.7442917 --2.8245003 --2.8642915 --3.0075487 --3.0926177 --3.1348484 --3.0926177 --3.1820803 --3.2264719 --3.1348484 --3.2264719 --3.2719261 --1.8198278 --2.0112498 --2.152717 --1.8596284 --2.0619194 --2.2110459 --1.8794771 --2.0871285 --2.2400265 --2.1217929 --2.3449777 --2.5099187 --2.1681977 --2.4040549 --2.5779261 --2.1913399 --2.433447 --2.6117154 --2.4237581 --2.6787056 --2.8671203 --2.4767669 --2.7461904 --2.9448063 --2.5032026 --2.7797655 --2.9834044 --0.92672065 --0.91693379 --0.89730916 --1.0291081 --1.0166781 --0.99169429 --1.104498 --1.0902085 --1.0614481 --1.2385834 --1.225503 --1.1992743 --1.3754266 --1.3588136 --1.3254222 --1.476187 --1.4570887 --1.4186497 --1.5504462 --1.5340723 --1.5012394 --1.721745 --1.7009492 --1.65915 --1.8478759 --1.8239689 --1.7758513 --0.86519534 --0.82272227 --0.76656418 --0.95062587 --0.89590996 --0.82272227 --1.0140488 --0.95062587 --0.86519534 --1.1563534 --1.0995872 --1.0245306 --1.2705333 --1.1974042 --1.0995872 --1.3552994 --1.2705333 --1.1563534 --1.4475115 --1.3764521 --1.2824971 --1.5904407 --1.4988985 --1.3764521 --1.6965501 --1.5904407 --1.4475115 --1.0614481 --0.99169429 --0.89730916 --1.0902085 --1.0166781 --0.91693379 --1.104498 --1.0291081 --0.92672065 --1.4186497 --1.3254222 --1.1992743 --1.4570887 --1.3588136 --1.225503 --1.476187 --1.3754266 --1.2385834 --1.7758513 --1.65915 --1.5012394 --1.8239689 --1.7009492 --1.5340723 --1.8478759 --1.721745 --1.5504462 --1.1605647 --1.1449304 --1.1134366 --1.1944851 --1.1780507 --1.1449304 --1.2113128 --1.1944851 --1.1605647 --1.5511214 --1.5302257 --1.4881336 --1.5964567 --1.5744917 --1.5302257 --1.6189474 --1.5964567 --1.5511214 --1.9416781 --1.915521 --1.8628306 --1.9984283 --1.9709328 --1.915521 --2.026582 --1.9984283 --1.9416781 --1.8794771 --1.8596284 --1.8198278 --2.0871285 --2.0619194 --2.0112498 --2.2400265 --2.2110459 --2.152717 --2.1913399 --2.1681977 --2.1217929 --2.433447 --2.4040549 --2.3449777 --2.6117154 --2.5779261 --2.5099187 --2.5032026 --2.4767669 --2.4237581 --2.7797655 --2.7461904 --2.6787056 --2.9834044 --2.9448063 --2.8671203 --1.754698 --1.6685586 --1.5546647 --1.9279592 --1.8169901 --1.6685586 --2.0565868 --1.9279592 --1.754698 --2.045856 --1.9454235 --1.8126311 --2.2478666 --2.1184844 --1.9454235 --2.3978374 --2.2478666 --2.045856 --2.3370141 --2.2222884 --2.0705975 --2.567774 --2.4199786 --2.2222884 --2.7390881 --2.567774 --2.3370141 --2.152717 --2.0112498 --1.8198278 --2.2110459 --2.0619194 --1.8596284 --2.2400265 --2.0871285 --1.8794771 --2.5099187 --2.3449777 --2.1217929 --2.5779261 --2.4040549 --2.1681977 --2.6117154 --2.433447 --2.1913399 --2.8671203 --2.6787056 --2.4237581 --2.9448063 --2.7461904 --2.4767669 --2.9834044 --2.7797655 --2.5032026 --2.3537351 --2.3220271 --2.2581548 --2.4225286 --2.3891982 --2.3220271 --2.456657 --2.4225286 --2.3537351 --2.7442917 --2.7073224 --2.6328517 --2.8245003 --2.7856392 --2.7073224 --2.8642915 --2.8245003 --2.7442917 --3.1348484 --3.0926177 --3.0075487 --3.2264719 --3.1820803 --3.0926177 --3.2719261 --3.2264719 --3.1348484 --1.2113128 --1.1944851 --1.1605647 --1.1944851 --1.1780507 --1.1449304 --1.1605647 --1.1449304 --1.1134366 --1.6189474 --1.5964567 --1.5511214 --1.5964567 --1.5744917 --1.5302257 --1.5511214 --1.5302257 --1.4881336 --2.026582 --1.9984283 --1.9416781 --1.9984283 --1.9709328 --1.915521 --1.9416781 --1.915521 --1.8628306 --1.104498 --1.0291081 --0.92672065 --1.0902085 --1.0166781 --0.91693379 --1.0614481 --0.99169429 --0.89730916 --1.476187 --1.3754266 --1.2385834 --1.4570887 --1.3588136 --1.225503 --1.4186497 --1.3254222 --1.1992743 --1.8478759 --1.721745 --1.5504462 --1.8239689 --1.7009492 --1.5340723 --1.7758513 --1.65915 --1.5012394 --1.0140488 --0.95062587 --0.86519534 --0.95062587 --0.89590996 --0.82272227 --0.86519534 --0.82272227 --0.76656418 --1.3552994 --1.2705333 --1.1563534 --1.2705333 --1.1974042 --1.0995872 --1.1563534 --1.0995872 --1.0245306 --1.6965501 --1.5904407 --1.4475115 --1.5904407 --1.4988985 --1.3764521 --1.4475115 --1.3764521 --1.2824971 --1.104498 --1.0902085 --1.0614481 --1.0291081 --1.0166781 --0.99169429 --0.92672065 --0.91693379 --0.89730916 --1.476187 --1.4570887 --1.4186497 --1.3754266 --1.3588136 --1.3254222 --1.2385834 --1.225503 --1.1992743 --1.8478759 --1.8239689 --1.7758513 --1.721745 --1.7009492 --1.65915 --1.5504462 --1.5340723 --1.5012394 --2.456657 --2.4225286 --2.3537351 --2.4225286 --2.3891982 --2.3220271 --2.3537351 --2.3220271 --2.2581548 --2.8642915 --2.8245003 --2.7442917 --2.8245003 --2.7856392 --2.7073224 --2.7442917 --2.7073224 --2.6328517 --3.2719261 --3.2264719 --3.1348484 --3.2264719 --3.1820803 --3.0926177 --3.1348484 --3.0926177 --3.0075487 --2.2400265 --2.0871285 --1.8794771 --2.2110459 --2.0619194 --1.8596284 --2.152717 --2.0112498 --1.8198278 --2.6117154 --2.433447 --2.1913399 --2.5779261 --2.4040549 --2.1681977 --2.5099187 --2.3449777 --2.1217929 --2.9834044 --2.7797655 --2.5032026 --2.9448063 --2.7461904 --2.4767669 --2.8671203 --2.6787056 --2.4237581 --2.0565868 --1.9279592 --1.754698 --1.9279592 --1.8169901 --1.6685586 --1.754698 --1.6685586 --1.5546647 --2.3978374 --2.2478666 --2.045856 --2.2478666 --2.1184844 --1.9454235 --2.045856 --1.9454235 --1.8126311 --2.7390881 --2.567774 --2.3370141 --2.567774 --2.4199786 --2.2222884 --2.3370141 --2.2222884 --2.0705975 --2.2400265 --2.2110459 --2.152717 --2.0871285 --2.0619194 --2.0112498 --1.8794771 --1.8596284 --1.8198278 --2.6117154 --2.5779261 --2.5099187 --2.433447 --2.4040549 --2.3449777 --2.1913399 --2.1681977 --2.1217929 --2.9834044 --2.9448063 --2.8671203 --2.7797655 --2.7461904 --2.6787056 --2.5032026 --2.4767669 --2.4237581 --0.92672065 --1.0291081 --1.104498 --0.91693379 --1.0166781 --1.0902085 --0.89730916 --0.99169429 --1.0614481 --1.2385834 --1.3754266 --1.476187 --1.225503 --1.3588136 --1.4570887 --1.1992743 --1.3254222 --1.4186497 --1.5504462 --1.721745 --1.8478759 --1.5340723 --1.7009492 --1.8239689 --1.5012394 --1.65915 --1.7758513 --1.1605647 --1.1944851 --1.2113128 --1.1449304 --1.1780507 --1.1944851 --1.1134366 --1.1449304 --1.1605647 --1.5511214 --1.5964567 --1.6189474 --1.5302257 --1.5744917 --1.5964567 --1.4881336 --1.5302257 --1.5511214 --1.9416781 --1.9984283 --2.026582 --1.915521 --1.9709328 --1.9984283 --1.8628306 --1.915521 --1.9416781 --1.0614481 --1.0902085 --1.104498 --0.99169429 --1.0166781 --1.0291081 --0.89730916 --0.91693379 --0.92672065 --1.4186497 --1.4570887 --1.476187 --1.3254222 --1.3588136 --1.3754266 --1.1992743 --1.225503 --1.2385834 --1.7758513 --1.8239689 --1.8478759 --1.65915 --1.7009492 --1.721745 --1.5012394 --1.5340723 --1.5504462 --0.86519534 --0.95062587 --1.0140488 --0.82272227 --0.89590996 --0.95062587 --0.76656418 --0.82272227 --0.86519534 --1.1563534 --1.2705333 --1.3552994 --1.0995872 --1.1974042 --1.2705333 --1.0245306 --1.0995872 --1.1563534 --1.4475115 --1.5904407 --1.6965501 --1.3764521 --1.4988985 --1.5904407 --1.2824971 --1.3764521 --1.4475115 --1.8794771 --2.0871285 --2.2400265 --1.8596284 --2.0619194 --2.2110459 --1.8198278 --2.0112498 --2.152717 --2.1913399 --2.433447 --2.6117154 --2.1681977 --2.4040549 --2.5779261 --2.1217929 --2.3449777 --2.5099187 --2.5032026 --2.7797655 --2.9834044 --2.4767669 --2.7461904 --2.9448063 --2.4237581 --2.6787056 --2.8671203 --2.3537351 --2.4225286 --2.456657 --2.3220271 --2.3891982 --2.4225286 --2.2581548 --2.3220271 --2.3537351 --2.7442917 --2.8245003 --2.8642915 --2.7073224 --2.7856392 --2.8245003 --2.6328517 --2.7073224 --2.7442917 --3.1348484 --3.2264719 --3.2719261 --3.0926177 --3.1820803 --3.2264719 --3.0075487 --3.0926177 --3.1348484 --2.152717 --2.2110459 --2.2400265 --2.0112498 --2.0619194 --2.0871285 --1.8198278 --1.8596284 --1.8794771 --2.5099187 --2.5779261 --2.6117154 --2.3449777 --2.4040549 --2.433447 --2.1217929 --2.1681977 --2.1913399 --2.8671203 --2.9448063 --2.9834044 --2.6787056 --2.7461904 --2.7797655 --2.4237581 --2.4767669 --2.5032026 --1.754698 --1.9279592 --2.0565868 --1.6685586 --1.8169901 --1.9279592 --1.5546647 --1.6685586 --1.754698 --2.045856 --2.2478666 --2.3978374 --1.9454235 --2.1184844 --2.2478666 --1.8126311 --1.9454235 --2.045856 --2.3370141 --2.567774 --2.7390881 --2.2222884 --2.4199786 --2.567774 --2.0705975 --2.2222884 --2.3370141 --2.3427651 --2.5143949 --2.6442006 --2.5143949 --2.7380703 --2.9052925 --2.6442006 --2.9052925 --3.0991248 --2.6007316 --2.7912598 --2.9353587 --2.7912598 --3.0395645 --3.2251999 --2.9353587 --3.2251999 --3.4403755 --2.858698 --3.0681247 --3.2265167 --3.0681247 --3.3410588 --3.5451073 --3.2265167 --3.5451073 --3.7816261 --2.7423465 --2.8023231 --2.8322336 --3.0308053 --3.1071607 --3.1451489 --3.243986 --3.3318834 --3.3755549 --3.0443116 --3.1108923 --3.1440964 --3.3645332 --3.4492962 --3.4914674 --3.6011876 --3.6987636 --3.7472439 --3.3462767 --3.4194616 --3.4559591 --3.6982611 --3.7914317 --3.8377859 --3.9583893 --4.0656437 --4.1189328 --3.4028729 --3.4991237 --3.5469054 --3.4991237 --3.6003457 --3.6505722 --3.5469054 --3.6505722 --3.7020011 --3.7775699 --3.8844191 --3.937462 --3.8844191 --3.9967867 --4.0525439 --3.937462 --4.0525439 --4.1096357 --4.1522669 --4.2697144 --4.3280187 --4.2697144 --4.3932278 --4.4545155 --4.3280187 --4.4545155 --4.5172703 --2.7423465 --3.0308053 --3.243986 --2.8023231 --3.1071607 --3.3318834 --2.8322336 --3.1451489 --3.3755549 --3.0443116 --3.3645332 --3.6011876 --3.1108923 --3.4492962 --3.6987636 --3.1440964 --3.4914674 --3.7472439 --3.3462767 --3.6982611 --3.9583893 --3.4194616 --3.7914317 --4.0656437 --3.4559591 --3.8377859 --4.1189328 --3.1308656 --3.3602312 --3.5337032 --3.3602312 --3.6591505 --3.8826258 --3.5337032 --3.8826258 --4.1416628 --3.388832 --3.6370961 --3.8248613 --3.6370961 --3.9606447 --4.2025332 --3.8248613 --4.2025332 --4.4829135 --3.6467985 --3.913961 --4.1160194 --3.913961 --4.262139 --4.5224406 --4.1160194 --4.5224406 --4.8241642 --3.6648652 --3.7450177 --3.7849901 --4.0503608 --4.1524019 --4.2031694 --4.335255 --4.4527208 --4.5110834 --3.9668303 --4.053587 --4.0968528 --4.3840887 --4.4945374 --4.5494878 --4.6924566 --4.819601 --4.8827723 --4.2687954 --4.3621562 --4.4087156 --4.7178166 --4.8366729 --4.8958063 --5.0496582 --5.1864812 --5.2544613 --4.5475911 --4.6762204 --4.7400757 --4.6762204 --4.8114932 --4.8786158 --4.7400757 --4.8786158 --4.9473453 --4.922288 --5.0615158 --5.1306324 --5.0615158 --5.2079342 --5.2805875 --5.1306324 --5.2805875 --5.3549799 --5.296985 --5.4468111 --5.521189 --5.4468111 --5.6043753 --5.6825591 --5.521189 --5.6825591 --5.7626144 --3.6648652 --4.0503608 --4.335255 --3.7450177 --4.1524019 --4.4527208 --3.7849901 --4.2031694 --4.5110834 --3.9668303 --4.3840887 --4.6924566 --4.053587 --4.4945374 --4.819601 --4.0968528 --4.5494878 --4.8827723 --4.2687954 --4.7178166 --5.0496582 --4.3621562 --4.8366729 --5.1864812 --4.4087156 --4.8958063 --5.2544613 --2.8322336 --2.8023231 --2.7423465 --3.1451489 --3.1071607 --3.0308053 --3.3755549 --3.3318834 --3.243986 --3.1440964 --3.1108923 --3.0443116 --3.4914674 --3.4492962 --3.3645332 --3.7472439 --3.6987636 --3.6011876 --3.4559591 --3.4194616 --3.3462767 --3.8377859 --3.7914317 --3.6982611 --4.1189328 --4.0656437 --3.9583893 --2.6442006 --2.5143949 --2.3427651 --2.9052925 --2.7380703 --2.5143949 --3.0991248 --2.9052925 --2.6442006 --2.9353587 --2.7912598 --2.6007316 --3.2251999 --3.0395645 --2.7912598 --3.4403755 --3.2251999 --2.9353587 --3.2265167 --3.0681247 --2.858698 --3.5451073 --3.3410588 --3.0681247 --3.7816261 --3.5451073 --3.2265167 --3.243986 --3.0308053 --2.7423465 --3.3318834 --3.1071607 --2.8023231 --3.3755549 --3.1451489 --2.8322336 --3.6011876 --3.3645332 --3.0443116 --3.6987636 --3.4492962 --3.1108923 --3.7472439 --3.4914674 --3.1440964 --3.9583893 --3.6982611 --3.3462767 --4.0656437 --3.7914317 --3.4194616 --4.1189328 --3.8377859 --3.4559591 --3.5469054 --3.4991237 --3.4028729 --3.6505722 --3.6003457 --3.4991237 --3.7020011 --3.6505722 --3.5469054 --3.937462 --3.8844191 --3.7775699 --4.0525439 --3.9967867 --3.8844191 --4.1096357 --4.0525439 --3.937462 --4.3280187 --4.2697144 --4.1522669 --4.4545155 --4.3932278 --4.2697144 --4.5172703 --4.4545155 --4.3280187 --3.7849901 --3.7450177 --3.6648652 --4.2031694 --4.1524019 --4.0503608 --4.5110834 --4.4527208 --4.335255 --4.0968528 --4.053587 --3.9668303 --4.5494878 --4.4945374 --4.3840887 --4.8827723 --4.819601 --4.6924566 --4.4087156 --4.3621562 --4.2687954 --4.8958063 --4.8366729 --4.7178166 --5.2544613 --5.1864812 --5.0496582 --3.5337032 --3.3602312 --3.1308656 --3.8826258 --3.6591505 --3.3602312 --4.1416628 --3.8826258 --3.5337032 --3.8248613 --3.6370961 --3.388832 --4.2025332 --3.9606447 --3.6370961 --4.4829135 --4.2025332 --3.8248613 --4.1160194 --3.913961 --3.6467985 --4.5224406 --4.262139 --3.913961 --4.8241642 --4.5224406 --4.1160194 --4.335255 --4.0503608 --3.6648652 --4.4527208 --4.1524019 --3.7450177 --4.5110834 --4.2031694 --3.7849901 --4.6924566 --4.3840887 --3.9668303 --4.819601 --4.4945374 --4.053587 --4.8827723 --4.5494878 --4.0968528 --5.0496582 --4.7178166 --4.2687954 --5.1864812 --4.8366729 --4.3621562 --5.2544613 --4.8958063 --4.4087156 --4.7400757 --4.6762204 --4.5475911 --4.8786158 --4.8114932 --4.6762204 --4.9473453 --4.8786158 --4.7400757 --5.1306324 --5.0615158 --4.922288 --5.2805875 --5.2079342 --5.0615158 --5.3549799 --5.2805875 --5.1306324 --5.521189 --5.4468111 --5.296985 --5.6825591 --5.6043753 --5.4468111 --5.7626144 --5.6825591 --5.521189 --3.7020011 --3.6505722 --3.5469054 --3.6505722 --3.6003457 --3.4991237 --3.5469054 --3.4991237 --3.4028729 --4.1096357 --4.0525439 --3.937462 --4.0525439 --3.9967867 --3.8844191 --3.937462 --3.8844191 --3.7775699 --4.5172703 --4.4545155 --4.3280187 --4.4545155 --4.3932278 --4.2697144 --4.3280187 --4.2697144 --4.1522669 --3.3755549 --3.1451489 --2.8322336 --3.3318834 --3.1071607 --2.8023231 --3.243986 --3.0308053 --2.7423465 --3.7472439 --3.4914674 --3.1440964 --3.6987636 --3.4492962 --3.1108923 --3.6011876 --3.3645332 --3.0443116 --4.1189328 --3.8377859 --3.4559591 --4.0656437 --3.7914317 --3.4194616 --3.9583893 --3.6982611 --3.3462767 --3.0991248 --2.9052925 --2.6442006 --2.9052925 --2.7380703 --2.5143949 --2.6442006 --2.5143949 --2.3427651 --3.4403755 --3.2251999 --2.9353587 --3.2251999 --3.0395645 --2.7912598 --2.9353587 --2.7912598 --2.6007316 --3.7816261 --3.5451073 --3.2265167 --3.5451073 --3.3410588 --3.0681247 --3.2265167 --3.0681247 --2.858698 --3.3755549 --3.3318834 --3.243986 --3.1451489 --3.1071607 --3.0308053 --2.8322336 --2.8023231 --2.7423465 --3.7472439 --3.6987636 --3.6011876 --3.4914674 --3.4492962 --3.3645332 --3.1440964 --3.1108923 --3.0443116 --4.1189328 --4.0656437 --3.9583893 --3.8377859 --3.7914317 --3.6982611 --3.4559591 --3.4194616 --3.3462767 --4.9473453 --4.8786158 --4.7400757 --4.8786158 --4.8114932 --4.6762204 --4.7400757 --4.6762204 --4.5475911 --5.3549799 --5.2805875 --5.1306324 --5.2805875 --5.2079342 --5.0615158 --5.1306324 --5.0615158 --4.922288 --5.7626144 --5.6825591 --5.521189 --5.6825591 --5.6043753 --5.4468111 --5.521189 --5.4468111 --5.296985 --4.5110834 --4.2031694 --3.7849901 --4.4527208 --4.1524019 --3.7450177 --4.335255 --4.0503608 --3.6648652 --4.8827723 --4.5494878 --4.0968528 --4.819601 --4.4945374 --4.053587 --4.6924566 --4.3840887 --3.9668303 --5.2544613 --4.8958063 --4.4087156 --5.1864812 --4.8366729 --4.3621562 --5.0496582 --4.7178166 --4.2687954 --4.1416628 --3.8826258 --3.5337032 --3.8826258 --3.6591505 --3.3602312 --3.5337032 --3.3602312 --3.1308656 --4.4829135 --4.2025332 --3.8248613 --4.2025332 --3.9606447 --3.6370961 --3.8248613 --3.6370961 --3.388832 --4.8241642 --4.5224406 --4.1160194 --4.5224406 --4.262139 --3.913961 --4.1160194 --3.913961 --3.6467985 --4.5110834 --4.4527208 --4.335255 --4.2031694 --4.1524019 --4.0503608 --3.7849901 --3.7450177 --3.6648652 --4.8827723 --4.819601 --4.6924566 --4.5494878 --4.4945374 --4.3840887 --4.0968528 --4.053587 --3.9668303 --5.2544613 --5.1864812 --5.0496582 --4.8958063 --4.8366729 --4.7178166 --4.4087156 --4.3621562 --4.2687954 --2.8322336 --3.1451489 --3.3755549 --2.8023231 --3.1071607 --3.3318834 --2.7423465 --3.0308053 --3.243986 --3.1440964 --3.4914674 --3.7472439 --3.1108923 --3.4492962 --3.6987636 --3.0443116 --3.3645332 --3.6011876 --3.4559591 --3.8377859 --4.1189328 --3.4194616 --3.7914317 --4.0656437 --3.3462767 --3.6982611 --3.9583893 --3.5469054 --3.6505722 --3.7020011 --3.4991237 --3.6003457 --3.6505722 --3.4028729 --3.4991237 --3.5469054 --3.937462 --4.0525439 --4.1096357 --3.8844191 --3.9967867 --4.0525439 --3.7775699 --3.8844191 --3.937462 --4.3280187 --4.4545155 --4.5172703 --4.2697144 --4.3932278 --4.4545155 --4.1522669 --4.2697144 --4.3280187 --3.243986 --3.3318834 --3.3755549 --3.0308053 --3.1071607 --3.1451489 --2.7423465 --2.8023231 --2.8322336 --3.6011876 --3.6987636 --3.7472439 --3.3645332 --3.4492962 --3.4914674 --3.0443116 --3.1108923 --3.1440964 --3.9583893 --4.0656437 --4.1189328 --3.6982611 --3.7914317 --3.8377859 --3.3462767 --3.4194616 --3.4559591 --2.6442006 --2.9052925 --3.0991248 --2.5143949 --2.7380703 --2.9052925 --2.3427651 --2.5143949 --2.6442006 --2.9353587 --3.2251999 --3.4403755 --2.7912598 --3.0395645 --3.2251999 --2.6007316 --2.7912598 --2.9353587 --3.2265167 --3.5451073 --3.7816261 --3.0681247 --3.3410588 --3.5451073 --2.858698 --3.0681247 --3.2265167 --3.7849901 --4.2031694 --4.5110834 --3.7450177 --4.1524019 --4.4527208 --3.6648652 --4.0503608 --4.335255 --4.0968528 --4.5494878 --4.8827723 --4.053587 --4.4945374 --4.819601 --3.9668303 --4.3840887 --4.6924566 --4.4087156 --4.8958063 --5.2544613 --4.3621562 --4.8366729 --5.1864812 --4.2687954 --4.7178166 --5.0496582 --4.7400757 --4.8786158 --4.9473453 --4.6762204 --4.8114932 --4.8786158 --4.5475911 --4.6762204 --4.7400757 --5.1306324 --5.2805875 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--2.6162574 --2.506761 --2.7842809 --2.9885928 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --3.0555531 --2.8547554 --2.5830523 --3.1383448 --2.9266755 --2.639545 --3.1794797 --2.9624572 --2.6677181 --2.357996 --2.4270069 --2.4612421 --2.7492597 --2.8297216 --2.8696374 --3.1405234 --3.2324363 --3.2780328 --3.3408769 --3.2958707 --3.2052108 --3.4385221 --3.391213 --3.2958707 --3.4869636 --3.4385221 --3.3408769 --1.1352953 --1.1202634 --1.0899943 --1.5173482 --1.4972577 --1.4568024 --1.8994011 --1.874252 --1.8236105 --1.0899943 --1.1202634 --1.1352953 --1.4568024 --1.4972577 --1.5173482 --1.8236105 --1.874252 --1.8994011 --1.1626657 --1.1966931 --1.2135736 --1.5539294 --1.5994078 --1.621969 --1.9451931 --2.0021225 --2.0303643 --2.2416195 --2.2104785 --2.1477066 --2.2104785 --2.1800655 --2.118774 --2.1477066 --2.118774 --2.0604927 --0.858661 --0.85072708 --0.83485064 --1.1476201 --1.1370163 --1.115797 --1.4365793 --1.4233054 --1.3967434 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --2.0439512 --1.9044368 --1.7149616 --2.0175074 --1.8814343 --1.6968504 --1.9642842 --1.8351999 --1.6605336 --0.80897011 --0.77494991 --0.73038568 --1.0812071 --1.0357383 --0.97617722 --1.3534441 --1.2965268 --1.2219688 --0.73038568 --0.77494991 --0.80897011 --0.97617722 --1.0357383 --1.0812071 --1.2219688 --1.2965268 --1.3534441 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --1.8765684 --1.7591999 --1.6011047 --1.7591999 --1.6579443 --1.5225053 --1.6011047 --1.5225053 --1.4185809 --0.83485064 --0.85072708 --0.858661 --1.115797 --1.1370163 --1.1476201 --1.3967434 --1.4233054 --1.4365793 --0.928038 --1.0307797 --1.1064189 --1.2403441 --1.3776608 --1.4787542 --1.5526502 --1.7245418 --1.8510895 --2.0439512 --2.0175074 --1.9642842 --1.9044368 --1.8814343 --1.8351999 --1.7149616 --1.6968504 --1.6605336 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --2.2106115 --2.2720001 --2.3024862 --2.5774196 --2.6489944 --2.6845391 --2.9442277 --3.0259887 --3.066592 --2.357996 --2.4270069 --2.4612421 --2.7492597 --2.8297216 --2.8696374 --3.1405234 --3.2324363 --3.2780328 --3.4869636 --3.4385221 --3.3408769 --3.4385221 --3.391213 --3.2958707 --3.3408769 --3.2958707 --3.2052108 --1.7414457 --1.725355 --1.693156 --2.0304048 --2.0116442 --1.9741024 --2.319364 --2.2979333 --2.2550488 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --3.1794797 --2.9624572 --2.6677181 --3.1383448 --2.9266755 --2.639545 --3.0555531 --2.8547554 --2.5830523 --1.6406679 --1.5716717 --1.4812912 --1.9129049 --1.8324601 --1.7270828 --2.1851419 --2.0932486 --1.9728743 --1.4812912 --1.5716717 --1.6406679 --1.7270828 --1.8324601 --1.9129049 --1.9728743 --2.0932486 --2.1851419 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --2.9191065 --2.7365332 --2.4906074 --2.7365332 --2.5790245 --2.3683416 --2.4906074 --2.3683416 --2.2066813 --1.693156 --1.725355 --1.7414457 --1.9741024 --2.0116442 --2.0304048 --2.2550488 --2.2979333 --2.319364 --1.8821488 --2.0905188 --2.2439221 --2.1944549 --2.4373998 --2.6162574 --2.506761 --2.7842809 --2.9885928 --3.1794797 --3.1383448 --3.0555531 --2.9624572 --2.9266755 --2.8547554 --2.6677181 --2.639545 --2.5830523 --1.1352953 --1.1202634 --1.0899943 --1.5173482 --1.4972577 --1.4568024 --1.8994011 --1.874252 --1.8236105 --1.0400626 --0.97314799 --0.8827835 --1.3900675 --1.3006346 --1.1798604 --1.7400724 --1.6281212 --1.4769373 --0.83485064 --0.85072708 --0.858661 --1.115797 --1.1370163 --1.1476201 --1.3967434 --1.4233054 --1.4365793 --1.7149616 --1.9044368 --2.0439512 --1.6968504 --1.8814343 --2.0175074 --1.6605336 --1.8351999 --1.9642842 --1.1352953 --1.1202634 --1.0899943 --1.5173482 --1.4972577 --1.4568024 --1.8994011 --1.874252 --1.8236105 --2.1477066 --2.2104785 --2.2416195 --2.118774 --2.1800655 --2.2104785 --2.0604927 --2.118774 --2.1477066 --0.858661 --0.85072708 --0.83485064 --1.1476201 --1.1370163 --1.115797 --1.4365793 --1.4233054 --1.3967434 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --1.9642842 --2.0175074 --2.0439512 --1.8351999 --1.8814343 --1.9044368 --1.6605336 --1.6968504 --1.7149616 --0.80897011 --0.77494991 --0.73038568 --1.0812071 --1.0357383 --0.97617722 --1.3534441 --1.2965268 --1.2219688 --0.73038568 --0.77494991 --0.80897011 --0.97617722 --1.0357383 --1.0812071 --1.2219688 --1.2965268 --1.3534441 --1.6011047 --1.7591999 --1.8765684 --1.5225053 --1.6579443 --1.7591999 --1.4185809 --1.5225053 --1.6011047 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --2.1093453 --1.9736361 --1.7903684 --2.4593502 --2.3011228 --2.0874453 --2.8093551 --2.6286094 --2.3845222 --1.693156 --1.725355 --1.7414457 --1.9741024 --2.0116442 --2.0304048 --2.2550488 --2.2979333 --2.319364 --2.6677181 --2.9624572 --3.1794797 --2.639545 --2.9266755 --3.1383448 --2.5830523 --2.8547554 --3.0555531 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --3.3408769 --3.4385221 --3.4869636 --3.2958707 --3.391213 --3.4385221 --3.2052108 --3.2958707 --3.3408769 --1.7414457 --1.725355 --1.693156 --2.0304048 --2.0116442 --1.9741024 --2.319364 --2.2979333 --2.2550488 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --3.0555531 --3.1383448 --3.1794797 --2.8547554 --2.9266755 --2.9624572 --2.5830523 --2.639545 --2.6677181 --1.6406679 --1.5716717 --1.4812912 --1.9129049 --1.8324601 --1.7270828 --2.1851419 --2.0932486 --1.9728743 --1.4812912 --1.5716717 --1.6406679 --1.7270828 --1.8324601 --1.9129049 --1.9728743 --2.0932486 --2.1851419 --2.4906074 --2.7365332 --2.9191065 --2.3683416 --2.5790245 --2.7365332 --2.2066813 --2.3683416 --2.4906074 --2.2321968 --2.3683935 --2.4723657 --2.4779883 --2.6291819 --2.7446027 --2.7237799 --2.8899704 --3.0168397 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --3.178628 --2.9741243 --2.6979533 --3.5286329 --3.3016109 --2.9950302 --3.8786378 --3.6290976 --3.2921071 --2.4723657 --2.3683935 --2.2321968 --2.7446027 --2.6291819 --2.4779883 --3.0168397 --2.8899704 --2.7237799 --2.9947818 --3.2141779 --3.38011 --3.2141779 --3.5001046 --3.7138665 --3.38011 --3.7138665 --3.9616445 --2.5514614 --2.5999829 --2.6242304 --2.8324078 --2.8862721 --2.9131896 --3.1133542 --3.1725612 --3.2021487 --2.8362596 --3.1502579 --3.3814253 --3.1485657 --3.4971389 --3.7537607 --3.4608718 --3.8440199 --4.126096 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --3.505571 --3.5822397 --3.6204746 --3.874311 --3.9719168 --4.0204776 --4.1468221 --4.2591823 --4.3150081 --3.5533263 --3.6573206 --3.7089105 --3.94459 --4.0600353 --4.1173059 --4.3358537 --4.46275 --4.5257012 --3.7089105 --3.6573206 --3.5533263 --4.1173059 --4.0600353 --3.94459 --4.5257012 --4.46275 --4.3358537 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --4.349929 --4.4729674 --4.5340472 --4.4729674 --4.6023605 --4.6665657 --4.5340472 --4.6665657 --4.7323078 --3.3814253 --3.1502579 --2.8362596 --3.7537607 --3.4971389 --3.1485657 --4.126096 --3.8440199 --3.4608718 --2.6242304 --2.5999829 --2.5514614 --2.9131896 --2.8862721 --2.8324078 --3.2021487 --3.1725612 --3.1133542 --3.505571 --3.874311 --4.1468221 --3.5822397 --3.9719168 --4.2591823 --3.6204746 --4.0204776 --4.3150081 --2.9831024 --3.1651153 --3.3040635 --3.2288939 --3.4259037 --3.5763005 --3.4746854 --3.6866922 --3.8485375 --3.6055383 --3.9746125 --4.2479107 --3.9026152 --4.3020991 --4.5979156 --4.1996921 --4.6295857 --4.9479206 --4.2479107 --3.9746125 --3.6055383 --4.5979156 --4.3020991 --3.9026152 --4.9479206 --4.6295857 --4.1996921 --3.3040635 --3.1651153 --2.9831024 --3.5763005 --3.4259037 --3.2288939 --3.8485375 --3.6866922 --3.4746854 --3.7828823 --4.0600142 --4.2696126 --4.0600142 --4.4211848 --4.6911998 --4.2696126 --4.6911998 --5.0041825 --3.4097669 --3.4746108 --3.5070151 --3.6907132 --3.7609 --3.7959743 --3.9716596 --4.0471891 --4.0849334 --3.7903705 --4.2099969 --4.5189286 --4.1026766 --4.556878 --4.8912639 --4.4149826 --4.903759 --5.2635992 --4.636868 --4.5754734 --4.4518459 --5.0189209 --4.9524678 --4.818654 --5.4009738 --5.3294621 --5.1854621 --4.4280896 --4.5249343 --4.5732311 --4.8938665 --5.0171581 --5.078498 --5.2380911 --5.3800197 --5.4505366 --4.7486566 --4.8876343 --4.956579 --5.1399203 --5.290349 --5.3649743 --5.5311839 --5.6930637 --5.7733697 --4.956579 --4.8876343 --4.7486566 --5.3649743 --5.290349 --5.1399203 --5.7733697 --5.6930637 --5.5311839 --4.636868 --4.5754734 --4.4518459 --5.0189209 --4.9524678 --4.818654 --5.4009738 --5.3294621 --5.1854621 --5.4946471 --5.6500641 --5.7272175 --5.6500641 --5.813508 --5.8946093 --5.7272175 --5.8946093 --5.9776519 --4.5189286 --4.2099969 --3.7903705 --4.8912639 --4.556878 --4.1026766 --5.2635992 --4.903759 --4.4149826 --3.5070151 --3.4746108 --3.4097669 --3.7959743 --3.7609 --3.6907132 --4.0849334 --4.0471891 --3.9716596 --4.4280896 --4.8938665 --5.2380911 --4.5249343 --5.0171581 --5.3800197 --4.5732311 --5.078498 --5.4505366 --2.6242304 --2.5999829 --2.5514614 --2.9131896 --2.8862721 --2.8324078 --3.2021487 --3.1725612 --3.1133542 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --3.3312287 --3.4237367 --3.4696771 --3.6980368 --3.8007311 --3.85173 --4.0648449 --4.1777254 --4.2337829 --3.6204746 --3.5822397 --3.505571 --4.0204776 --3.9719168 --3.874311 --4.3150081 --4.2591823 --4.1468221 --2.4723657 --2.3683935 --2.2321968 --2.7446027 --2.6291819 --2.4779883 --3.0168397 --2.8899704 --2.7237799 --2.2321968 --2.3683935 --2.4723657 --2.4779883 --2.6291819 --2.7446027 --2.7237799 --2.8899704 --3.0168397 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --3.38011 --3.2141779 --2.9947818 --3.7138665 --3.5001046 --3.2141779 --3.9616445 --3.7138665 --3.38011 --2.5514614 --2.5999829 --2.6242304 --2.8324078 --2.8862721 --2.9131896 --3.1133542 --3.1725612 --3.2021487 --2.8362596 --3.1502579 --3.3814253 --3.1485657 --3.4971389 --3.7537607 --3.4608718 --3.8440199 --4.126096 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --4.1468221 --3.874311 --3.505571 --4.2591823 --3.9719168 --3.5822397 --4.3150081 --4.0204776 --3.6204746 --3.5533263 --3.6573206 --3.7089105 --3.94459 --4.0600353 --4.1173059 --4.3358537 --4.46275 --4.5257012 --4.5340472 --4.4729674 --4.349929 --4.6665657 --4.6023605 --4.4729674 --4.7323078 --4.6665657 --4.5340472 --3.5070151 --3.4746108 --3.4097669 --3.7959743 --3.7609 --3.6907132 --4.0849334 --4.0471891 --3.9716596 --3.6055383 --3.9746125 --4.2479107 --3.9026152 --4.3020991 --4.5979156 --4.1996921 --4.6295857 --4.9479206 --4.4518459 --4.5754734 --4.636868 --4.818654 --4.9524678 --5.0189209 --5.1854621 --5.3294621 --5.4009738 --4.5732311 --4.5249343 --4.4280896 --5.078498 --5.0171581 --4.8938665 --5.4505366 --5.3800197 --5.2380911 --3.3040635 --3.1651153 --2.9831024 --3.5763005 --3.4259037 --3.2288939 --3.8485375 --3.6866922 --3.4746854 --2.9831024 --3.1651153 --3.3040635 --3.2288939 --3.4259037 --3.5763005 --3.4746854 --3.6866922 --3.8485375 --3.6055383 --3.9746125 --4.2479107 --3.9026152 --4.3020991 --4.5979156 --4.1996921 --4.6295857 --4.9479206 --4.2696126 --4.0600142 --3.7828823 --4.6911998 --4.4211848 --4.0600142 --5.0041825 --4.6911998 --4.2696126 --3.4097669 --3.4746108 --3.5070151 --3.6907132 --3.7609 --3.7959743 --3.9716596 --4.0471891 --4.0849334 --3.7903705 --4.2099969 --4.5189286 --4.1026766 --4.556878 --4.8912639 --4.4149826 --4.903759 --5.2635992 --4.636868 --4.5754734 --4.4518459 --5.0189209 --4.9524678 --4.818654 --5.4009738 --5.3294621 --5.1854621 --5.2380911 --4.8938665 --4.4280896 --5.3800197 --5.0171581 --4.5249343 --5.4505366 --5.078498 --4.5732311 --4.7486566 --4.8876343 --4.956579 --5.1399203 --5.290349 --5.3649743 --5.5311839 --5.6930637 --5.7733697 --5.7272175 --5.6500641 --5.4946471 --5.8946093 --5.813508 --5.6500641 --5.9776519 --5.8946093 --5.7272175 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --3.3312287 --3.4237367 --3.4696771 --3.6980368 --3.8007311 --3.85173 --4.0648449 --4.1777254 --4.2337829 --3.5533263 --3.6573206 --3.7089105 --3.94459 --4.0600353 --4.1173059 --4.3358537 --4.46275 --4.5257012 --4.7323078 --4.6665657 --4.5340472 --4.6665657 --4.6023605 --4.4729674 --4.5340472 --4.4729674 --4.349929 --2.6242304 --2.5999829 --2.5514614 --2.9131896 --2.8862721 --2.8324078 --3.2021487 --3.1725612 --3.1133542 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --4.3150081 --4.0204776 --3.6204746 --4.2591823 --3.9719168 --3.5822397 --4.1468221 --3.874311 --3.505571 --2.4723657 --2.3683935 --2.2321968 --2.7446027 --2.6291819 --2.4779883 --3.0168397 --2.8899704 --2.7237799 --2.2321968 --2.3683935 --2.4723657 --2.4779883 --2.6291819 --2.7446027 --2.7237799 --2.8899704 --3.0168397 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --3.9616445 --3.7138665 --3.38011 --3.7138665 --3.5001046 --3.2141779 --3.38011 --3.2141779 --2.9947818 --2.5514614 --2.5999829 --2.6242304 --2.8324078 --2.8862721 --2.9131896 --3.1133542 --3.1725612 --3.2021487 --2.8362596 --3.1502579 --3.3814253 --3.1485657 --3.4971389 --3.7537607 --3.4608718 --3.8440199 --4.126096 --4.3150081 --4.2591823 --4.1468221 --4.0204776 --3.9719168 --3.874311 --3.6204746 --3.5822397 --3.505571 --4.636868 --4.5754734 --4.4518459 --5.0189209 --4.9524678 --4.818654 --5.4009738 --5.3294621 --5.1854621 --4.4518459 --4.5754734 --4.636868 --4.818654 --4.9524678 --5.0189209 --5.1854621 --5.3294621 --5.4009738 --4.7486566 --4.8876343 --4.956579 --5.1399203 --5.290349 --5.3649743 --5.5311839 --5.6930637 --5.7733697 --5.9776519 --5.8946093 --5.7272175 --5.8946093 --5.813508 --5.6500641 --5.7272175 --5.6500641 --5.4946471 --3.5070151 --3.4746108 --3.4097669 --3.7959743 --3.7609 --3.6907132 --4.0849334 --4.0471891 --3.9716596 --3.6055383 --3.9746125 --4.2479107 --3.9026152 --4.3020991 --4.5979156 --4.1996921 --4.6295857 --4.9479206 --5.4505366 --5.078498 --4.5732311 --5.3800197 --5.0171581 --4.5249343 --5.2380911 --4.8938665 --4.4280896 --3.3040635 --3.1651153 --2.9831024 --3.5763005 --3.4259037 --3.2288939 --3.8485375 --3.6866922 --3.4746854 --2.9831024 --3.1651153 --3.3040635 --3.2288939 --3.4259037 --3.5763005 --3.4746854 --3.6866922 --3.8485375 --3.6055383 --3.9746125 --4.2479107 --3.9026152 --4.3020991 --4.5979156 --4.1996921 --4.6295857 --4.9479206 --5.0041825 --4.6911998 --4.2696126 --4.6911998 --4.4211848 --4.0600142 --4.2696126 --4.0600142 --3.7828823 --3.4097669 --3.4746108 --3.5070151 --3.6907132 --3.7609 --3.7959743 --3.9716596 --4.0471891 --4.0849334 --3.7903705 --4.2099969 --4.5189286 --4.1026766 --4.556878 --4.8912639 --4.4149826 --4.903759 --5.2635992 --5.4505366 --5.3800197 --5.2380911 --5.078498 --5.0171581 --4.8938665 --4.5732311 --4.5249343 --4.4280896 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --3.178628 --2.9741243 --2.6979533 --3.5286329 --3.3016109 --2.9950302 --3.8786378 --3.6290976 --3.2921071 --2.5514614 --2.5999829 --2.6242304 --2.8324078 --2.8862721 --2.9131896 --3.1133542 --3.1725612 --3.2021487 --3.6204746 --4.0204776 --4.3150081 --3.5822397 --3.9719168 --4.2591823 --3.505571 --3.874311 --4.1468221 --3.4696771 --3.4237367 --3.3312287 --3.85173 --3.8007311 --3.6980368 --4.2337829 --4.1777254 --4.0648449 --4.5340472 --4.6665657 --4.7323078 --4.4729674 --4.6023605 --4.6665657 --4.349929 --4.4729674 --4.5340472 --2.6242304 --2.5999829 --2.5514614 --2.9131896 --2.8862721 --2.8324078 --3.2021487 --3.1725612 --3.1133542 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --4.1468221 --4.2591823 --4.3150081 --3.874311 --3.9719168 --4.0204776 --3.505571 --3.5822397 --3.6204746 --2.4723657 --2.3683935 --2.2321968 --2.7446027 --2.6291819 --2.4779883 --3.0168397 --2.8899704 --2.7237799 --2.2321968 --2.3683935 --2.4723657 --2.4779883 --2.6291819 --2.7446027 --2.7237799 --2.8899704 --3.0168397 --3.38011 --3.7138665 --3.9616445 --3.2141779 --3.5001046 --3.7138665 --2.9947818 --3.2141779 --3.38011 --4.636868 --4.5754734 --4.4518459 --5.0189209 --4.9524678 --4.818654 --5.4009738 --5.3294621 --5.1854621 --4.2479107 --3.9746125 --3.6055383 --4.5979156 --4.3020991 --3.9026152 --4.9479206 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--1.9454235 --2.1184844 --2.2478666 --1.8126311 --1.9454235 --2.045856 --2.3370141 --2.567774 --2.7390881 --2.2222884 --2.4199786 --2.567774 --2.0705975 --2.2222884 --2.3370141 --2.3427651 --2.5143949 --2.6442006 --2.5143949 --2.7380703 --2.9052925 --2.6442006 --2.9052925 --3.0991248 --2.6007316 --2.7912598 --2.9353587 --2.7912598 --3.0395645 --3.2251999 --2.9353587 --3.2251999 --3.4403755 --2.858698 --3.0681247 --3.2265167 --3.0681247 --3.3410588 --3.5451073 --3.2265167 --3.5451073 --3.7816261 --2.7423465 --2.8023231 --2.8322336 --3.0308053 --3.1071607 --3.1451489 --3.243986 --3.3318834 --3.3755549 --3.0443116 --3.1108923 --3.1440964 --3.3645332 --3.4492962 --3.4914674 --3.6011876 --3.6987636 --3.7472439 --3.3462767 --3.4194616 --3.4559591 --3.6982611 --3.7914317 --3.8377859 --3.9583893 --4.0656437 --4.1189328 --3.4028729 --3.4991237 --3.5469054 --3.4991237 --3.6003457 --3.6505722 --3.5469054 --3.6505722 --3.7020011 --3.7775699 --3.8844191 --3.937462 --3.8844191 --3.9967867 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--4.8827723 --4.2687954 --4.3621562 --4.4087156 --4.7178166 --4.8366729 --4.8958063 --5.0496582 --5.1864812 --5.2544613 --4.5475911 --4.6762204 --4.7400757 --4.6762204 --4.8114932 --4.8786158 --4.7400757 --4.8786158 --4.9473453 --4.922288 --5.0615158 --5.1306324 --5.0615158 --5.2079342 --5.2805875 --5.1306324 --5.2805875 --5.3549799 --5.296985 --5.4468111 --5.521189 --5.4468111 --5.6043753 --5.6825591 --5.521189 --5.6825591 --5.7626144 --3.6648652 --4.0503608 --4.335255 --3.7450177 --4.1524019 --4.4527208 --3.7849901 --4.2031694 --4.5110834 --3.9668303 --4.3840887 --4.6924566 --4.053587 --4.4945374 --4.819601 --4.0968528 --4.5494878 --4.8827723 --4.2687954 --4.7178166 --5.0496582 --4.3621562 --4.8366729 --5.1864812 --4.4087156 --4.8958063 --5.2544613 --2.8322336 --2.8023231 --2.7423465 --3.1451489 --3.1071607 --3.0308053 --3.3755549 --3.3318834 --3.243986 --3.1440964 --3.1108923 --3.0443116 --3.4914674 --3.4492962 --3.3645332 --3.7472439 --3.6987636 --3.6011876 --3.4559591 --3.4194616 --3.3462767 --3.8377859 --3.7914317 --3.6982611 --4.1189328 --4.0656437 --3.9583893 --2.6442006 --2.5143949 --2.3427651 --2.9052925 --2.7380703 --2.5143949 --3.0991248 --2.9052925 --2.6442006 --2.9353587 --2.7912598 --2.6007316 --3.2251999 --3.0395645 --2.7912598 --3.4403755 --3.2251999 --2.9353587 --3.2265167 --3.0681247 --2.858698 --3.5451073 --3.3410588 --3.0681247 --3.7816261 --3.5451073 --3.2265167 --3.243986 --3.0308053 --2.7423465 --3.3318834 --3.1071607 --2.8023231 --3.3755549 --3.1451489 --2.8322336 --3.6011876 --3.3645332 --3.0443116 --3.6987636 --3.4492962 --3.1108923 --3.7472439 --3.4914674 --3.1440964 --3.9583893 --3.6982611 --3.3462767 --4.0656437 --3.7914317 --3.4194616 --4.1189328 --3.8377859 --3.4559591 --3.5469054 --3.4991237 --3.4028729 --3.6505722 --3.6003457 --3.4991237 --3.7020011 --3.6505722 --3.5469054 --3.937462 --3.8844191 --3.7775699 --4.0525439 --3.9967867 --3.8844191 --4.1096357 --4.0525439 --3.937462 --4.3280187 --4.2697144 --4.1522669 --4.4545155 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--4.8958063 --4.4087156 --4.7400757 --4.6762204 --4.5475911 --4.8786158 --4.8114932 --4.6762204 --4.9473453 --4.8786158 --4.7400757 --5.1306324 --5.0615158 --4.922288 --5.2805875 --5.2079342 --5.0615158 --5.3549799 --5.2805875 --5.1306324 --5.521189 --5.4468111 --5.296985 --5.6825591 --5.6043753 --5.4468111 --5.7626144 --5.6825591 --5.521189 --3.7020011 --3.6505722 --3.5469054 --3.6505722 --3.6003457 --3.4991237 --3.5469054 --3.4991237 --3.4028729 --4.1096357 --4.0525439 --3.937462 --4.0525439 --3.9967867 --3.8844191 --3.937462 --3.8844191 --3.7775699 --4.5172703 --4.4545155 --4.3280187 --4.4545155 --4.3932278 --4.2697144 --4.3280187 --4.2697144 --4.1522669 --3.3755549 --3.1451489 --2.8322336 --3.3318834 --3.1071607 --2.8023231 --3.243986 --3.0308053 --2.7423465 --3.7472439 --3.4914674 --3.1440964 --3.6987636 --3.4492962 --3.1108923 --3.6011876 --3.3645332 --3.0443116 --4.1189328 --3.8377859 --3.4559591 --4.0656437 --3.7914317 --3.4194616 --3.9583893 --3.6982611 --3.3462767 --3.0991248 --2.9052925 --2.6442006 --2.9052925 --2.7380703 --2.5143949 --2.6442006 --2.5143949 --2.3427651 --3.4403755 --3.2251999 --2.9353587 --3.2251999 --3.0395645 --2.7912598 --2.9353587 --2.7912598 --2.6007316 --3.7816261 --3.5451073 --3.2265167 --3.5451073 --3.3410588 --3.0681247 --3.2265167 --3.0681247 --2.858698 --3.3755549 --3.3318834 --3.243986 --3.1451489 --3.1071607 --3.0308053 --2.8322336 --2.8023231 --2.7423465 --3.7472439 --3.6987636 --3.6011876 --3.4914674 --3.4492962 --3.3645332 --3.1440964 --3.1108923 --3.0443116 --4.1189328 --4.0656437 --3.9583893 --3.8377859 --3.7914317 --3.6982611 --3.4559591 --3.4194616 --3.3462767 --4.9473453 --4.8786158 --4.7400757 --4.8786158 --4.8114932 --4.6762204 --4.7400757 --4.6762204 --4.5475911 --5.3549799 --5.2805875 --5.1306324 --5.2805875 --5.2079342 --5.0615158 --5.1306324 --5.0615158 --4.922288 --5.7626144 --5.6825591 --5.521189 --5.6825591 --5.6043753 --5.4468111 --5.521189 --5.4468111 --5.296985 --4.5110834 --4.2031694 --3.7849901 --4.4527208 --4.1524019 --3.7450177 --4.335255 --4.0503608 --3.6648652 --4.8827723 --4.5494878 --4.0968528 --4.819601 --4.4945374 --4.053587 --4.6924566 --4.3840887 --3.9668303 --5.2544613 --4.8958063 --4.4087156 --5.1864812 --4.8366729 --4.3621562 --5.0496582 --4.7178166 --4.2687954 --4.1416628 --3.8826258 --3.5337032 --3.8826258 --3.6591505 --3.3602312 --3.5337032 --3.3602312 --3.1308656 --4.4829135 --4.2025332 --3.8248613 --4.2025332 --3.9606447 --3.6370961 --3.8248613 --3.6370961 --3.388832 --4.8241642 --4.5224406 --4.1160194 --4.5224406 --4.262139 --3.913961 --4.1160194 --3.913961 --3.6467985 --4.5110834 --4.4527208 --4.335255 --4.2031694 --4.1524019 --4.0503608 --3.7849901 --3.7450177 --3.6648652 --4.8827723 --4.819601 --4.6924566 --4.5494878 --4.4945374 --4.3840887 --4.0968528 --4.053587 --3.9668303 --5.2544613 --5.1864812 --5.0496582 --4.8958063 --4.8366729 --4.7178166 --4.4087156 --4.3621562 --4.2687954 --2.8322336 --3.1451489 --3.3755549 --2.8023231 --3.1071607 --3.3318834 --2.7423465 --3.0308053 --3.243986 --3.1440964 --3.4914674 --3.7472439 --3.1108923 --3.4492962 --3.6987636 --3.0443116 --3.3645332 --3.6011876 --3.4559591 --3.8377859 --4.1189328 --3.4194616 --3.7914317 --4.0656437 --3.3462767 --3.6982611 --3.9583893 --3.5469054 --3.6505722 --3.7020011 --3.4991237 --3.6003457 --3.6505722 --3.4028729 --3.4991237 --3.5469054 --3.937462 --4.0525439 --4.1096357 --3.8844191 --3.9967867 --4.0525439 --3.7775699 --3.8844191 --3.937462 --4.3280187 --4.4545155 --4.5172703 --4.2697144 --4.3932278 --4.4545155 --4.1522669 --4.2697144 --4.3280187 --3.243986 --3.3318834 --3.3755549 --3.0308053 --3.1071607 --3.1451489 --2.7423465 --2.8023231 --2.8322336 --3.6011876 --3.6987636 --3.7472439 --3.3645332 --3.4492962 --3.4914674 --3.0443116 --3.1108923 --3.1440964 --3.9583893 --4.0656437 --4.1189328 --3.6982611 --3.7914317 --3.8377859 --3.3462767 --3.4194616 --3.4559591 --2.6442006 --2.9052925 --3.0991248 --2.5143949 --2.7380703 --2.9052925 --2.3427651 --2.5143949 --2.6442006 --2.9353587 --3.2251999 --3.4403755 --2.7912598 --3.0395645 --3.2251999 --2.6007316 --2.7912598 --2.9353587 --3.2265167 --3.5451073 --3.7816261 --3.0681247 --3.3410588 --3.5451073 --2.858698 --3.0681247 --3.2265167 --3.7849901 --4.2031694 --4.5110834 --3.7450177 --4.1524019 --4.4527208 --3.6648652 --4.0503608 --4.335255 --4.0968528 --4.5494878 --4.8827723 --4.053587 --4.4945374 --4.819601 --3.9668303 --4.3840887 --4.6924566 --4.4087156 --4.8958063 --5.2544613 --4.3621562 --4.8366729 --5.1864812 --4.2687954 --4.7178166 --5.0496582 --4.7400757 --4.8786158 --4.9473453 --4.6762204 --4.8114932 --4.8786158 --4.5475911 --4.6762204 --4.7400757 --5.1306324 --5.2805875 --5.3549799 --5.0615158 --5.2079342 --5.2805875 --4.922288 --5.0615158 --5.1306324 --5.521189 --5.6825591 --5.7626144 --5.4468111 --5.6043753 --5.6825591 --5.296985 --5.4468111 --5.521189 --4.335255 --4.4527208 --4.5110834 --4.0503608 --4.1524019 --4.2031694 --3.6648652 --3.7450177 --3.7849901 --4.6924566 --4.819601 --4.8827723 --4.3840887 --4.4945374 --4.5494878 --3.9668303 --4.053587 --4.0968528 --5.0496582 --5.1864812 --5.2544613 --4.7178166 --4.8366729 --4.8958063 --4.2687954 --4.3621562 --4.4087156 --3.5337032 --3.8826258 --4.1416628 --3.3602312 --3.6591505 --3.8826258 --3.1308656 --3.3602312 --3.5337032 --3.8248613 --4.2025332 --4.4829135 --3.6370961 --3.9606447 --4.2025332 --3.388832 --3.6370961 --3.8248613 --4.1160194 --4.5224406 --4.8241642 --3.913961 --4.262139 --4.5224406 --3.6467985 --3.913961 --4.1160194 --0.66732668 --0.54778926 --0.42825185 --0.70804339 --0.58121244 --0.45438148 --0.7391264 --0.60672759 --0.47432877 --0.89189742 --0.73213292 --0.57236842 --0.94631623 --0.77680375 --0.60729128 --0.98785939 --0.81090534 --0.63395129 --1.1164682 --0.91647657 --0.71648499 --1.1845891 --0.97239507 --0.76020107 --1.2365924 --1.0150831 --0.7935738 --0.30213384 --0.18259642 --0.063059004 --0.32056843 --0.19373748 --0.066906527 --0.33464134 --0.20224253 --0.069843715 --0.40380881 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--1.0307797 --0.928038 --1.4787542 --1.3776608 --1.2403441 --1.8510895 --1.7245418 --1.5526502 --1.6605336 --1.8351999 --1.9642842 --1.6968504 --1.8814343 --2.0175074 --1.7149616 --1.9044368 --2.0439512 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --2.1093453 --1.9736361 --1.7903684 --2.4593502 --2.3011228 --2.0874453 --2.8093551 --2.6286094 --2.3845222 --2.2066813 --2.3683416 --2.4906074 --2.3683416 --2.5790245 --2.7365332 --2.4906074 --2.7365332 --2.9191065 --1.8821488 --2.0905188 --2.2439221 --2.1944549 --2.4373998 --2.6162574 --2.506761 --2.7842809 --2.9885928 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --2.5830523 --2.639545 --2.6677181 --2.8547554 --2.9266755 --2.9624572 --3.0555531 --3.1383448 --3.1794797 --2.357996 --2.4270069 --2.4612421 --2.7492597 --2.8297216 --2.8696374 --3.1405234 --3.2324363 --3.2780328 --2.4612421 --2.4270069 --2.357996 --2.8696374 --2.8297216 --2.7492597 --3.2780328 --3.2324363 --3.1405234 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --3.2052108 --3.2958707 --3.3408769 --3.2958707 --3.391213 --3.4385221 --3.3408769 --3.4385221 --3.4869636 --2.2439221 --2.0905188 --1.8821488 --2.6162574 --2.4373998 --2.1944549 --2.9885928 --2.7842809 --2.506761 --2.5830523 --2.8547554 --3.0555531 --2.639545 --2.9266755 --3.1383448 --2.6677181 --2.9624572 --3.1794797 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --1.0899943 --1.1202634 --1.1352953 --1.4568024 --1.4972577 --1.5173482 --1.8236105 --1.874252 --1.8994011 --1.7149616 --1.6968504 --1.6605336 --1.9044368 --1.8814343 --1.8351999 --2.0439512 --2.0175074 --1.9642842 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --1.6011047 --1.5225053 --1.4185809 --1.7591999 --1.6579443 --1.5225053 --1.8765684 --1.7591999 --1.6011047 --0.928038 --1.0307797 --1.1064189 --1.2403441 --1.3776608 --1.4787542 --1.5526502 --1.7245418 --1.8510895 --1.1352953 --1.1202634 --1.0899943 --1.5173482 --1.4972577 --1.4568024 --1.8994011 --1.874252 --1.8236105 --1.9642842 --1.8351999 --1.6605336 --2.0175074 --1.8814343 --1.6968504 --2.0439512 --1.9044368 --1.7149616 --1.1626657 --1.1966931 --1.2135736 --1.5539294 --1.5994078 --1.621969 --1.9451931 --2.0021225 --2.0303643 --2.1477066 --2.118774 --2.0604927 --2.2104785 --2.1800655 --2.118774 --2.2416195 --2.2104785 --2.1477066 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --2.2106115 --2.2720001 --2.3024862 --2.5774196 --2.6489944 --2.6845391 --2.9442277 --3.0259887 --3.066592 --2.6677181 --2.639545 --2.5830523 --2.9624572 --2.9266755 --2.8547554 --3.1794797 --3.1383448 --3.0555531 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --2.4906074 --2.3683416 --2.2066813 --2.7365332 --2.5790245 --2.3683416 --2.9191065 --2.7365332 --2.4906074 --1.8821488 --2.0905188 --2.2439221 --2.1944549 --2.4373998 --2.6162574 --2.506761 --2.7842809 --2.9885928 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --3.0555531 --2.8547554 --2.5830523 --3.1383448 --2.9266755 --2.639545 --3.1794797 --2.9624572 --2.6677181 --2.357996 --2.4270069 --2.4612421 --2.7492597 --2.8297216 --2.8696374 --3.1405234 --3.2324363 --3.2780328 --3.3408769 --3.2958707 --3.2052108 --3.4385221 --3.391213 --3.2958707 --3.4869636 --3.4385221 --3.3408769 --1.1352953 --1.1202634 --1.0899943 --1.5173482 --1.4972577 --1.4568024 --1.8994011 --1.874252 --1.8236105 --1.0899943 --1.1202634 --1.1352953 --1.4568024 --1.4972577 --1.5173482 --1.8236105 --1.874252 --1.8994011 --1.1626657 --1.1966931 --1.2135736 --1.5539294 --1.5994078 --1.621969 --1.9451931 --2.0021225 --2.0303643 --2.2416195 --2.2104785 --2.1477066 --2.2104785 --2.1800655 --2.118774 --2.1477066 --2.118774 --2.0604927 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --2.0439512 --1.9044368 --1.7149616 --2.0175074 --1.8814343 --1.6968504 --1.9642842 --1.8351999 --1.6605336 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --1.8765684 --1.7591999 --1.6011047 --1.7591999 --1.6579443 --1.5225053 --1.6011047 --1.5225053 --1.4185809 --0.928038 --1.0307797 --1.1064189 --1.2403441 --1.3776608 --1.4787542 --1.5526502 --1.7245418 --1.8510895 --2.0439512 --2.0175074 --1.9642842 --1.9044368 --1.8814343 --1.8351999 --1.7149616 --1.6968504 --1.6605336 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --2.2106115 --2.2720001 --2.3024862 --2.5774196 --2.6489944 --2.6845391 --2.9442277 --3.0259887 --3.066592 --2.357996 --2.4270069 --2.4612421 --2.7492597 --2.8297216 --2.8696374 --3.1405234 --3.2324363 --3.2780328 --3.4869636 --3.4385221 --3.3408769 --3.4385221 --3.391213 --3.2958707 --3.3408769 --3.2958707 --3.2052108 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --3.1794797 --2.9624572 --2.6677181 --3.1383448 --2.9266755 --2.639545 --3.0555531 --2.8547554 --2.5830523 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --2.9191065 --2.7365332 --2.4906074 --2.7365332 --2.5790245 --2.3683416 --2.4906074 --2.3683416 --2.2066813 --1.8821488 --2.0905188 --2.2439221 --2.1944549 --2.4373998 --2.6162574 --2.506761 --2.7842809 --2.9885928 --3.1794797 --3.1383448 --3.0555531 --2.9624572 --2.9266755 --2.8547554 --2.6677181 --2.639545 --2.5830523 --1.1352953 --1.1202634 --1.0899943 --1.5173482 --1.4972577 --1.4568024 --1.8994011 --1.874252 --1.8236105 --1.0400626 --0.97314799 --0.8827835 --1.3900675 --1.3006346 --1.1798604 --1.7400724 --1.6281212 --1.4769373 --1.7149616 --1.9044368 --2.0439512 --1.6968504 --1.8814343 --2.0175074 --1.6605336 --1.8351999 --1.9642842 --1.1352953 --1.1202634 --1.0899943 --1.5173482 --1.4972577 --1.4568024 --1.8994011 --1.874252 --1.8236105 --2.1477066 --2.2104785 --2.2416195 --2.118774 --2.1800655 --2.2104785 --2.0604927 --2.118774 --2.1477066 --0.8827835 --0.97314799 --1.0400626 --1.1798604 --1.3006346 --1.3900675 --1.4769373 --1.6281212 --1.7400724 --1.9642842 --2.0175074 --2.0439512 --1.8351999 --1.8814343 --1.9044368 --1.6605336 --1.6968504 --1.7149616 --1.6011047 --1.7591999 --1.8765684 --1.5225053 --1.6579443 --1.7591999 --1.4185809 --1.5225053 --1.6011047 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --2.1093453 --1.9736361 --1.7903684 --2.4593502 --2.3011228 --2.0874453 --2.8093551 --2.6286094 --2.3845222 --2.6677181 --2.9624572 --3.1794797 --2.639545 --2.9266755 --3.1383448 --2.5830523 --2.8547554 --3.0555531 --2.3024862 --2.2720001 --2.2106115 --2.6845391 --2.6489944 --2.5774196 --3.066592 --3.0259887 --2.9442277 --3.3408769 --3.4385221 --3.4869636 --3.2958707 --3.391213 --3.4385221 --3.2052108 --3.2958707 --3.3408769 --1.7903684 --1.9736361 --2.1093453 --2.0874453 --2.3011228 --2.4593502 --2.3845222 --2.6286094 --2.8093551 --3.0555531 --3.1383448 --3.1794797 --2.8547554 --2.9266755 --2.9624572 --2.5830523 --2.639545 --2.6677181 --2.4906074 --2.7365332 --2.9191065 --2.3683416 --2.5790245 --2.7365332 --2.2066813 --2.3683416 --2.4906074 --2.6979533 --2.9741243 --3.178628 --2.9950302 --3.3016109 --3.5286329 --3.2921071 --3.6290976 --3.8786378 --3.178628 --2.9741243 --2.6979533 --3.5286329 --3.3016109 --2.9950302 --3.8786378 --3.6290976 --3.2921071 --2.9947818 --3.2141779 --3.38011 --3.2141779 --3.5001046 --3.7138665 --3.38011 --3.7138665 --3.9616445 --2.8362596 --3.1502579 --3.3814253 --3.1485657 --3.4971389 --3.7537607 --3.4608718 --3.8440199 --4.126096 --3.4696771 --3.4237367 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--1.2385834 --1.225503 --1.1992743 --1.8478759 --1.8239689 --1.7758513 --1.721745 --1.7009492 --1.65915 --1.5504462 --1.5340723 --1.5012394 --2.456657 --2.4225286 --2.3537351 --2.4225286 --2.3891982 --2.3220271 --2.3537351 --2.3220271 --2.2581548 --2.8642915 --2.8245003 --2.7442917 --2.8245003 --2.7856392 --2.7073224 --2.7442917 --2.7073224 --2.6328517 --3.2719261 --3.2264719 --3.1348484 --3.2264719 --3.1820803 --3.0926177 --3.1348484 --3.0926177 --3.0075487 --2.2400265 --2.0871285 --1.8794771 --2.2110459 --2.0619194 --1.8596284 --2.152717 --2.0112498 --1.8198278 --2.6117154 --2.433447 --2.1913399 --2.5779261 --2.4040549 --2.1681977 --2.5099187 --2.3449777 --2.1217929 --2.9834044 --2.7797655 --2.5032026 --2.9448063 --2.7461904 --2.4767669 --2.8671203 --2.6787056 --2.4237581 --2.0565868 --1.9279592 --1.754698 --1.9279592 --1.8169901 --1.6685586 --1.754698 --1.6685586 --1.5546647 --2.3978374 --2.2478666 --2.045856 --2.2478666 --2.1184844 --1.9454235 --2.045856 --1.9454235 --1.8126311 --2.7390881 --2.567774 --2.3370141 --2.567774 --2.4199786 --2.2222884 --2.3370141 --2.2222884 --2.0705975 --2.2400265 --2.2110459 --2.152717 --2.0871285 --2.0619194 --2.0112498 --1.8794771 --1.8596284 --1.8198278 --2.6117154 --2.5779261 --2.5099187 --2.433447 --2.4040549 --2.3449777 --2.1913399 --2.1681977 --2.1217929 --2.9834044 --2.9448063 --2.8671203 --2.7797655 --2.7461904 --2.6787056 --2.5032026 --2.4767669 --2.4237581 --0.92672065 --1.0291081 --1.104498 --0.91693379 --1.0166781 --1.0902085 --0.89730916 --0.99169429 --1.0614481 --1.2385834 --1.3754266 --1.476187 --1.225503 --1.3588136 --1.4570887 --1.1992743 --1.3254222 --1.4186497 --1.5504462 --1.721745 --1.8478759 --1.5340723 --1.7009492 --1.8239689 --1.5012394 --1.65915 --1.7758513 --1.1605647 --1.1944851 --1.2113128 --1.1449304 --1.1780507 --1.1944851 --1.1134366 --1.1449304 --1.1605647 --1.5511214 --1.5964567 --1.6189474 --1.5302257 --1.5744917 --1.5964567 --1.4881336 --1.5302257 --1.5511214 --1.9416781 --1.9984283 --2.026582 --1.915521 --1.9709328 --1.9984283 --1.8628306 --1.915521 --1.9416781 --1.0614481 --1.0902085 --1.104498 --0.99169429 --1.0166781 --1.0291081 --0.89730916 --0.91693379 --0.92672065 --1.4186497 --1.4570887 --1.476187 --1.3254222 --1.3588136 --1.3754266 --1.1992743 --1.225503 --1.2385834 --1.7758513 --1.8239689 --1.8478759 --1.65915 --1.7009492 --1.721745 --1.5012394 --1.5340723 --1.5504462 --0.86519534 --0.95062587 --1.0140488 --0.82272227 --0.89590996 --0.95062587 --0.76656418 --0.82272227 --0.86519534 --1.1563534 --1.2705333 --1.3552994 --1.0995872 --1.1974042 --1.2705333 --1.0245306 --1.0995872 --1.1563534 --1.4475115 --1.5904407 --1.6965501 --1.3764521 --1.4988985 --1.5904407 --1.2824971 --1.3764521 --1.4475115 --1.8794771 --2.0871285 --2.2400265 --1.8596284 --2.0619194 --2.2110459 --1.8198278 --2.0112498 --2.152717 --2.1913399 --2.433447 --2.6117154 --2.1681977 --2.4040549 --2.5779261 --2.1217929 --2.3449777 --2.5099187 --2.5032026 --2.7797655 --2.9834044 --2.4767669 --2.7461904 --2.9448063 --2.4237581 --2.6787056 --2.8671203 --2.3537351 --2.4225286 --2.456657 --2.3220271 --2.3891982 --2.4225286 --2.2581548 --2.3220271 --2.3537351 --2.7442917 --2.8245003 --2.8642915 --2.7073224 --2.7856392 --2.8245003 --2.6328517 --2.7073224 --2.7442917 --3.1348484 --3.2264719 --3.2719261 --3.0926177 --3.1820803 --3.2264719 --3.0075487 --3.0926177 --3.1348484 --2.152717 --2.2110459 --2.2400265 --2.0112498 --2.0619194 --2.0871285 --1.8198278 --1.8596284 --1.8794771 --2.5099187 --2.5779261 --2.6117154 --2.3449777 --2.4040549 --2.433447 --2.1217929 --2.1681977 --2.1913399 --2.8671203 --2.9448063 --2.9834044 --2.6787056 --2.7461904 --2.7797655 --2.4237581 --2.4767669 --2.5032026 --1.754698 --1.9279592 --2.0565868 --1.6685586 --1.8169901 --1.9279592 --1.5546647 --1.6685586 --1.754698 --2.045856 --2.2478666 --2.3978374 --1.9454235 --2.1184844 --2.2478666 --1.8126311 --1.9454235 --2.045856 --2.3370141 --2.567774 --2.7390881 --2.2222884 --2.4199786 --2.567774 --2.0705975 --2.2222884 --2.3370141 --2.3427651 --2.5143949 --2.6442006 --2.5143949 --2.7380703 --2.9052925 --2.6442006 --2.9052925 --3.0991248 --2.6007316 --2.7912598 --2.9353587 --2.7912598 --3.0395645 --3.2251999 --2.9353587 --3.2251999 --3.4403755 --2.858698 --3.0681247 --3.2265167 --3.0681247 --3.3410588 --3.5451073 --3.2265167 --3.5451073 --3.7816261 --2.7423465 --2.8023231 --2.8322336 --3.0308053 --3.1071607 --3.1451489 --3.243986 --3.3318834 --3.3755549 --3.0443116 --3.1108923 --3.1440964 --3.3645332 --3.4492962 --3.4914674 --3.6011876 --3.6987636 --3.7472439 --3.3462767 --3.4194616 --3.4559591 --3.6982611 --3.7914317 --3.8377859 --3.9583893 --4.0656437 --4.1189328 --3.4028729 --3.4991237 --3.5469054 --3.4991237 --3.6003457 --3.6505722 --3.5469054 --3.6505722 --3.7020011 --3.7775699 --3.8844191 --3.937462 --3.8844191 --3.9967867 --4.0525439 --3.937462 --4.0525439 --4.1096357 --4.1522669 --4.2697144 --4.3280187 --4.2697144 --4.3932278 --4.4545155 --4.3280187 --4.4545155 --4.5172703 --2.7423465 --3.0308053 --3.243986 --2.8023231 --3.1071607 --3.3318834 --2.8322336 --3.1451489 --3.3755549 --3.0443116 --3.3645332 --3.6011876 --3.1108923 --3.4492962 --3.6987636 --3.1440964 --3.4914674 --3.7472439 --3.3462767 --3.6982611 --3.9583893 --3.4194616 --3.7914317 --4.0656437 --3.4559591 --3.8377859 --4.1189328 --3.1308656 --3.3602312 --3.5337032 --3.3602312 --3.6591505 --3.8826258 --3.5337032 --3.8826258 --4.1416628 --3.388832 --3.6370961 --3.8248613 --3.6370961 --3.9606447 --4.2025332 --3.8248613 --4.2025332 --4.4829135 --3.6467985 --3.913961 --4.1160194 --3.913961 --4.262139 --4.5224406 --4.1160194 --4.5224406 --4.8241642 --3.6648652 --3.7450177 --3.7849901 --4.0503608 --4.1524019 --4.2031694 --4.335255 --4.4527208 --4.5110834 --3.9668303 --4.053587 --4.0968528 --4.3840887 --4.4945374 --4.5494878 --4.6924566 --4.819601 --4.8827723 --4.2687954 --4.3621562 --4.4087156 --4.7178166 --4.8366729 --4.8958063 --5.0496582 --5.1864812 --5.2544613 --4.5475911 --4.6762204 --4.7400757 --4.6762204 --4.8114932 --4.8786158 --4.7400757 --4.8786158 --4.9473453 --4.922288 --5.0615158 --5.1306324 --5.0615158 --5.2079342 --5.2805875 --5.1306324 --5.2805875 --5.3549799 --5.296985 --5.4468111 --5.521189 --5.4468111 --5.6043753 --5.6825591 --5.521189 --5.6825591 --5.7626144 --3.6648652 --4.0503608 --4.335255 --3.7450177 --4.1524019 --4.4527208 --3.7849901 --4.2031694 --4.5110834 --3.9668303 --4.3840887 --4.6924566 --4.053587 --4.4945374 --4.819601 --4.0968528 --4.5494878 --4.8827723 --4.2687954 --4.7178166 --5.0496582 --4.3621562 --4.8366729 --5.1864812 --4.4087156 --4.8958063 --5.2544613 --2.8322336 --2.8023231 --2.7423465 --3.1451489 --3.1071607 --3.0308053 --3.3755549 --3.3318834 --3.243986 --3.1440964 --3.1108923 --3.0443116 --3.4914674 --3.4492962 --3.3645332 --3.7472439 --3.6987636 --3.6011876 --3.4559591 --3.4194616 --3.3462767 --3.8377859 --3.7914317 --3.6982611 --4.1189328 --4.0656437 --3.9583893 --2.6442006 --2.5143949 --2.3427651 --2.9052925 --2.7380703 --2.5143949 --3.0991248 --2.9052925 --2.6442006 --2.9353587 --2.7912598 --2.6007316 --3.2251999 --3.0395645 --2.7912598 --3.4403755 --3.2251999 --2.9353587 --3.2265167 --3.0681247 --2.858698 --3.5451073 --3.3410588 --3.0681247 --3.7816261 --3.5451073 --3.2265167 --3.243986 --3.0308053 --2.7423465 --3.3318834 --3.1071607 --2.8023231 --3.3755549 --3.1451489 --2.8322336 --3.6011876 --3.3645332 --3.0443116 --3.6987636 --3.4492962 --3.1108923 --3.7472439 --3.4914674 --3.1440964 --3.9583893 --3.6982611 --3.3462767 --4.0656437 --3.7914317 --3.4194616 --4.1189328 --3.8377859 --3.4559591 --3.5469054 --3.4991237 --3.4028729 --3.6505722 --3.6003457 --3.4991237 --3.7020011 --3.6505722 --3.5469054 --3.937462 --3.8844191 --3.7775699 --4.0525439 --3.9967867 --3.8844191 --4.1096357 --4.0525439 --3.937462 --4.3280187 --4.2697144 --4.1522669 --4.4545155 --4.3932278 --4.2697144 --4.5172703 --4.4545155 --4.3280187 --3.7849901 --3.7450177 --3.6648652 --4.2031694 --4.1524019 --4.0503608 --4.5110834 --4.4527208 --4.335255 --4.0968528 --4.053587 --3.9668303 --4.5494878 --4.4945374 --4.3840887 --4.8827723 --4.819601 --4.6924566 --4.4087156 --4.3621562 --4.2687954 --4.8958063 --4.8366729 --4.7178166 --5.2544613 --5.1864812 --5.0496582 --3.5337032 --3.3602312 --3.1308656 --3.8826258 --3.6591505 --3.3602312 --4.1416628 --3.8826258 --3.5337032 --3.8248613 --3.6370961 --3.388832 --4.2025332 --3.9606447 --3.6370961 --4.4829135 --4.2025332 --3.8248613 --4.1160194 --3.913961 --3.6467985 --4.5224406 --4.262139 --3.913961 --4.8241642 --4.5224406 --4.1160194 --4.335255 --4.0503608 --3.6648652 --4.4527208 --4.1524019 --3.7450177 --4.5110834 --4.2031694 --3.7849901 --4.6924566 --4.3840887 --3.9668303 --4.819601 --4.4945374 --4.053587 --4.8827723 --4.5494878 --4.0968528 --5.0496582 --4.7178166 --4.2687954 --5.1864812 --4.8366729 --4.3621562 --5.2544613 --4.8958063 --4.4087156 --4.7400757 --4.6762204 --4.5475911 --4.8786158 --4.8114932 --4.6762204 --4.9473453 --4.8786158 --4.7400757 --5.1306324 --5.0615158 --4.922288 --5.2805875 --5.2079342 --5.0615158 --5.3549799 --5.2805875 --5.1306324 --5.521189 --5.4468111 --5.296985 --5.6825591 --5.6043753 --5.4468111 --5.7626144 --5.6825591 --5.521189 --3.7020011 --3.6505722 --3.5469054 --3.6505722 --3.6003457 --3.4991237 --3.5469054 --3.4991237 --3.4028729 --4.1096357 --4.0525439 --3.937462 --4.0525439 --3.9967867 --3.8844191 --3.937462 --3.8844191 --3.7775699 --4.5172703 --4.4545155 --4.3280187 --4.4545155 --4.3932278 --4.2697144 --4.3280187 --4.2697144 --4.1522669 --3.3755549 --3.1451489 --2.8322336 --3.3318834 --3.1071607 --2.8023231 --3.243986 --3.0308053 --2.7423465 --3.7472439 --3.4914674 --3.1440964 --3.6987636 --3.4492962 --3.1108923 --3.6011876 --3.3645332 --3.0443116 --4.1189328 --3.8377859 --3.4559591 --4.0656437 --3.7914317 --3.4194616 --3.9583893 --3.6982611 --3.3462767 --3.0991248 --2.9052925 --2.6442006 --2.9052925 --2.7380703 --2.5143949 --2.6442006 --2.5143949 --2.3427651 --3.4403755 --3.2251999 --2.9353587 --3.2251999 --3.0395645 --2.7912598 --2.9353587 --2.7912598 --2.6007316 --3.7816261 --3.5451073 --3.2265167 --3.5451073 --3.3410588 --3.0681247 --3.2265167 --3.0681247 --2.858698 --3.3755549 --3.3318834 --3.243986 --3.1451489 --3.1071607 --3.0308053 --2.8322336 --2.8023231 --2.7423465 --3.7472439 --3.6987636 --3.6011876 --3.4914674 --3.4492962 --3.3645332 --3.1440964 --3.1108923 --3.0443116 --4.1189328 --4.0656437 --3.9583893 --3.8377859 --3.7914317 --3.6982611 --3.4559591 --3.4194616 --3.3462767 --4.9473453 --4.8786158 --4.7400757 --4.8786158 --4.8114932 --4.6762204 --4.7400757 --4.6762204 --4.5475911 --5.3549799 --5.2805875 --5.1306324 --5.2805875 --5.2079342 --5.0615158 --5.1306324 --5.0615158 --4.922288 --5.7626144 --5.6825591 --5.521189 --5.6825591 --5.6043753 --5.4468111 --5.521189 --5.4468111 --5.296985 --4.5110834 --4.2031694 --3.7849901 --4.4527208 --4.1524019 --3.7450177 --4.335255 --4.0503608 --3.6648652 --4.8827723 --4.5494878 --4.0968528 --4.819601 --4.4945374 --4.053587 --4.6924566 --4.3840887 --3.9668303 --5.2544613 --4.8958063 --4.4087156 --5.1864812 --4.8366729 --4.3621562 --5.0496582 --4.7178166 --4.2687954 --4.1416628 --3.8826258 --3.5337032 --3.8826258 --3.6591505 --3.3602312 --3.5337032 --3.3602312 --3.1308656 --4.4829135 --4.2025332 --3.8248613 --4.2025332 --3.9606447 --3.6370961 --3.8248613 --3.6370961 --3.388832 --4.8241642 --4.5224406 --4.1160194 --4.5224406 --4.262139 --3.913961 --4.1160194 --3.913961 --3.6467985 --4.5110834 --4.4527208 --4.335255 --4.2031694 --4.1524019 --4.0503608 --3.7849901 --3.7450177 --3.6648652 --4.8827723 --4.819601 --4.6924566 --4.5494878 --4.4945374 --4.3840887 --4.0968528 --4.053587 --3.9668303 --5.2544613 --5.1864812 --5.0496582 --4.8958063 --4.8366729 --4.7178166 --4.4087156 --4.3621562 --4.2687954 --2.8322336 --3.1451489 --3.3755549 --2.8023231 --3.1071607 --3.3318834 --2.7423465 --3.0308053 --3.243986 --3.1440964 --3.4914674 --3.7472439 --3.1108923 --3.4492962 --3.6987636 --3.0443116 --3.3645332 --3.6011876 --3.4559591 --3.8377859 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+0.95683170883849689 +0.95683170883849711 +0.95683170883849711 +0.95683170883849711 +0.95683170883849711 +0.95683170883849711 +END BLOCK EXTERIOR_COORDINATE diff --git a/tests/geometry/volume.cpp b/tests/geometry/volume.cpp index 1732d48..3fb3121 100644 --- a/tests/geometry/volume.cpp +++ b/tests/geometry/volume.cpp @@ -1,25 +1,27 @@ +#include +#include #include #include -#include #include -#include -#include -#include #include #include +#include +#include import mean_field; import test_helpers; using namespace mean_field; - -TEST_CASE("STROID Volume vs sphere", tags::geometry & tags::volume) { - auto args = test_utils::setup_args(); - fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); +TEST_CASE( + "STROID Volume vs sphere", + tags::geometry &tags::volume +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); const double analytic_vol = (4.0 / 3.0) * M_PI * std::pow(utils::RADIUS, 3); - const double stroid_vol = analysis::get_mesh_volume(f); + const double stroid_vol = analysis::get_mesh_volume(f); - double s = analytic_vol / stroid_vol; + double s = analytic_vol / stroid_vol; CHECK_THAT(stroid_vol, Catch::Matchers::WithinRel(analytic_vol, 1e-6)); } \ No newline at end of file diff --git a/tests/integrators/centrifugal.cpp b/tests/integrators/centrifugal.cpp new file mode 100644 index 0000000..397ecbe --- /dev/null +++ b/tests/integrators/centrifugal.cpp @@ -0,0 +1,1394 @@ +#include +#include + +#include + +import mean_field; +import test_helpers; + +using namespace mean_field; + +namespace { + double compute_roche_surface_scale( + const double rotation_fraction, + const double sine_theta_squared + ) { + const double eta = (8.0 / 27.0) * rotation_fraction * rotation_fraction; + double surface_scale = 1.0; + + for (int iteration = 0; iteration < 20; ++iteration) { + const double residual = + 1.0 / surface_scale + + 0.5 * eta * surface_scale * surface_scale * sine_theta_squared - + 1.0; + const double derivative = -1.0 / (surface_scale * surface_scale) + + eta * surface_scale * sine_theta_squared; + surface_scale -= residual / derivative; + } + + return surface_scale; + } +} // namespace + +TEST_CASE( + "Centrifugal Integrator Matches Manufactured Cartesian Load", + tags::unit &tags::solver &tags::integrator &tags::centrifugal +) { + constexpr int dim = 3; + constexpr double density = 1.7; + constexpr double omega_value = 2.3; + constexpr double tolerance = 1.0e-12; + + mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D( + 1, 1, 1, mfem::Element::HEXAHEDRON, 1.0, 1.0, 1.0 + ); + + mfem::H1_FECollection velocity_fec(1, dim); + mfem::L2_FECollection density_fec(0, dim); + mfem::H1_FECollection displacement_fec(1, dim); + + mfem::FiniteElementSpace velocity_fes(&mesh, &velocity_fec); + mfem::FiniteElementSpace density_fes(&mesh, &density_fec); + mfem::FiniteElementSpace displacement_fes( + &mesh, &displacement_fec, dim, mfem::Ordering::byVDIM + ); + + mfem::GridFunction displacement(&displacement_fes); + displacement = 0.0; + + mapping::DomainMapper domain_mapper(displacement, 1.0, 2.0); + + mfem::Vector omega(dim); + omega = 0.0; + omega(2) = omega_value; + + integrators::CentrifugalForceIntegrator integrator(domain_mapper, omega); + + const mfem::FiniteElement *velocity_element = velocity_fes.GetFE(0); + const mfem::FiniteElement *density_element = density_fes.GetFE(0); + const mfem::FiniteElement *displacement_element = displacement_fes.GetFE(0); + mfem::ElementTransformation *transformation = + mesh.GetElementTransformation(0); + + quadrature::RuleSet rule_set = + quadrature::make_rule_set(quadrature::Mode::production); + quadrature::Policy policy(std::move(rule_set)); + quadrature::RuleFactory quadrature_factory(std::move(policy)); + + const quadrature::MappingKind mapping_kind = + !domain_mapper.HasDisplacementField() + ? quadrature::MappingKind::none + : quadrature::MappingKind::general; + const int position_order = displacement_element->GetOrder(); + + quadrature_factory.configure_centrifugal( + integrator, quadrature::QuadratureRole::discretization, + *density_element, *velocity_element, *transformation, position_order, + utils::DOMAINS::STELLAR, mapping_kind + ); + + const int velocity_dofs_count = velocity_element->GetDof(); + const int density_dofs_count = density_element->GetDof(); + + mfem::Vector velocity_dofs(dim * velocity_dofs_count); + mfem::Vector density_dofs(density_dofs_count); + velocity_dofs = 0.0; + density_dofs = density; + + mfem::Array elements(2); + elements[0] = velocity_element; + elements[1] = density_element; + + mfem::Array element_state(2); + element_state[0] = &velocity_dofs; + element_state[1] = &density_dofs; + + mfem::Vector velocity_residual; + mfem::Vector density_residual; + + mfem::Array element_residual(2); + element_residual[0] = &velocity_residual; + element_residual[1] = &density_residual; + + integrator.AssembleElementVector( + elements, *transformation, element_state, element_residual + ); + + auto residual_action = [&](const int component, + const int coordinate_weight) { + mfem::Vector test_dofs(dim * velocity_dofs_count); + mfem::Vector x_physical(dim); + test_dofs = 0.0; + + const mfem::IntegrationRule &nodes = velocity_element->GetNodes(); + + for (int i = 0; i < velocity_dofs_count; ++i) { + transformation->Transform(nodes.IntPoint(i), x_physical); + test_dofs(i + component * velocity_dofs_count) = + coordinate_weight < 0 ? 1.0 : x_physical(coordinate_weight); + } + + return test_dofs * velocity_residual; + }; + + constexpr double force_scale = density * omega_value * omega_value; + + CHECK_THAT( + residual_action(0, -1), + Catch::Matchers::WithinAbs(-0.5 * force_scale, tolerance) + ); + CHECK_THAT( + residual_action(1, -1), + Catch::Matchers::WithinAbs(-0.5 * force_scale, tolerance) + ); + CHECK_THAT( + residual_action(2, -1), Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + residual_action(0, 0), + Catch::Matchers::WithinAbs(-force_scale / 3.0, tolerance) + ); + CHECK_THAT( + residual_action(1, 1), + Catch::Matchers::WithinAbs(-force_scale / 3.0, tolerance) + ); +} + +TEST_CASE( + "Centrifugal Integrator Jacobian Matches Residual Linearization", + tags::unit &tags::solver &tags::integrator &tags::centrifugal +) { + constexpr int dim = 3; + constexpr double step = 1.0e-6; + constexpr double finite_difference_tolerance = 1.0e-9; + constexpr double exact_tolerance = 1.0e-12; + + mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D( + 1, 1, 1, mfem::Element::HEXAHEDRON, 1.0, 1.0, 1.0 + ); + + mfem::H1_FECollection velocity_fec(1, dim); + mfem::L2_FECollection density_fec(1, dim); + mfem::H1_FECollection displacement_fec(1, dim); + + mfem::FiniteElementSpace velocity_fes(&mesh, &velocity_fec); + mfem::FiniteElementSpace density_fes(&mesh, &density_fec); + mfem::FiniteElementSpace displacement_fes( + &mesh, &displacement_fec, dim, mfem::Ordering::byVDIM + ); + + mfem::GridFunction displacement(&displacement_fes); + displacement = 0.0; + + mapping::DomainMapper domain_mapper(displacement, 1.0, 2.0); + + mfem::Vector omega(dim); + omega(0) = 0.7; + omega(1) = -1.1; + omega(2) = 1.6; + + integrators::CentrifugalForceIntegrator integrator(domain_mapper, omega); + + const mfem::FiniteElement *velocity_element = velocity_fes.GetFE(0); + const mfem::FiniteElement *density_element = density_fes.GetFE(0); + const mfem::FiniteElement *displacement_element = displacement_fes.GetFE(0); + mfem::ElementTransformation *transformation = + mesh.GetElementTransformation(0); + + quadrature::RuleSet rule_set = + quadrature::make_rule_set(quadrature::Mode::production); + quadrature::Policy policy(std::move(rule_set)); + quadrature::RuleFactory quadrature_factory(std::move(policy)); + + const quadrature::MappingKind mapping_kind = + !domain_mapper.HasDisplacementField() + ? quadrature::MappingKind::none + : quadrature::MappingKind::general; + const int position_order = displacement_element->GetOrder(); + + quadrature_factory.configure_centrifugal( + integrator, quadrature::QuadratureRole::discretization, + *density_element, *velocity_element, *transformation, position_order, + utils::DOMAINS::STELLAR, mapping_kind + ); + + const int velocity_size = dim * velocity_element->GetDof(); + const int density_size = density_element->GetDof(); + + mfem::Vector velocity_dofs(velocity_size); + mfem::Vector density_dofs(density_size); + mfem::Vector velocity_direction(velocity_size); + mfem::Vector density_direction(density_size); + + for (int i = 0; i < velocity_size; ++i) { + velocity_dofs(i) = 0.03 * static_cast(i + 1); + velocity_direction(i) = + (i % 2 == 0 ? 0.04 : -0.02) * static_cast(i + 1); + } + + for (int i = 0; i < density_size; ++i) { + density_dofs(i) = 1.0 + 0.08 * static_cast(i + 1); + density_direction(i) = + (i % 2 == 0 ? 0.05 : -0.03) * static_cast(i + 1); + } + + mfem::Array elements(2); + elements[0] = velocity_element; + elements[1] = density_element; + + auto assemble_velocity_residual = [&](const mfem::Vector &velocity, + const mfem::Vector &density) { + mfem::Array element_state(2); + element_state[0] = &velocity; + element_state[1] = &density; + + mfem::Vector velocity_residual; + mfem::Vector density_residual; + + mfem::Array element_residual(2); + element_residual[0] = &velocity_residual; + element_residual[1] = &density_residual; + + integrator.AssembleElementVector( + elements, *transformation, element_state, element_residual + ); + return velocity_residual; + }; + + mfem::Array element_state(2); + element_state[0] = &velocity_dofs; + element_state[1] = &density_dofs; + + mfem::DenseMatrix dv_dv(velocity_size, velocity_size); + mfem::DenseMatrix dv_drho(velocity_size, density_size); + mfem::DenseMatrix drho_dv(density_size, velocity_size); + mfem::DenseMatrix drho_drho(density_size, density_size); + + mfem::Array2D element_jacobian(2, 2); + element_jacobian(0, 0) = &dv_dv; + element_jacobian(0, 1) = &dv_drho; + element_jacobian(1, 0) = &drho_dv; + element_jacobian(1, 1) = &drho_drho; + + integrator.AssembleElementGrad( + elements, *transformation, element_state, element_jacobian + ); + + mfem::Vector velocity_plus(velocity_dofs); + mfem::Vector velocity_minus(velocity_dofs); + mfem::Vector density_plus(density_dofs); + mfem::Vector density_minus(density_dofs); + + velocity_plus.Add(step, velocity_direction); + velocity_minus.Add(-step, velocity_direction); + density_plus.Add(step, density_direction); + density_minus.Add(-step, density_direction); + + mfem::Vector residual_plus = + assemble_velocity_residual(velocity_plus, density_plus); + mfem::Vector residual_minus = + assemble_velocity_residual(velocity_minus, density_minus); + mfem::Vector finite_difference(residual_plus); + finite_difference -= residual_minus; + finite_difference /= 2.0 * step; + + mfem::Vector jacobian_action(velocity_size); + mfem::Vector velocity_block_action(velocity_size); + mfem::Vector density_block_action(velocity_size); + + dv_dv.Mult(velocity_direction, velocity_block_action); + dv_drho.Mult(density_direction, density_block_action); + add(velocity_block_action, density_block_action, jacobian_action); + + mfem::Vector finite_difference_error(jacobian_action); + finite_difference_error -= finite_difference; + + const double finite_difference_scale = + std::max(1.0, finite_difference.Norml2()); + const double relative_finite_difference_error = + finite_difference_error.Norml2() / finite_difference_scale; + + CHECK_THAT( + relative_finite_difference_error, + Catch::Matchers::WithinAbs(0.0, finite_difference_tolerance) + ); + CHECK_THAT( + velocity_block_action.Norml2(), + Catch::Matchers::WithinAbs(0.0, exact_tolerance) + ); + + mfem::Vector density_direction_residual = + assemble_velocity_residual(velocity_dofs, density_direction); + mfem::Vector density_linearity_error(density_block_action); + density_linearity_error -= density_direction_residual; + + CHECK_THAT( + density_linearity_error.Norml2(), + Catch::Matchers::WithinAbs(0.0, exact_tolerance) + ); + + double inactive_block_maximum = 0.0; + + for (int i = 0; i < drho_dv.Height(); ++i) { + for (int j = 0; j < drho_dv.Width(); ++j) { + inactive_block_maximum = + std::max(inactive_block_maximum, std::abs(drho_dv(i, j))); + } + } + + for (int i = 0; i < drho_drho.Height(); ++i) { + for (int j = 0; j < drho_drho.Width(); ++j) { + inactive_block_maximum = + std::max(inactive_block_maximum, std::abs(drho_drho(i, j))); + } + } + + CHECK_THAT( + inactive_block_maximum, Catch::Matchers::WithinAbs(0.0, exact_tolerance) + ); +} + +TEST_CASE( + "Centrifugal Integrator Preserves Rotation Identities", + tags::unit &tags::solver &tags::integrator &tags::centrifugal +) { + constexpr int dim = 3; + constexpr double density = 1.4; + constexpr double omega_scale = 2.3; + constexpr double tolerance = 1.0e-12; + + mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D( + 1, 1, 1, mfem::Element::HEXAHEDRON, 1.0, 1.0, 1.0 + ); + + mfem::H1_FECollection velocity_fec(1, dim); + mfem::L2_FECollection density_fec(0, dim); + mfem::H1_FECollection displacement_fec(1, dim); + + mfem::FiniteElementSpace velocity_fes(&mesh, &velocity_fec); + mfem::FiniteElementSpace density_fes(&mesh, &density_fec); + mfem::FiniteElementSpace displacement_fes( + &mesh, &displacement_fec, dim, mfem::Ordering::byVDIM + ); + + mfem::GridFunction displacement(&displacement_fes); + displacement = 0.0; + + mapping::DomainMapper domain_mapper(displacement, 1.0, 2.0); + + mfem::Vector omega(dim); + omega(0) = 0.7; + omega(1) = -1.1; + omega(2) = 1.6; + + integrators::CentrifugalForceIntegrator integrator(domain_mapper, omega); + + const mfem::FiniteElement *velocity_element = velocity_fes.GetFE(0); + const mfem::FiniteElement *density_element = density_fes.GetFE(0); + const mfem::FiniteElement *displacement_element = displacement_fes.GetFE(0); + mfem::ElementTransformation *transformation = + mesh.GetElementTransformation(0); + + quadrature::RuleSet rule_set = + quadrature::make_rule_set(quadrature::Mode::production); + quadrature::Policy policy(std::move(rule_set)); + quadrature::RuleFactory quadrature_factory(std::move(policy)); + + const quadrature::MappingKind mapping_kind = + !domain_mapper.HasDisplacementField() + ? quadrature::MappingKind::none + : quadrature::MappingKind::general; + const int position_order = displacement_element->GetOrder(); + + quadrature_factory.configure_centrifugal( + integrator, quadrature::QuadratureRole::discretization, + *density_element, *velocity_element, *transformation, position_order, + utils::DOMAINS::STELLAR, mapping_kind + ); + + const int velocity_dofs_count = velocity_element->GetDof(); + const int velocity_size = dim * velocity_dofs_count; + const int density_size = density_element->GetDof(); + + mfem::Vector velocity_dofs(velocity_size); + mfem::Vector density_dofs(density_size); + velocity_dofs = 0.0; + density_dofs = density; + + mfem::Array elements(2); + elements[0] = velocity_element; + elements[1] = density_element; + + auto assemble_velocity_residual = [&](const mfem::Vector &rotation) { + integrator.SetOmega(rotation); + + mfem::Array element_state(2); + element_state[0] = &velocity_dofs; + element_state[1] = &density_dofs; + + mfem::Vector velocity_residual; + mfem::Vector density_residual; + + mfem::Array element_residual(2); + element_residual[0] = &velocity_residual; + element_residual[1] = &density_residual; + + integrator.AssembleElementVector( + elements, *transformation, element_state, element_residual + ); + return velocity_residual; + }; + + const mfem::Vector baseline_residual = assemble_velocity_residual(omega); + + mfem::Vector zero_omega(dim); + zero_omega = 0.0; + + const mfem::Vector zero_residual = assemble_velocity_residual(zero_omega); + CHECK_THAT( + zero_residual.Norml2(), Catch::Matchers::WithinAbs(0.0, tolerance) + ); + + mfem::Vector negative_omega(omega); + negative_omega *= -1.0; + + mfem::Vector sign_error = assemble_velocity_residual(negative_omega); + sign_error -= baseline_residual; + CHECK_THAT(sign_error.Norml2(), Catch::Matchers::WithinAbs(0.0, tolerance)); + + mfem::Vector scaled_omega(omega); + scaled_omega *= omega_scale; + + mfem::Vector expected_scaled_residual(baseline_residual); + expected_scaled_residual *= omega_scale * omega_scale; + + mfem::Vector scaling_error = assemble_velocity_residual(scaled_omega); + scaling_error -= expected_scaled_residual; + + const double scaling_error_relative = + scaling_error.Norml2() / + std::max(1.0, expected_scaled_residual.Norml2()); + CHECK_THAT( + scaling_error_relative, Catch::Matchers::WithinAbs(0.0, tolerance) + ); + + mfem::Vector axis_test_dofs(velocity_size); + mfem::Vector torque_test_dofs(velocity_size); + mfem::Vector x_physical(dim); + mfem::Vector azimuthal_direction(dim); + + axis_test_dofs = 0.0; + torque_test_dofs = 0.0; + + const mfem::IntegrationRule &nodes = velocity_element->GetNodes(); + + for (int i = 0; i < velocity_dofs_count; ++i) { + transformation->Transform(nodes.IntPoint(i), x_physical); + + azimuthal_direction(0) = + omega(1) * x_physical(2) - omega(2) * x_physical(1); + azimuthal_direction(1) = + omega(2) * x_physical(0) - omega(0) * x_physical(2); + azimuthal_direction(2) = + omega(0) * x_physical(1) - omega(1) * x_physical(0); + + for (int c = 0; c < dim; ++c) { + axis_test_dofs(i + c * velocity_dofs_count) = omega(c); + torque_test_dofs(i + c * velocity_dofs_count) = + azimuthal_direction(c); + } + } + + const double axial_force = axis_test_dofs * baseline_residual; + const double axial_torque = torque_test_dofs * baseline_residual; + + CHECK_THAT(axial_force, Catch::Matchers::WithinAbs(0.0, tolerance)); + CHECK_THAT(axial_torque, Catch::Matchers::WithinAbs(0.0, tolerance)); +} + +TEST_CASE( + "Centrifugal Integrator Matches Rotational Virial On Roche Mappings", + tags::integration &tags::solver &tags::integrator &tags::centrifugal +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + constexpr int dim = 3; + constexpr double concentration = 4.0; + constexpr double assembly_tolerance = 1.0e-7; + constexpr double position_tolerance = 1.0e-6; + + const double radius = utils::RADIUS; + + auto reference_density = [radius](const mfem::Vector &x) { + const double normalized_radius_squared = (x * x) / (radius * radius); + + if (normalized_radius_squared >= 1.0) { + return 0.0; + } + + const double denominator = + 1.0 + concentration * normalized_radius_squared; + return (1.0 - normalized_radius_squared) / (denominator * denominator); + }; + + mfem::FunctionCoefficient density_coefficient(reference_density); + mfem::ParGridFunction density(f.densityFes.get()); + density.ProjectCoefficient(density_coefficient); + + mfem::ParGridFunction displacement(f.displacementFes.get()); + + const mfem::FiniteElement &representative_velocity_element = + *f.displacementFes->GetTypicalFE(); + const mfem::FiniteElement &representative_density_element = + *f.densityFes->GetTypicalFE(); + mfem::ElementTransformation &representative_transformation = + *f.mesh->GetElementTransformation(0); + const int position_order = f.displacementFes->GetMaxElementOrder(); + + for (constexpr std::array rotation_fractions = + {0.0001, 0.1, 0.25, 0.50, 0.70, 0.85, 0.95, 0.99}; + const double rotation_fraction : rotation_fractions) { + CAPTURE(rotation_fraction); + + auto rotation_displacement = [radius, rotation_fraction]( + const mfem::Vector &x, + mfem::Vector &displacement_value + ) { + displacement_value.SetSize(dim); + + const double radius_squared = x * x; + + if (radius_squared <= 1.0e-28) { + displacement_value = 0.0; + return; + } + + const double cylindrical_radius_squared = x(0) * x(0) + x(1) * x(1); + const double sine_theta_squared = + cylindrical_radius_squared / radius_squared; + const double surface_scale = compute_roche_surface_scale( + rotation_fraction, sine_theta_squared + ); + const double radial_weight = + std::min(radius_squared / (radius * radius), 1.0); + const double mapped_scale = + 1.0 + radial_weight * (surface_scale - 1.0); + + for (int d = 0; d < dim; ++d) { + displacement_value(d) = (mapped_scale - 1.0) * x(d); + } + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + dim, rotation_displacement + ); + displacement.ProjectCoefficient(displacement_coefficient); + f.mapping->SetDisplacement(displacement); + + mfem::Vector omega(dim); + omega = 0.0; + omega(2) = rotation_fraction; + + integrators::CentrifugalForceIntegrator integrator(*f.mapping, omega); + + const quadrature::MappingKind mapping_kind = + !f.mapping->HasDisplacementField() + ? quadrature::MappingKind::none + : quadrature::MappingKind::general; + f.quadratureFactory->configure_centrifugal( + integrator, quadrature::QuadratureRole::discretization, + representative_density_element, representative_velocity_element, + representative_transformation, position_order, + utils::DOMAINS::STELLAR, mapping_kind + ); + + const int reference_order = + 2 * std::max( + f.displacementFes->GetMaxElementOrder(), + f.densityFes->GetMaxElementOrder() + ) + + 16; + + double local_residual_action = 0.0; + double local_discrete_reference_action = 0.0; + double local_continuous_reference_action = 0.0; + double local_minimum_map_determinant = + std::numeric_limits::infinity(); + double local_maximum_map_determinant = + std::numeric_limits::lowest(); + + for (int elem_id = 0; elem_id < f.mesh->GetNE(); ++elem_id) { + if (f.mesh->GetAttribute(elem_id) == 3) { + continue; + } + + const mfem::FiniteElement *velocity_element = + f.displacementFes->GetFE(elem_id); + const mfem::FiniteElement *density_element = + f.densityFes->GetFE(elem_id); + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(elem_id); + + const int velocity_dofs_count = velocity_element->GetDof(); + const int velocity_size = dim * velocity_dofs_count; + const int density_size = density_element->GetDof(); + + mfem::Array density_dof_indices; + mfem::Vector density_dofs; + f.densityFes->GetElementDofs(elem_id, density_dof_indices); + density.GetSubVector(density_dof_indices, density_dofs); + + mfem::Vector velocity_dofs(velocity_size); + velocity_dofs = 0.0; + + mfem::Array elements(2); + elements[0] = velocity_element; + elements[1] = density_element; + + mfem::Array element_state(2); + element_state[0] = &velocity_dofs; + element_state[1] = &density_dofs; + + mfem::Vector velocity_residual(velocity_size); + mfem::Vector density_residual(density_size); + velocity_residual = 0.0; + density_residual = 0.0; + + mfem::Array element_residual(2); + element_residual[0] = &velocity_residual; + element_residual[1] = &density_residual; + + integrator.AssembleElementVector( + elements, *transformation, element_state, element_residual + ); + + mfem::Vector position_test_dofs(velocity_size); + mfem::Vector x_physical(dim); + position_test_dofs = 0.0; + + const mfem::IntegrationRule &velocity_nodes = + velocity_element->GetNodes(); + + for (int i = 0; i < velocity_dofs_count; ++i) { + const mfem::IntegrationPoint &node = velocity_nodes.IntPoint(i); + transformation->SetIntPoint(&node); + f.mapping->GetPhysicalPoint(*transformation, node, x_physical); + + for (int d = 0; d < dim; ++d) { + position_test_dofs(i + d * velocity_dofs_count) = + x_physical(d); + } + } + + local_residual_action += position_test_dofs * velocity_residual; + + mfem::Vector velocity_shape(velocity_dofs_count); + mfem::Vector position_test_value(dim); + mfem::Vector omega_cross_position(dim); + mfem::Vector centrifugal_acceleration(dim); + + const mfem::IntegrationRule &reference_rule = mfem::IntRules.Get( + transformation->GetGeometryType(), reference_order + ); + + for (int q = 0; q < reference_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + reference_rule.IntPoint(q); + transformation->SetIntPoint(&integration_point); + + const double signed_map_determinant = + f.mapping->ComputeDetJ(*transformation, integration_point); + const mapping::VolumeQuadratureContext context = + f.mapping->GetQuadratureContext( + *transformation, integration_point + ); + + local_minimum_map_determinant = std::min( + local_minimum_map_determinant, signed_map_determinant + ); + local_maximum_map_determinant = std::max( + local_maximum_map_determinant, signed_map_determinant + ); + + f.mapping->GetPhysicalPoint( + *transformation, integration_point, x_physical + ); + velocity_element->CalcShape(integration_point, velocity_shape); + + position_test_value = 0.0; + + for (int i = 0; i < velocity_dofs_count; ++i) { + for (int d = 0; d < dim; ++d) { + position_test_value(d) += + position_test_dofs(i + d * velocity_dofs_count) * + velocity_shape(i); + } + } + + omega_cross_position(0) = + omega(1) * x_physical(2) - omega(2) * x_physical(1); + omega_cross_position(1) = + omega(2) * x_physical(0) - omega(0) * x_physical(2); + omega_cross_position(2) = + omega(0) * x_physical(1) - omega(1) * x_physical(0); + + centrifugal_acceleration(0) = + omega(1) * omega_cross_position(2) - + omega(2) * omega_cross_position(1); + centrifugal_acceleration(1) = + omega(2) * omega_cross_position(0) - + omega(0) * omega_cross_position(2); + centrifugal_acceleration(2) = + omega(0) * omega_cross_position(1) - + omega(1) * omega_cross_position(0); + + const double density_value = + density.GetValue(elem_id, integration_point); + + local_discrete_reference_action += + density_value * + (position_test_value * centrifugal_acceleration) * + context.weight; + local_continuous_reference_action += + density_value * (x_physical * centrifugal_acceleration) * + context.weight; + } + } + + double global_residual_action = 0.0; + double global_discrete_reference_action = 0.0; + double global_continuous_reference_action = 0.0; + double global_minimum_map_determinant = 0.0; + double global_maximum_map_determinant = 0.0; + + MPI_Comm communicator = f.mesh->GetComm(); + MPI_Allreduce( + &local_residual_action, &global_residual_action, 1, MPI_DOUBLE, + MPI_SUM, communicator + ); + MPI_Allreduce( + &local_discrete_reference_action, &global_discrete_reference_action, + 1, MPI_DOUBLE, MPI_SUM, communicator + ); + MPI_Allreduce( + &local_continuous_reference_action, + &global_continuous_reference_action, 1, MPI_DOUBLE, MPI_SUM, + communicator + ); + MPI_Allreduce( + &local_minimum_map_determinant, &global_minimum_map_determinant, 1, + MPI_DOUBLE, MPI_MIN, communicator + ); + MPI_Allreduce( + &local_maximum_map_determinant, &global_maximum_map_determinant, 1, + MPI_DOUBLE, MPI_MAX, communicator + ); + + const double relative_assembly_error = + std::abs( + global_residual_action - global_discrete_reference_action + ) / + std::abs(global_discrete_reference_action); + const double relative_position_error = + std::abs( + global_discrete_reference_action - + global_continuous_reference_action + ) / + std::abs(global_continuous_reference_action); + const double equatorial_scale = + compute_roche_surface_scale(rotation_fraction, 1.0); + + INFO("Rotation fraction = " << rotation_fraction); + INFO("Roche equatorial scale = " << equatorial_scale); + INFO( + "Minimum mapping determinant = " << global_minimum_map_determinant + ); + INFO( + "Maximum mapping determinant = " << global_maximum_map_determinant + ); + INFO("Assembled centrifugal virial = " << global_residual_action); + INFO( + "Discrete reference virial = " << global_discrete_reference_action + ); + INFO( + "Continuous reference virial = " + << global_continuous_reference_action + ); + INFO("Relative assembly error = " << relative_assembly_error); + INFO( + "Relative position representation error = " + << relative_position_error + ); + + REQUIRE(equatorial_scale > 1.0); + REQUIRE(global_minimum_map_determinant > 0.0); + CHECK_THAT( + relative_assembly_error, + Catch::Matchers::WithinAbs(0.0, assembly_tolerance) + ); + CHECK_THAT( + relative_position_error, + Catch::Matchers::WithinAbs(0.0, position_tolerance) + ); + } + + f.mapping->ResetDisplacement(); +} + +TEST_CASE( + "Centrifugal Virial Position Representation Is Consistent At The " + "Registered Order", + tags::integration &tags::solver &tags::integrator &tags::centrifugal +) { + constexpr int dim = 3; + constexpr double concentration = 4.0; + constexpr std::array velocity_orders = { + field::Displacement::Vector::familyOrder + }; + constexpr std::array rotation_fractions = {0.70, 0.99}; + + std::array< + std::array, rotation_fractions.size()> + position_errors{}; + std::array< + std::array, rotation_fractions.size()> + minimum_determinants{}; + + for (std::size_t order_index = 0; order_index < velocity_orders.size(); + ++order_index) { + auto args = test_utils::setup_args(); + + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + constexpr double radius = utils::RADIUS; + + auto reference_density = [radius](const mfem::Vector &x) { + const double normalized_radius_squared = + (x * x) / (radius * radius); + + if (normalized_radius_squared >= 1.0) { + return 0.0; + } + + const double denominator = + 1.0 + concentration * normalized_radius_squared; + return (1.0 - normalized_radius_squared) / + (denominator * denominator); + }; + + mfem::FunctionCoefficient density_coefficient(reference_density); + mfem::ParGridFunction density(f.densityFes.get()); + density.ProjectCoefficient(density_coefficient); + + mfem::ParGridFunction displacement(f.displacementFes.get()); + + for (std::size_t rotation_index = 0; + rotation_index < rotation_fractions.size(); ++rotation_index) { + const double rotation_fraction = rotation_fractions[rotation_index]; + + auto rotation_displacement = [radius, rotation_fraction]( + const mfem::Vector &x, + mfem::Vector &displacement_value + ) { + displacement_value.SetSize(dim); + + const double radius_squared = x * x; + + if (radius_squared <= 1.0e-28) { + displacement_value = 0.0; + return; + } + + const double cylindrical_radius_squared = + x(0) * x(0) + x(1) * x(1); + const double sine_theta_squared = + cylindrical_radius_squared / radius_squared; + const double surface_scale = compute_roche_surface_scale( + rotation_fraction, sine_theta_squared + ); + const double radial_weight = + std::min(radius_squared / (radius * radius), 1.0); + const double mapped_scale = + 1.0 + radial_weight * (surface_scale - 1.0); + + for (int d = 0; d < dim; ++d) { + displacement_value(d) = (mapped_scale - 1.0) * x(d); + } + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + dim, rotation_displacement + ); + displacement.ProjectCoefficient(displacement_coefficient); + f.mapping->SetDisplacement(displacement); + + mfem::Vector omega(dim); + omega = 0.0; + omega(2) = rotation_fraction; + + const int reference_order = + 2 * std::max( + f.displacementFes->GetMaxElementOrder(), + f.densityFes->GetMaxElementOrder() + ) + + 16; + + double local_discrete_action = 0.0; + double local_continuous_action = 0.0; + double local_minimum_determinant = + std::numeric_limits::infinity(); + + for (int elem_id = 0; elem_id < f.mesh->GetNE(); ++elem_id) { + if (f.mesh->GetAttribute(elem_id) == 3) { + continue; + } + + const mfem::FiniteElement *velocity_element = + f.displacementFes->GetFE(elem_id); + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(elem_id); + + const int velocity_dofs_count = velocity_element->GetDof(); + const int velocity_size = dim * velocity_dofs_count; + + mfem::Vector position_test_dofs(velocity_size); + mfem::Vector x_physical(dim); + position_test_dofs = 0.0; + + const mfem::IntegrationRule &velocity_nodes = + velocity_element->GetNodes(); + + for (int i = 0; i < velocity_dofs_count; ++i) { + const mfem::IntegrationPoint &node = + velocity_nodes.IntPoint(i); + transformation->SetIntPoint(&node); + f.mapping->GetPhysicalPoint( + *transformation, node, x_physical + ); + + for (int d = 0; d < dim; ++d) { + position_test_dofs(i + d * velocity_dofs_count) = + x_physical(d); + } + } + + mfem::Vector velocity_shape(velocity_dofs_count); + mfem::Vector position_test_value(dim); + mfem::Vector omega_cross_position(dim); + mfem::Vector centrifugal_acceleration(dim); + + const mfem::IntegrationRule &reference_rule = + mfem::IntRules.Get( + transformation->GetGeometryType(), reference_order + ); + + for (int q = 0; q < reference_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + reference_rule.IntPoint(q); + transformation->SetIntPoint(&integration_point); + + const double signed_map_determinant = + f.mapping->ComputeDetJ( + *transformation, integration_point + ); + const mapping::VolumeQuadratureContext context = + f.mapping->GetQuadratureContext( + *transformation, integration_point + ); + + local_minimum_determinant = std::min( + local_minimum_determinant, signed_map_determinant + ); + + f.mapping->GetPhysicalPoint( + *transformation, integration_point, x_physical + ); + velocity_element->CalcShape( + integration_point, velocity_shape + ); + + position_test_value = 0.0; + + for (int i = 0; i < velocity_dofs_count; ++i) { + for (int d = 0; d < dim; ++d) { + position_test_value(d) += + position_test_dofs( + i + d * velocity_dofs_count + ) * + velocity_shape(i); + } + } + + omega_cross_position(0) = + omega(1) * x_physical(2) - omega(2) * x_physical(1); + omega_cross_position(1) = + omega(2) * x_physical(0) - omega(0) * x_physical(2); + omega_cross_position(2) = + omega(0) * x_physical(1) - omega(1) * x_physical(0); + + centrifugal_acceleration(0) = + omega(1) * omega_cross_position(2) - + omega(2) * omega_cross_position(1); + centrifugal_acceleration(1) = + omega(2) * omega_cross_position(0) - + omega(0) * omega_cross_position(2); + centrifugal_acceleration(2) = + omega(0) * omega_cross_position(1) - + omega(1) * omega_cross_position(0); + + const double density_value = + density.GetValue(elem_id, integration_point); + + local_discrete_action += + density_value * + (position_test_value * centrifugal_acceleration) * + context.weight; + local_continuous_action += + density_value * + (x_physical * centrifugal_acceleration) * + context.weight; + } + } + + double global_discrete_action = 0.0; + double global_continuous_action = 0.0; + double global_minimum_determinant = 0.0; + + MPI_Comm communicator = f.mesh->GetComm(); + MPI_Allreduce( + &local_discrete_action, &global_discrete_action, 1, MPI_DOUBLE, + MPI_SUM, communicator + ); + MPI_Allreduce( + &local_continuous_action, &global_continuous_action, 1, + MPI_DOUBLE, MPI_SUM, communicator + ); + MPI_Allreduce( + &local_minimum_determinant, &global_minimum_determinant, 1, + MPI_DOUBLE, MPI_MIN, communicator + ); + + position_errors[rotation_index][order_index] = + std::abs(global_discrete_action - global_continuous_action) / + std::abs(global_continuous_action); + minimum_determinants[rotation_index][order_index] = + global_minimum_determinant; + } + + f.mapping->ResetDisplacement(); + } + + for (std::size_t rotation_index = 0; + rotation_index < rotation_fractions.size(); ++rotation_index) { + constexpr double consistency_tolerance = 1.0e-1; + const double registered_order_error = + position_errors[rotation_index][0]; + + CAPTURE(rotation_fractions[rotation_index]); + INFO( + "Registered displacement family order = " << velocity_orders.front() + ); + INFO("Position error = " << registered_order_error); + INFO( + "Minimum determinant = " << minimum_determinants[rotation_index][0] + ); + + REQUIRE(minimum_determinants[rotation_index][0] > 0.0); + REQUIRE(std::isfinite(registered_order_error)); + CHECK(registered_order_error < consistency_tolerance); + } +} + +TEST_CASE( + "Centrifugal Virial Position Representation Converges Under H Refinement", + tags::integration &tags::solver &tags::integrator &tags::convergence + &tags::h_refinement &tags::centrifugal +) { + constexpr int dim = 3; + constexpr double concentration = 4.0; + constexpr double minimum_rate = 1.5; + constexpr double finest_level_tolerance = 1.0e-5; + constexpr std::array refinement_levels = {0, 1, 2}; + constexpr std::array rotation_fractions = {0.70, 0.85}; + + std::array< + std::array, rotation_fractions.size()> + position_errors{}; + std::array< + std::array, rotation_fractions.size()> + minimum_determinants{}; + + for (std::size_t refinement_index = 0; + refinement_index < refinement_levels.size(); ++refinement_index) { + auto args = test_utils::setup_args(); + + fem::FEM f = fem::setup_fem( + args.mesh_file, args, refinement_levels[refinement_index] + ); + + const double radius = utils::RADIUS; + + auto reference_density = [radius](const mfem::Vector &x) { + const double normalized_radius_squared = + (x * x) / (radius * radius); + + if (normalized_radius_squared >= 1.0) { + return 0.0; + } + + const double denominator = + 1.0 + concentration * normalized_radius_squared; + return (1.0 - normalized_radius_squared) / + (denominator * denominator); + }; + + mfem::FunctionCoefficient density_coefficient(reference_density); + mfem::ParGridFunction density(f.densityFes.get()); + density.ProjectCoefficient(density_coefficient); + + mfem::ParGridFunction displacement(f.displacementFes.get()); + + for (std::size_t rotation_index = 0; + rotation_index < rotation_fractions.size(); ++rotation_index) { + const double rotation_fraction = rotation_fractions[rotation_index]; + + auto rotation_displacement = [radius, rotation_fraction]( + const mfem::Vector &x, + mfem::Vector &displacement_value + ) { + displacement_value.SetSize(dim); + + const double radius_squared = x * x; + + if (radius_squared <= 1.0e-28) { + displacement_value = 0.0; + return; + } + + const double cylindrical_radius_squared = + x(0) * x(0) + x(1) * x(1); + const double sine_theta_squared = + cylindrical_radius_squared / radius_squared; + const double surface_scale = compute_roche_surface_scale( + rotation_fraction, sine_theta_squared + ); + const double radial_weight = + std::min(radius_squared / (radius * radius), 1.0); + const double mapped_scale = + 1.0 + radial_weight * (surface_scale - 1.0); + + for (int d = 0; d < dim; ++d) { + displacement_value(d) = (mapped_scale - 1.0) * x(d); + } + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + dim, rotation_displacement + ); + displacement.ProjectCoefficient(displacement_coefficient); + f.mapping->SetDisplacement(displacement); + + mfem::Vector omega(dim); + omega = 0.0; + omega(2) = rotation_fraction; + + const int reference_order = + 2 * std::max( + f.displacementFes->GetMaxElementOrder(), + f.densityFes->GetMaxElementOrder() + ) + + 16; + + double local_discrete_action = 0.0; + double local_continuous_action = 0.0; + double local_minimum_determinant = + std::numeric_limits::infinity(); + + for (int elem_id = 0; elem_id < f.mesh->GetNE(); ++elem_id) { + if (f.mesh->GetAttribute(elem_id) == 3) { + continue; + } + + const mfem::FiniteElement *velocity_element = + f.displacementFes->GetFE(elem_id); + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(elem_id); + + const int velocity_dofs_count = velocity_element->GetDof(); + const int velocity_size = dim * velocity_dofs_count; + + mfem::Vector position_test_dofs(velocity_size); + mfem::Vector x_physical(dim); + position_test_dofs = 0.0; + + const mfem::IntegrationRule &velocity_nodes = + velocity_element->GetNodes(); + + for (int i = 0; i < velocity_dofs_count; ++i) { + const mfem::IntegrationPoint &node = + velocity_nodes.IntPoint(i); + transformation->SetIntPoint(&node); + f.mapping->GetPhysicalPoint( + *transformation, node, x_physical + ); + + for (int d = 0; d < dim; ++d) { + position_test_dofs(i + d * velocity_dofs_count) = + x_physical(d); + } + } + + mfem::Vector velocity_shape(velocity_dofs_count); + mfem::Vector position_test_value(dim); + mfem::Vector omega_cross_position(dim); + mfem::Vector centrifugal_acceleration(dim); + + const mfem::IntegrationRule &reference_rule = + mfem::IntRules.Get( + transformation->GetGeometryType(), reference_order + ); + + for (int q = 0; q < reference_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + reference_rule.IntPoint(q); + transformation->SetIntPoint(&integration_point); + + const double signed_map_determinant = + f.mapping->ComputeDetJ( + *transformation, integration_point + ); + const mapping::VolumeQuadratureContext context = + f.mapping->GetQuadratureContext( + *transformation, integration_point + ); + + local_minimum_determinant = std::min( + local_minimum_determinant, signed_map_determinant + ); + + f.mapping->GetPhysicalPoint( + *transformation, integration_point, x_physical + ); + velocity_element->CalcShape( + integration_point, velocity_shape + ); + + position_test_value = 0.0; + + for (int i = 0; i < velocity_dofs_count; ++i) { + for (int d = 0; d < dim; ++d) { + position_test_value(d) += + position_test_dofs( + i + d * velocity_dofs_count + ) * + velocity_shape(i); + } + } + + omega_cross_position(0) = + omega(1) * x_physical(2) - omega(2) * x_physical(1); + omega_cross_position(1) = + omega(2) * x_physical(0) - omega(0) * x_physical(2); + omega_cross_position(2) = + omega(0) * x_physical(1) - omega(1) * x_physical(0); + + centrifugal_acceleration(0) = + omega(1) * omega_cross_position(2) - + omega(2) * omega_cross_position(1); + centrifugal_acceleration(1) = + omega(2) * omega_cross_position(0) - + omega(0) * omega_cross_position(2); + centrifugal_acceleration(2) = + omega(0) * omega_cross_position(1) - + omega(1) * omega_cross_position(0); + + const double density_value = + density.GetValue(elem_id, integration_point); + + local_discrete_action += + density_value * + (position_test_value * centrifugal_acceleration) * + context.weight; + local_continuous_action += + density_value * + (x_physical * centrifugal_acceleration) * + context.weight; + } + } + + double global_discrete_action = 0.0; + double global_continuous_action = 0.0; + double global_minimum_determinant = 0.0; + + MPI_Comm communicator = f.mesh->GetComm(); + MPI_Allreduce( + &local_discrete_action, &global_discrete_action, 1, MPI_DOUBLE, + MPI_SUM, communicator + ); + MPI_Allreduce( + &local_continuous_action, &global_continuous_action, 1, + MPI_DOUBLE, MPI_SUM, communicator + ); + MPI_Allreduce( + &local_minimum_determinant, &global_minimum_determinant, 1, + MPI_DOUBLE, MPI_MIN, communicator + ); + + position_errors[rotation_index][refinement_index] = + std::abs(global_discrete_action - global_continuous_action) / + std::abs(global_continuous_action); + minimum_determinants[rotation_index][refinement_index] = + global_minimum_determinant; + } + + f.mapping->ResetDisplacement(); + } + + for (std::size_t rotation_index = 0; + rotation_index < rotation_fractions.size(); ++rotation_index) { + const double error_h = position_errors[rotation_index][0]; + const double error_h2 = position_errors[rotation_index][1]; + const double error_h4 = position_errors[rotation_index][2]; + + REQUIRE(error_h > 0.0); + REQUIRE(error_h2 > 0.0); + REQUIRE(error_h4 > 0.0); + + const double rate_h_h2 = std::log(error_h / error_h2) / std::log(2.0); + const double rate_h2_h4 = std::log(error_h2 / error_h4) / std::log(2.0); + + CAPTURE(rotation_fractions[rotation_index]); + INFO("Level 0 position error = " << error_h); + INFO("Level 1 position error = " << error_h2); + INFO("Level 2 position error = " << error_h4); + INFO("Level 0 to 1 reduction = " << error_h / error_h2); + INFO("Level 1 to 2 reduction = " << error_h2 / error_h4); + INFO("Observed level 0 to 1 rate = " << rate_h_h2); + INFO("Observed level 1 to 2 rate = " << rate_h2_h4); + INFO( + "Level 0 minimum determinant = " + << minimum_determinants[rotation_index][0] + ); + INFO( + "Level 1 minimum determinant = " + << minimum_determinants[rotation_index][1] + ); + INFO( + "Level 2 minimum determinant = " + << minimum_determinants[rotation_index][2] + ); + + REQUIRE(minimum_determinants[rotation_index][0] > 0.0); + REQUIRE(minimum_determinants[rotation_index][1] > 0.0); + REQUIRE(minimum_determinants[rotation_index][2] > 0.0); + + CHECK(error_h2 < error_h); + CHECK(error_h4 < error_h2); + CHECK(rate_h_h2 > minimum_rate); + CHECK(rate_h2_h4 > minimum_rate); + CHECK_THAT( + error_h4, Catch::Matchers::WithinAbs(0.0, finest_level_tolerance) + ); + } +} diff --git a/tests/integrators/gravity.cpp b/tests/integrators/gravity.cpp new file mode 100644 index 0000000..e7ebada --- /dev/null +++ b/tests/integrators/gravity.cpp @@ -0,0 +1,931 @@ +#include +#include + +#include + +import mean_field; +import test_helpers; + +using namespace mean_field; + +TEST_CASE( + "Gravity Force Integrator Jacobian Matches Residual Linearization", + tags::unit &tags::solver &tags::integrator &tags::gravity +) { + constexpr int dim = 3; + constexpr double finite_difference_step = 1.0e-3; + constexpr double jacobian_tolerance = 1.0e-8; + constexpr double zero_tolerance = 1.0e-14; + + constexpr int velocity_block = + solver::block_index(solver::FieldBlock::velocity); + constexpr int density_block = + solver::block_index(solver::FieldBlock::density); + constexpr int gravity_gradient_block = + solver::block_index(solver::FieldBlock::gravity_gradient); + constexpr int gravity_potential_block = + solver::block_index(solver::FieldBlock::gravity_potential); + constexpr int displacement_block = + solver::block_index(solver::FieldBlock::displacement); + constexpr int block_count = solver::field_block_count; + + mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D( + 1, 1, 1, mfem::Element::HEXAHEDRON, 1.0, 1.0, 1.0 + ); + + mfem::H1_FECollection velocity_fec(2, dim); + mfem::L2_FECollection density_fec(1, dim); + mfem::RT_FECollection gravity_gradient_fec(1, dim); + mfem::L2_FECollection gravity_potential_fec(1, dim); + mfem::H1_FECollection displacement_fec(2, dim); + + mfem::FiniteElementSpace velocity_fes( + &mesh, &velocity_fec, dim, mfem::Ordering::byVDIM + ); + mfem::FiniteElementSpace density_fes(&mesh, &density_fec); + mfem::FiniteElementSpace gravity_gradient_fes(&mesh, &gravity_gradient_fec); + mfem::FiniteElementSpace gravity_potential_fes( + &mesh, &gravity_potential_fec + ); + mfem::FiniteElementSpace displacement_fes( + &mesh, &displacement_fec, dim, mfem::Ordering::byVDIM + ); + + mfem::GridFunction displacement(&displacement_fes); + displacement = 0.0; + + mapping::DomainMapper domain_mapper(displacement, 1.0, 2.0); + INFO( + std::format( + "Domain mapping is has displacement field: {}", + domain_mapper.HasDisplacementField() + ) + ); + INFO( + std::format( + "Domain mapping is identity: {}", domain_mapper.CalcIsIdentity() + ) + ); + + REQUIRE(domain_mapper.CalcIsIdentity()); + + const mfem::FiniteElement *velocity_element = velocity_fes.GetFE(0); + const mfem::FiniteElement *density_element = density_fes.GetFE(0); + const mfem::FiniteElement *gravity_gradient_element = + gravity_gradient_fes.GetFE(0); + const mfem::FiniteElement *gravity_potential_element = + gravity_potential_fes.GetFE(0); + const mfem::FiniteElement *displacement_element = displacement_fes.GetFE(0); + mfem::ElementTransformation *transformation = + mesh.GetElementTransformation(0); + + const int velocity_dofs_count = velocity_element->GetDof(); + const int density_dofs_count = density_element->GetDof(); + const int gravity_gradient_dofs_count = gravity_gradient_element->GetDof(); + const int gravity_potential_dofs_count = + gravity_potential_element->GetDof(); + const int displacement_dofs_count = displacement_element->GetDof(); + const int velocity_size = dim * velocity_dofs_count; + const int displacement_size = dim * displacement_dofs_count; + + mfem::Vector velocity_dofs(velocity_size); + mfem::Vector density_dofs(density_dofs_count); + mfem::Vector gravity_gradient_dofs(gravity_gradient_dofs_count); + mfem::Vector gravity_potential_dofs(gravity_potential_dofs_count); + mfem::Vector displacement_dofs(displacement_size); + velocity_dofs = 0.0; + gravity_potential_dofs = 0.0; + displacement_dofs = 0.0; + + for (int i = 0; i < density_dofs_count; ++i) { + density_dofs(i) = 0.8 + 0.07 * static_cast(i + 1); + } + + for (int i = 0; i < gravity_gradient_dofs_count; ++i) { + const double sign = i % 2 == 0 ? 1.0 : -1.0; + gravity_gradient_dofs(i) = sign * 0.04 * static_cast(i + 1); + } + + mfem::Vector density_direction(density_dofs_count); + mfem::Vector gravity_gradient_direction(gravity_gradient_dofs_count); + mfem::Vector velocity_direction(velocity_size); + mfem::Vector displacement_direction(displacement_size); + + for (int i = 0; i < density_dofs_count; ++i) { + density_direction(i) = 0.13 - 0.02 * static_cast(i); + } + + for (int i = 0; i < gravity_gradient_dofs_count; ++i) { + const double sign = i % 3 == 0 ? -1.0 : 1.0; + gravity_gradient_direction(i) = + sign * (0.03 + 0.005 * static_cast(i)); + } + + for (int i = 0; i < velocity_size; ++i) { + velocity_direction(i) = 0.01 * static_cast(i + 1); + } + + for (int i = 0; i < displacement_size; ++i) { + displacement_direction(i) = -0.008 * static_cast(i + 1); + } + + mfem::Array elements(block_count); + elements[velocity_block] = velocity_element; + elements[density_block] = density_element; + elements[gravity_gradient_block] = gravity_gradient_element; + elements[gravity_potential_block] = gravity_potential_element; + elements[displacement_block] = displacement_element; + + mfem::Array element_state(block_count); + element_state[velocity_block] = &velocity_dofs; + element_state[density_block] = &density_dofs; + element_state[gravity_gradient_block] = &gravity_gradient_dofs; + element_state[gravity_potential_block] = &gravity_potential_dofs; + element_state[displacement_block] = &displacement_dofs; + + mfem::Vector velocity_residual(velocity_size); + mfem::Vector density_residual(density_dofs_count); + mfem::Vector gravity_gradient_residual(gravity_gradient_dofs_count); + mfem::Vector gravity_potential_residual(gravity_potential_dofs_count); + mfem::Vector displacement_residual(displacement_size); + + mfem::Array element_residual(block_count); + element_residual[velocity_block] = &velocity_residual; + element_residual[density_block] = &density_residual; + element_residual[gravity_gradient_block] = &gravity_gradient_residual; + element_residual[gravity_potential_block] = &gravity_potential_residual; + element_residual[displacement_block] = &displacement_residual; + + integrators::GravityMomentumIntegrator integrator( + domain_mapper, integrators::GravityForceJacobianMode::field_coupled + ); + + const int maximum_order = std::max( + velocity_element->GetOrder(), + std::max( + density_element->GetOrder(), gravity_gradient_element->GetOrder() + ) + ); + const mfem::IntegrationRule &integration_rule = mfem::IntRules.Get( + velocity_element->GetGeomType(), 2 * maximum_order + 8 + ); + integrator.SetIntegrationRule(integration_rule); + + mfem::DenseMatrix dv_dv(velocity_size, velocity_size); + mfem::DenseMatrix dv_drho(velocity_size, density_dofs_count); + mfem::DenseMatrix dv_dgrad_phi(velocity_size, gravity_gradient_dofs_count); + mfem::DenseMatrix dv_ddisplacement(velocity_size, displacement_size); + dv_dv = 1.0; + dv_drho = 1.0; + dv_dgrad_phi = 1.0; + dv_ddisplacement = 1.0; + + mfem::Array2D element_matrices( + block_count, block_count + ); + + for (int row = 0; row < block_count; ++row) { + for (int column = 0; column < block_count; ++column) { + element_matrices(row, column) = nullptr; + } + } + + element_matrices(velocity_block, velocity_block) = &dv_dv; + element_matrices(velocity_block, density_block) = &dv_drho; + element_matrices(velocity_block, gravity_gradient_block) = &dv_dgrad_phi; + element_matrices(velocity_block, displacement_block) = &dv_ddisplacement; + + integrator.AssembleElementGrad( + elements, *transformation, element_state, element_matrices + ); + + auto assemble_velocity_residual = + [&](const mfem::Vector &density_state, + const mfem::Vector &gravity_gradient_state) { + element_state[density_block] = &density_state; + element_state[gravity_gradient_block] = &gravity_gradient_state; + integrator.AssembleElementVector( + elements, *transformation, element_state, element_residual + ); + return mfem::Vector(velocity_residual); + }; + + auto relative_error = [](mfem::Vector computed, + const mfem::Vector &reference) { + computed -= reference; + return computed.Norml2() / std::max(reference.Norml2(), 1.0e-30); + }; + + mfem::Vector density_plus(density_dofs); + mfem::Vector density_minus(density_dofs); + density_plus.Add(finite_difference_step, density_direction); + density_minus.Add(-finite_difference_step, density_direction); + + mfem::Vector density_residual_plus = + assemble_velocity_residual(density_plus, gravity_gradient_dofs); + mfem::Vector density_residual_minus = + assemble_velocity_residual(density_minus, gravity_gradient_dofs); + mfem::Vector density_finite_difference(density_residual_plus); + density_finite_difference -= density_residual_minus; + density_finite_difference *= 0.5 / finite_difference_step; + + mfem::Vector density_jacobian_action(velocity_size); + dv_drho.Mult(density_direction, density_jacobian_action); + + mfem::Vector gravity_gradient_plus(gravity_gradient_dofs); + mfem::Vector gravity_gradient_minus(gravity_gradient_dofs); + gravity_gradient_plus.Add( + finite_difference_step, gravity_gradient_direction + ); + gravity_gradient_minus.Add( + -finite_difference_step, gravity_gradient_direction + ); + + mfem::Vector gravity_residual_plus = + assemble_velocity_residual(density_dofs, gravity_gradient_plus); + mfem::Vector gravity_residual_minus = + assemble_velocity_residual(density_dofs, gravity_gradient_minus); + mfem::Vector gravity_finite_difference(gravity_residual_plus); + gravity_finite_difference -= gravity_residual_minus; + gravity_finite_difference *= 0.5 / finite_difference_step; + + mfem::Vector gravity_jacobian_action(velocity_size); + dv_dgrad_phi.Mult(gravity_gradient_direction, gravity_jacobian_action); + + mfem::Vector combined_density_plus(density_dofs); + mfem::Vector combined_density_minus(density_dofs); + mfem::Vector combined_gravity_plus(gravity_gradient_dofs); + mfem::Vector combined_gravity_minus(gravity_gradient_dofs); + combined_density_plus.Add(finite_difference_step, density_direction); + combined_density_minus.Add(-finite_difference_step, density_direction); + combined_gravity_plus.Add( + finite_difference_step, gravity_gradient_direction + ); + combined_gravity_minus.Add( + -finite_difference_step, gravity_gradient_direction + ); + + mfem::Vector combined_residual_plus = assemble_velocity_residual( + combined_density_plus, combined_gravity_plus + ); + mfem::Vector combined_residual_minus = assemble_velocity_residual( + combined_density_minus, combined_gravity_minus + ); + mfem::Vector combined_finite_difference(combined_residual_plus); + combined_finite_difference -= combined_residual_minus; + combined_finite_difference *= 0.5 / finite_difference_step; + + mfem::Vector combined_jacobian_action(density_jacobian_action); + combined_jacobian_action += gravity_jacobian_action; + + mfem::Vector inactive_velocity_action(velocity_size); + mfem::Vector inactive_displacement_action(velocity_size); + dv_dv.Mult(velocity_direction, inactive_velocity_action); + dv_ddisplacement.Mult(displacement_direction, inactive_displacement_action); + + const double density_relative_error = + relative_error(density_finite_difference, density_jacobian_action); + const double gravity_relative_error = + relative_error(gravity_finite_difference, gravity_jacobian_action); + const double combined_relative_error = + relative_error(combined_finite_difference, combined_jacobian_action); + + INFO("Density Jacobian relative error = " << density_relative_error); + INFO( + "Gravity-gradient Jacobian relative error = " << gravity_relative_error + ); + INFO("Combined Jacobian relative error = " << combined_relative_error); + + CHECK_THAT( + density_relative_error, + Catch::Matchers::WithinAbs(0.0, jacobian_tolerance) + ); + CHECK_THAT( + gravity_relative_error, + Catch::Matchers::WithinAbs(0.0, jacobian_tolerance) + ); + CHECK_THAT( + combined_relative_error, + Catch::Matchers::WithinAbs(0.0, jacobian_tolerance) + ); + CHECK_THAT( + inactive_velocity_action.Norml2(), + Catch::Matchers::WithinAbs(0.0, zero_tolerance) + ); + CHECK_THAT( + inactive_displacement_action.Norml2(), + Catch::Matchers::WithinAbs(0.0, zero_tolerance) + ); + + mfem::Vector field_coupled_density_action(density_jacobian_action); + + integrator.SetJacobianMode(integrators::GravityForceJacobianMode::minimal); + dv_dv = 1.0; + dv_drho = 1.0; + dv_dgrad_phi = 1.0; + dv_ddisplacement = 1.0; + element_state[density_block] = &density_dofs; + element_state[gravity_gradient_block] = &gravity_gradient_dofs; + integrator.AssembleElementGrad( + elements, *transformation, element_state, element_matrices + ); + + mfem::Vector minimal_density_action(velocity_size); + mfem::Vector minimal_gravity_action(velocity_size); + dv_drho.Mult(density_direction, minimal_density_action); + dv_dgrad_phi.Mult(gravity_gradient_direction, minimal_gravity_action); + + const double minimal_density_difference = + relative_error(minimal_density_action, field_coupled_density_action); + + INFO( + "Minimal-mode density-block difference = " << minimal_density_difference + ); + + CHECK_THAT( + minimal_density_difference, + Catch::Matchers::WithinAbs(0.0, zero_tolerance) + ); + CHECK_THAT( + minimal_gravity_action.Norml2(), + Catch::Matchers::WithinAbs(0.0, zero_tolerance) + ); +} + +TEST_CASE( + "Gravity Force Integrator Matches Manufactured Cartesian Load", + tags::unit &tags::solver &tags::integrator &tags::gravity +) { + constexpr int dim = 3; + constexpr double tolerance = 1.0e-12; + + constexpr int velocity_block = + solver::block_index(solver::FieldBlock::velocity); + constexpr int density_block = + solver::block_index(solver::FieldBlock::density); + constexpr int gravity_gradient_block = + solver::block_index(solver::FieldBlock::gravity_gradient); + constexpr int gravity_potential_block = + solver::block_index(solver::FieldBlock::gravity_potential); + constexpr int displacement_block = + solver::block_index(solver::FieldBlock::displacement); + constexpr int block_count = solver::field_block_count; + + mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D( + 1, 1, 1, mfem::Element::HEXAHEDRON, 1.0, 1.0, 1.0 + ); + + mfem::H1_FECollection velocity_fec(1, dim); + mfem::L2_FECollection density_fec(1, dim); + mfem::RT_FECollection gravity_gradient_fec(0, dim); + mfem::H1_FECollection displacement_fec(1, dim); + + mfem::FiniteElementSpace velocity_fes( + &mesh, &velocity_fec, dim, mfem::Ordering::byVDIM + ); + mfem::FiniteElementSpace density_fes(&mesh, &density_fec); + mfem::FiniteElementSpace gravity_gradient_fes(&mesh, &gravity_gradient_fec); + mfem::FiniteElementSpace displacement_fes( + &mesh, &displacement_fec, dim, mfem::Ordering::byVDIM + ); + + mfem::GridFunction displacement(&displacement_fes); + displacement = 0.0; + + mapping::DomainMapper domain_mapper(displacement, 1.0, 2.0); + + REQUIRE(domain_mapper.CalcIsIdentity()); + + auto reference_density = [](const mfem::Vector &x) { return 1.0 + x(0); }; + + auto reference_gravity_gradient = [](const mfem::Vector &x, + mfem::Vector &gradient) { + gradient.SetSize(3); + gradient(0) = 2.0 * x(0); + gradient(1) = 3.0 * x(1); + gradient(2) = 4.0 * x(2); + }; + + mfem::FunctionCoefficient density_coefficient(reference_density); + mfem::VectorFunctionCoefficient gravity_gradient_coefficient( + dim, reference_gravity_gradient + ); + + mfem::GridFunction density(&density_fes); + mfem::GridFunction gravity_gradient(&gravity_gradient_fes); + density.ProjectCoefficient(density_coefficient); + gravity_gradient.ProjectCoefficient(gravity_gradient_coefficient); + + const mfem::FiniteElement *velocity_element = velocity_fes.GetFE(0); + const mfem::FiniteElement *density_element = density_fes.GetFE(0); + const mfem::FiniteElement *gravity_gradient_element = + gravity_gradient_fes.GetFE(0); + const mfem::FiniteElement *displacement_element = displacement_fes.GetFE(0); + mfem::ElementTransformation *transformation = + mesh.GetElementTransformation(0); + + const int velocity_dofs_count = velocity_element->GetDof(); + const int density_dofs_count = density_element->GetDof(); + const int gravity_gradient_dofs_count = gravity_gradient_element->GetDof(); + const int displacement_dofs_count = displacement_element->GetDof(); + const int velocity_size = dim * velocity_dofs_count; + const int displacement_size = dim * displacement_dofs_count; + + mfem::Array density_dof_indices; + mfem::Array gravity_gradient_dof_indices; + mfem::Vector density_dofs; + mfem::Vector gravity_gradient_dofs; + density_fes.GetElementDofs(0, density_dof_indices); + gravity_gradient_fes.GetElementVDofs(0, gravity_gradient_dof_indices); + density.GetSubVector(density_dof_indices, density_dofs); + gravity_gradient.GetSubVector( + gravity_gradient_dof_indices, gravity_gradient_dofs + ); + + REQUIRE(density_dofs.Size() == density_dofs_count); + REQUIRE(gravity_gradient_dofs.Size() == gravity_gradient_dofs_count); + + mfem::Vector velocity_dofs(velocity_size); + mfem::Vector gravity_potential_dofs(density_dofs_count); + mfem::Vector displacement_dofs(displacement_size); + velocity_dofs = 0.0; + gravity_potential_dofs = 0.0; + displacement_dofs = 0.0; + + mfem::Array elements(block_count); + elements[velocity_block] = velocity_element; + elements[density_block] = density_element; + elements[gravity_gradient_block] = gravity_gradient_element; + elements[gravity_potential_block] = density_element; + elements[displacement_block] = displacement_element; + + mfem::Array element_state(block_count); + element_state[velocity_block] = &velocity_dofs; + element_state[density_block] = &density_dofs; + element_state[gravity_gradient_block] = &gravity_gradient_dofs; + element_state[gravity_potential_block] = &gravity_potential_dofs; + element_state[displacement_block] = &displacement_dofs; + + mfem::Vector velocity_residual(velocity_size); + mfem::Vector density_residual(density_dofs_count); + mfem::Vector gravity_gradient_residual(gravity_gradient_dofs_count); + mfem::Vector gravity_potential_residual(density_dofs_count); + mfem::Vector displacement_residual(displacement_size); + + mfem::Array element_residual(block_count); + element_residual[velocity_block] = &velocity_residual; + element_residual[density_block] = &density_residual; + element_residual[gravity_gradient_block] = &gravity_gradient_residual; + element_residual[gravity_potential_block] = &gravity_potential_residual; + element_residual[displacement_block] = &displacement_residual; + + integrators::GravityMomentumIntegrator integrator( + domain_mapper, integrators::GravityForceJacobianMode::field_coupled + ); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(velocity_element->GetGeomType(), 8); + integrator.SetIntegrationRule(integration_rule); + integrator.AssembleElementVector( + elements, *transformation, element_state, element_residual + ); + + mfem::Vector reference_velocity_residual(velocity_residual); + + auto residual_action = [&](const int component, + const int coordinate_weight) { + mfem::Vector test_dofs(velocity_size); + mfem::Vector x_physical(dim); + test_dofs = 0.0; + + const mfem::IntegrationRule &velocity_nodes = + velocity_element->GetNodes(); + + for (int i = 0; i < velocity_dofs_count; ++i) { + const mfem::IntegrationPoint &node = velocity_nodes.IntPoint(i); + transformation->SetIntPoint(&node); + domain_mapper.GetPhysicalPoint(*transformation, node, x_physical); + test_dofs(i + component * velocity_dofs_count) = + coordinate_weight < 0 ? 1.0 : x_physical(coordinate_weight); + } + + return test_dofs * velocity_residual; + }; + + CHECK_THAT( + residual_action(0, -1), Catch::Matchers::WithinAbs(5.0 / 3.0, tolerance) + ); + CHECK_THAT( + residual_action(1, -1), Catch::Matchers::WithinAbs(9.0 / 4.0, tolerance) + ); + CHECK_THAT( + residual_action(2, -1), Catch::Matchers::WithinAbs(3.0, tolerance) + ); + CHECK_THAT( + residual_action(0, 0), Catch::Matchers::WithinAbs(7.0 / 6.0, tolerance) + ); + CHECK_THAT( + residual_action(1, 1), Catch::Matchers::WithinAbs(3.0 / 2.0, tolerance) + ); + CHECK_THAT( + residual_action(2, 2), Catch::Matchers::WithinAbs(2.0, tolerance) + ); + CHECK_THAT( + residual_action(1, 0), Catch::Matchers::WithinAbs(5.0 / 4.0, tolerance) + ); + + CHECK_THAT( + density_residual.Norml2(), Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + gravity_gradient_residual.Norml2(), + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + gravity_potential_residual.Norml2(), + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + displacement_residual.Norml2(), + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + + integrator.SetJacobianMode(integrators::GravityForceJacobianMode::minimal); + integrator.AssembleElementVector( + elements, *transformation, element_state, element_residual + ); + + mfem::Vector minimal_difference(velocity_residual); + minimal_difference -= reference_velocity_residual; + + integrator.SetJacobianMode(integrators::GravityForceJacobianMode::exact); + integrator.AssembleElementVector( + elements, *transformation, element_state, element_residual + ); + + mfem::Vector exact_difference(velocity_residual); + exact_difference -= reference_velocity_residual; + + CHECK_THAT( + minimal_difference.Norml2(), Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + exact_difference.Norml2(), Catch::Matchers::WithinAbs(0.0, tolerance) + ); +} +TEST_CASE( + "Gravity Force Integrator Preserves Gravity Identities", + tags::unit &tags::solver &tags::integrator &tags::gravity +) { + constexpr int dim = 3; + constexpr double density_value = 1.7; + constexpr double gravity_scale = 2.4; + constexpr double density_scale = 0.6; + constexpr double tolerance = 1.0e-12; + + constexpr int velocity_block = + solver::block_index(solver::FieldBlock::velocity); + constexpr int density_block = + solver::block_index(solver::FieldBlock::density); + constexpr int gravity_gradient_block = + solver::block_index(solver::FieldBlock::gravity_gradient); + constexpr int gravity_potential_block = + solver::block_index(solver::FieldBlock::gravity_potential); + constexpr int displacement_block = + solver::block_index(solver::FieldBlock::displacement); + constexpr int block_count = solver::field_block_count; + + mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D( + 1, 1, 1, mfem::Element::HEXAHEDRON, 1.0, 1.0, 1.0 + ); + + mfem::H1_FECollection velocity_fec(1, dim); + mfem::L2_FECollection density_fec(0, dim); + mfem::RT_FECollection gravity_gradient_fec(0, dim); + mfem::H1_FECollection displacement_fec(1, dim); + + mfem::FiniteElementSpace velocity_fes( + &mesh, &velocity_fec, dim, mfem::Ordering::byVDIM + ); + mfem::FiniteElementSpace density_fes(&mesh, &density_fec); + mfem::FiniteElementSpace gravity_gradient_fes(&mesh, &gravity_gradient_fec); + mfem::FiniteElementSpace displacement_fes( + &mesh, &displacement_fec, dim, mfem::Ordering::byVDIM + ); + + mfem::GridFunction displacement(&displacement_fes); + displacement = 0.0; + + mapping::DomainMapper domain_mapper(displacement, 1.0, 2.0); + + REQUIRE(domain_mapper.HasDisplacementField()); + + auto radial_gravity = [](const mfem::Vector &x, mfem::Vector &gravity) { + gravity.SetSize(3); + gravity(0) = x(0) - 0.5; + gravity(1) = x(1) - 0.5; + gravity(2) = x(2) - 0.5; + }; + + mfem::ConstantCoefficient density_coefficient(density_value); + mfem::VectorFunctionCoefficient gravity_coefficient(dim, radial_gravity); + + mfem::GridFunction density(&density_fes); + mfem::GridFunction gravity_gradient(&gravity_gradient_fes); + density.ProjectCoefficient(density_coefficient); + gravity_gradient.ProjectCoefficient(gravity_coefficient); + + const mfem::FiniteElement *velocity_element = velocity_fes.GetFE(0); + const mfem::FiniteElement *density_element = density_fes.GetFE(0); + const mfem::FiniteElement *gravity_gradient_element = + gravity_gradient_fes.GetFE(0); + const mfem::FiniteElement *displacement_element = displacement_fes.GetFE(0); + mfem::ElementTransformation *transformation = + mesh.GetElementTransformation(0); + + const int velocity_dofs_count = velocity_element->GetDof(); + const int density_dofs_count = density_element->GetDof(); + const int gravity_gradient_dofs_count = gravity_gradient_element->GetDof(); + const int displacement_dofs_count = displacement_element->GetDof(); + const int velocity_size = dim * velocity_dofs_count; + const int displacement_size = dim * displacement_dofs_count; + + mfem::Array density_dof_indices; + mfem::Array gravity_gradient_dof_indices; + mfem::Vector density_dofs; + mfem::Vector gravity_gradient_dofs; + density_fes.GetElementDofs(0, density_dof_indices); + gravity_gradient_fes.GetElementVDofs(0, gravity_gradient_dof_indices); + density.GetSubVector(density_dof_indices, density_dofs); + gravity_gradient.GetSubVector( + gravity_gradient_dof_indices, gravity_gradient_dofs + ); + + mfem::Vector zero_density(density_dofs_count); + mfem::Vector zero_gravity(gravity_gradient_dofs_count); + mfem::Vector velocity_dofs(velocity_size); + mfem::Vector gravity_potential_dofs(density_dofs_count); + mfem::Vector displacement_dofs(displacement_size); + zero_density = 0.0; + zero_gravity = 0.0; + velocity_dofs = 0.0; + gravity_potential_dofs = 0.0; + displacement_dofs = 0.0; + + mfem::Array elements(block_count); + elements[velocity_block] = velocity_element; + elements[density_block] = density_element; + elements[gravity_gradient_block] = gravity_gradient_element; + elements[gravity_potential_block] = density_element; + elements[displacement_block] = displacement_element; + + mfem::Array element_state(block_count); + element_state[velocity_block] = &velocity_dofs; + element_state[density_block] = &density_dofs; + element_state[gravity_gradient_block] = &gravity_gradient_dofs; + element_state[gravity_potential_block] = &gravity_potential_dofs; + element_state[displacement_block] = &displacement_dofs; + + mfem::Vector velocity_residual(velocity_size); + mfem::Vector density_residual(density_dofs_count); + mfem::Vector gravity_gradient_residual(gravity_gradient_dofs_count); + mfem::Vector gravity_potential_residual(density_dofs_count); + mfem::Vector displacement_residual(displacement_size); + + mfem::Array element_residual(block_count); + element_residual[velocity_block] = &velocity_residual; + element_residual[density_block] = &density_residual; + element_residual[gravity_gradient_block] = &gravity_gradient_residual; + element_residual[gravity_potential_block] = &gravity_potential_residual; + element_residual[displacement_block] = &displacement_residual; + + integrators::GravityMomentumIntegrator integrator( + domain_mapper, integrators::GravityForceJacobianMode::field_coupled + ); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(velocity_element->GetGeomType(), 8); + integrator.SetIntegrationRule(integration_rule); + + auto assemble_velocity_residual = [&](const mfem::Vector &density_state, + const mfem::Vector &gravity_state) { + element_state[density_block] = &density_state; + element_state[gravity_gradient_block] = &gravity_state; + integrator.AssembleElementVector( + elements, *transformation, element_state, element_residual + ); + return mfem::Vector(velocity_residual); + }; + + auto scaled_difference_norm = [](mfem::Vector computed, + const mfem::Vector &reference, + const double scale) { + computed.Add(-scale, reference); + return computed.Norml2(); + }; + + const mfem::Vector base_residual = + assemble_velocity_residual(density_dofs, gravity_gradient_dofs); + + REQUIRE(base_residual.Norml2() > tolerance); + + const mfem::Vector zero_field_residual = + assemble_velocity_residual(density_dofs, zero_gravity); + + mfem::Vector reversed_gravity(gravity_gradient_dofs); + reversed_gravity *= -1.0; + const mfem::Vector reversed_residual = + assemble_velocity_residual(density_dofs, reversed_gravity); + + mfem::Vector scaled_gravity(gravity_gradient_dofs); + scaled_gravity *= gravity_scale; + const mfem::Vector gravity_scaled_residual = + assemble_velocity_residual(density_dofs, scaled_gravity); + + mfem::Vector scaled_density(density_dofs); + scaled_density *= density_scale; + const mfem::Vector density_scaled_residual = + assemble_velocity_residual(scaled_density, gravity_gradient_dofs); + const mfem::Vector jointly_scaled_residual = + assemble_velocity_residual(scaled_density, scaled_gravity); + + CHECK_THAT( + zero_field_residual.Norml2(), Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + scaled_difference_norm(reversed_residual, base_residual, -1.0), + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + scaled_difference_norm( + gravity_scaled_residual, base_residual, gravity_scale + ), + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + scaled_difference_norm( + density_scaled_residual, base_residual, density_scale + ), + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + scaled_difference_norm( + jointly_scaled_residual, base_residual, + density_scale * gravity_scale + ), + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + + auto make_test_dofs = [&](auto &&test_function) { + mfem::Vector test_dofs(velocity_size); + mfem::Vector x_physical(dim); + mfem::Vector centered_position(dim); + mfem::Vector test_value(dim); + test_dofs = 0.0; + + const mfem::IntegrationRule &velocity_nodes = + velocity_element->GetNodes(); + + for (int i = 0; i < velocity_dofs_count; ++i) { + const mfem::IntegrationPoint &node = velocity_nodes.IntPoint(i); + transformation->SetIntPoint(&node); + domain_mapper.GetPhysicalPoint(*transformation, node, x_physical); + + for (int component = 0; component < dim; ++component) { + centered_position(component) = x_physical(component) - 0.5; + } + + test_function(centered_position, test_value); + + for (int component = 0; component < dim; ++component) { + test_dofs(i + component * velocity_dofs_count) = + test_value(component); + } + } + + return test_dofs; + }; + + const mfem::Vector force_x_test = + make_test_dofs([](const mfem::Vector &, mfem::Vector &value) { + value.SetSize(3); + value = 0.0; + value(0) = 1.0; + }); + + const mfem::Vector force_y_test = + make_test_dofs([](const mfem::Vector &, mfem::Vector &value) { + value.SetSize(3); + value = 0.0; + value(1) = 1.0; + }); + + const mfem::Vector force_z_test = + make_test_dofs([](const mfem::Vector &, mfem::Vector &value) { + value.SetSize(3); + value = 0.0; + value(2) = 1.0; + }); + + const mfem::Vector torque_x_test = + make_test_dofs([](const mfem::Vector &position, mfem::Vector &value) { + value.SetSize(3); + value(0) = 0.0; + value(1) = -position(2); + value(2) = position(1); + }); + + const mfem::Vector torque_y_test = + make_test_dofs([](const mfem::Vector &position, mfem::Vector &value) { + value.SetSize(3); + value(0) = position(2); + value(1) = 0.0; + value(2) = -position(0); + }); + + const mfem::Vector torque_z_test = + make_test_dofs([](const mfem::Vector &position, mfem::Vector &value) { + value.SetSize(3); + value(0) = -position(1); + value(1) = position(0); + value(2) = 0.0; + }); + + CHECK_THAT( + force_x_test * base_residual, Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + force_y_test * base_residual, Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + force_z_test * base_residual, Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + torque_x_test * base_residual, + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + torque_y_test * base_residual, + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + torque_z_test * base_residual, + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + + mfem::DenseMatrix dv_drho(velocity_size, density_dofs_count); + mfem::DenseMatrix dv_dgrad_phi(velocity_size, gravity_gradient_dofs_count); + + mfem::Array2D element_matrices( + block_count, block_count + ); + + for (int row = 0; row < block_count; ++row) { + for (int column = 0; column < block_count; ++column) { + element_matrices(row, column) = nullptr; + } + } + + element_matrices(velocity_block, density_block) = &dv_drho; + element_matrices(velocity_block, gravity_gradient_block) = &dv_dgrad_phi; + + element_state[density_block] = &density_dofs; + element_state[gravity_gradient_block] = &zero_gravity; + integrator.AssembleElementGrad( + elements, *transformation, element_state, element_matrices + ); + + mfem::Vector zero_gravity_density_action(velocity_size); + mfem::Vector zero_gravity_field_action(velocity_size); + dv_drho.Mult(density_dofs, zero_gravity_density_action); + dv_dgrad_phi.Mult(gravity_gradient_dofs, zero_gravity_field_action); + + CHECK_THAT( + zero_gravity_density_action.Norml2(), + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + scaled_difference_norm(zero_gravity_field_action, base_residual, 1.0), + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + + element_state[density_block] = &zero_density; + element_state[gravity_gradient_block] = &gravity_gradient_dofs; + integrator.AssembleElementGrad( + elements, *transformation, element_state, element_matrices + ); + + mfem::Vector zero_density_density_action(velocity_size); + mfem::Vector zero_density_field_action(velocity_size); + dv_drho.Mult(density_dofs, zero_density_density_action); + dv_dgrad_phi.Mult(gravity_gradient_dofs, zero_density_field_action); + + CHECK_THAT( + scaled_difference_norm(zero_density_density_action, base_residual, 1.0), + Catch::Matchers::WithinAbs(0.0, tolerance) + ); + CHECK_THAT( + zero_density_field_action.Norml2(), + Catch::Matchers::WithinAbs(0.0, tolerance) + ); +} \ No newline at end of file diff --git a/tests/mapping/compactification/kelvin.cpp b/tests/mapping/compactification/kelvin.cpp new file mode 100644 index 0000000..997c502 --- /dev/null +++ b/tests/mapping/compactification/kelvin.cpp @@ -0,0 +1,922 @@ +#include +#include +#include +#include +#include +#include +#include + +import mean_field; +import test_helpers; + +using namespace mean_field; +using Catch::Matchers::WithinAbs; + +namespace { + constexpr int dimension = 3; + + mfem::Vector make_vector( + const double x, + const double y, + const double z + ) { + mfem::Vector vector(dimension); + vector(0) = x; + vector(1) = y; + vector(2) = z; + return vector; + } + + mfem::DenseMatrix make_identity() { + mfem::DenseMatrix matrix(dimension); + matrix = 0.0; + for (int i = 0; i < dimension; ++i) + matrix(i, i) = 1.0; + return matrix; + } + + void check_vector( + const mfem::Vector &actual, + const mfem::Vector &expected, + const double tolerance + ) { + REQUIRE(actual.Size() == expected.Size()); + for (int i = 0; i < actual.Size(); ++i) + CHECK_THAT(actual(i), WithinAbs(expected(i), tolerance)); + } + + void check_matrix( + const mfem::DenseMatrix &actual, + const mfem::DenseMatrix &expected, + const double tolerance + ) { + REQUIRE(actual.Height() == expected.Height()); + REQUIRE(actual.Width() == expected.Width()); + + for (int i = 0; i < actual.Height(); ++i) { + for (int j = 0; j < actual.Width(); ++j) + CHECK_THAT(actual(i, j), WithinAbs(expected(i, j), tolerance)); + } + } + + struct AnalyticFactors { + double computational_radius; + double scale; + double scale_derivative; + }; + + AnalyticFactors compute_analytic_factors( + const double r_star, + const double r_inf, + const double coordinate + ) { + const double radial_extent = r_inf - r_star; + const double computational_radius = r_star + coordinate * radial_extent; + const double scale = + r_star / (computational_radius * (1.0 - coordinate)); + const double scale_derivative = + scale * + (1.0 / (1.0 - coordinate) - radial_extent / computational_radius); + return { + .computational_radius = computational_radius, + .scale = scale, + .scale_derivative = scale_derivative + }; + } + + mapping::MappingStatus evaluate_affine_map( + const mapping::compactification::ExteriorDomainMap &exterior_map, + const mfem::Vector &reference_position, + const mfem::DenseMatrix &affine_jacobian, + const mfem::Vector &offset, + const double compactification_coordinate, + const mfem::Vector &compactification_coordinate_gradient, + mapping::compactification::ExteriorMapResult &result + ) { + mfem::Vector displaced_position(dimension); + affine_jacobian.Mult(reference_position, displaced_position); + displaced_position += offset; + + const mapping::compactification::ExteriorMapInput input{ + .reference_position = reference_position, + .displaced_position = displaced_position, + .displacement_jacobian = affine_jacobian, + .compactification_coordinate = compactification_coordinate, + .compactification_coordinate_gradient = + compactification_coordinate_gradient + }; + + return exterior_map.Evaluate(input, result); + } +} // namespace + +TEST_CASE( + "Kelvin Compactification Validates Its Configuration", + tags::unit &tags::mapping &tags::kelvin +) { + CHECK_NOTHROW( + mapping::compactification::KelvinCompactification( + {.r_star_ref = 1.0, .r_inf_ref = 4.0} + ) + ); + CHECK_THROWS_AS( + mapping::compactification::KelvinCompactification( + {.r_star_ref = 0.0, .r_inf_ref = 4.0} + ), + std::invalid_argument + ); + CHECK_THROWS_AS( + mapping::compactification::KelvinCompactification( + {.r_star_ref = -1.0, .r_inf_ref = 4.0} + ), + std::invalid_argument + ); + CHECK_THROWS_AS( + mapping::compactification::KelvinCompactification( + {.r_star_ref = 2.0, .r_inf_ref = 2.0} + ), + std::invalid_argument + ); + CHECK_THROWS_AS( + mapping::compactification::KelvinCompactification( + {.r_star_ref = 3.0, .r_inf_ref = 2.0} + ), + std::invalid_argument + ); + CHECK_THROWS_AS( + mapping::compactification::KelvinCompactification( + {.r_star_ref = 1.0, + .r_inf_ref = std::numeric_limits::infinity()} + ), + std::invalid_argument + ); + CHECK_THROWS_AS( + mapping::compactification::KelvinCompactification( + {.r_star_ref = 1.0, + .r_inf_ref = 4.0, + .coordinate_tolerance = -1.0e-12} + ), + std::invalid_argument + ); + CHECK_THROWS_AS( + mapping::compactification::KelvinCompactification( + {.r_star_ref = 1.0, .r_inf_ref = 4.0, .coordinate_tolerance = 1.0} + ), + std::invalid_argument + ); + CHECK_THROWS_AS( + mapping::compactification::KelvinCompactification( + {.r_star_ref = 1.0, + .r_inf_ref = 4.0, + .coordinate_tolerance = std::numeric_limits::quiet_NaN()} + ), + std::invalid_argument + ); +} + +TEST_CASE( + "Kelvin Compactification Reports Its Configuration", + tags::unit &tags::mapping &tags::kelvin +) { + constexpr double coordinate_tolerance = 3.0e-11; + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = 1.25, + .r_inf_ref = 5.5, + .coordinate_tolerance = coordinate_tolerance} + ); + + CHECK(compactification.GetName() == "KelvinCompactification"); + CHECK_THAT( + compactification.GetReferenceStellarRadius(), WithinAbs(1.25, 0.0) + ); + CHECK_THAT( + compactification.GetReferenceInfinityRadius(), WithinAbs(5.5, 0.0) + ); + CHECK_THAT( + compactification.GetCoordinateTolerance(), + WithinAbs(coordinate_tolerance, 0.0) + ); +} + +TEST_CASE( + "Kelvin Compactification Uses The Exterior Coordinate Rather Than " + "Euclidean Radius", + tags::unit &tags::mapping &tags::kelvin +) { + constexpr double tolerance = 0.0; + constexpr double coordinate = 0.37; + + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = 1.0, .r_inf_ref = 4.0} + ); + const mfem::DenseMatrix displacement_jacobian = make_identity(); + const mfem::Vector displaced_position = make_vector(1.4, -0.2, 0.3); + const mfem::Vector coordinate_gradient = make_vector(0.2, -0.1, 0.05); + const mfem::Vector reference_a = make_vector(0.2, 0.1, -0.1); + const mfem::Vector reference_b = make_vector(12.0, -7.0, 4.0); + + const mapping::compactification::ExteriorMapInput input_a{ + reference_a, displaced_position, displacement_jacobian, coordinate, + coordinate_gradient + }; + const mapping::compactification::ExteriorMapInput input_b{ + reference_b, displaced_position, displacement_jacobian, coordinate, + coordinate_gradient + }; + + mapping::compactification::ExteriorMapResult result_a; + mapping::compactification::ExteriorMapResult result_b; + + REQUIRE( + compactification.Evaluate(input_a, result_a) == + mapping::MappingStatus::valid + ); + REQUIRE( + compactification.Evaluate(input_b, result_b) == + mapping::MappingStatus::valid + ); + + check_vector( + result_a.physical_position, result_b.physical_position, tolerance + ); + check_matrix( + result_a.mapping_jacobian, result_b.mapping_jacobian, tolerance + ); +} + +TEST_CASE( + "Kelvin Compactification Matches Its Analytic Radial Map", + tags::unit &tags::mapping &tags::kelvin +) { + constexpr double r_star = 1.0; + constexpr double r_inf = 4.0; + constexpr double radial_extent = r_inf - r_star; + constexpr double tolerance = 2.0e-12; + + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = r_star, .r_inf_ref = r_inf} + ); + const mfem::DenseMatrix identity = make_identity(); + const mfem::Vector coordinate_gradient = + make_vector(1.0 / radial_extent, 0.0, 0.0); + + for (const double computational_radius : + std::array{1.0, 1.25, 2.0, 3.0, 3.75}) { + CAPTURE(computational_radius); + + const double coordinate = + (computational_radius - r_star) / radial_extent; + const mfem::Vector reference_position = + make_vector(computational_radius, 0.0, 0.0); + const mfem::Vector displaced_position(reference_position); + const mapping::compactification::ExteriorMapInput input{ + reference_position, displaced_position, identity, coordinate, + coordinate_gradient + }; + mapping::compactification::ExteriorMapResult result; + + REQUIRE( + compactification.Evaluate(input, result) == + mapping::MappingStatus::valid + ); + + const double expected_radius = + r_star * radial_extent / (r_inf - computational_radius); + const double expected_radial_derivative = + r_star * radial_extent / + std::pow(r_inf - computational_radius, 2.0); + const double expected_tangential_scale = + expected_radius / computational_radius; + + const mfem::Vector expected_position = + make_vector(expected_radius, 0.0, 0.0); + mfem::DenseMatrix expected_jacobian(dimension); + expected_jacobian = 0.0; + expected_jacobian(0, 0) = expected_radial_derivative; + expected_jacobian(1, 1) = expected_tangential_scale; + expected_jacobian(2, 2) = expected_tangential_scale; + + check_vector(result.physical_position, expected_position, tolerance); + check_matrix(result.mapping_jacobian, expected_jacobian, tolerance); + CHECK(result.mapping_jacobian.Det() > 0.0); + } +} + +TEST_CASE( + "Kelvin Compactification Matches Its Full Cartesian Formula", + tags::unit &tags::mapping &tags::kelvin +) { + constexpr double r_star = 1.0; + constexpr double r_inf = 4.0; + constexpr double coordinate = 0.42; + constexpr double tolerance = 1.0e-12; + + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = r_star, .r_inf_ref = r_inf} + ); + const mfem::Vector reference_position = make_vector(0.8, 0.4, -0.2); + const mfem::Vector displaced_position = make_vector(1.1, 0.5, -0.1); + const mfem::Vector coordinate_gradient = make_vector(0.20, -0.10, 0.05); + + mfem::DenseMatrix displacement_jacobian(dimension); + displacement_jacobian(0, 0) = 1.10; + displacement_jacobian(0, 1) = 0.05; + displacement_jacobian(0, 2) = 0.00; + displacement_jacobian(1, 0) = -0.02; + displacement_jacobian(1, 1) = 0.95; + displacement_jacobian(1, 2) = 0.03; + displacement_jacobian(2, 0) = 0.01; + displacement_jacobian(2, 1) = -0.04; + displacement_jacobian(2, 2) = 1.05; + + const mapping::compactification::ExteriorMapInput input{ + reference_position, displaced_position, displacement_jacobian, + coordinate, coordinate_gradient + }; + mapping::compactification::ExteriorMapResult result; + + REQUIRE( + compactification.Evaluate(input, result) == + mapping::MappingStatus::valid + ); + + const AnalyticFactors factors = + compute_analytic_factors(r_star, r_inf, coordinate); + mfem::Vector expected_position(displaced_position); + expected_position *= factors.scale; + + mfem::DenseMatrix expected_jacobian(displacement_jacobian); + expected_jacobian *= factors.scale; + + for (int i = 0; i < dimension; ++i) { + for (int j = 0; j < dimension; ++j) + expected_jacobian(i, j) += displaced_position(i) * + factors.scale_derivative * + coordinate_gradient(j); + } + + check_vector(result.physical_position, expected_position, tolerance); + check_matrix(result.mapping_jacobian, expected_jacobian, tolerance); +} + +TEST_CASE( + "Kelvin Compactification Jacobian Matches Coordinate Finite Differences", + tags::unit &tags::mapping &tags::kelvin +) { + constexpr double base_coordinate = 0.38; + constexpr double difference_step = 1.0e-6; + constexpr double tolerance = 3.0e-9; + + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = 1.0, .r_inf_ref = 4.0} + ); + + mfem::DenseMatrix affine_jacobian(dimension); + affine_jacobian(0, 0) = 1.05; + affine_jacobian(0, 1) = 0.02; + affine_jacobian(0, 2) = 0.00; + affine_jacobian(1, 0) = -0.01; + affine_jacobian(1, 1) = 0.98; + affine_jacobian(1, 2) = 0.03; + affine_jacobian(2, 0) = 0.02; + affine_jacobian(2, 1) = 0.00; + affine_jacobian(2, 2) = 1.02; + + const mfem::Vector offset = make_vector(0.04, -0.03, 0.02); + const mfem::Vector reference_position = make_vector(1.4, 0.3, -0.2); + const mfem::Vector coordinate_gradient = make_vector(0.11, -0.07, 0.05); + + mapping::compactification::ExteriorMapResult base_result; + REQUIRE( + evaluate_affine_map( + compactification, reference_position, affine_jacobian, offset, + base_coordinate, coordinate_gradient, base_result + ) == mapping::MappingStatus::valid + ); + + for (int coordinate = 0; coordinate < dimension; ++coordinate) { + mfem::Vector reference_plus(reference_position); + mfem::Vector reference_minus(reference_position); + reference_plus(coordinate) += difference_step; + reference_minus(coordinate) -= difference_step; + + const double compactification_plus = + base_coordinate + difference_step * coordinate_gradient(coordinate); + const double compactification_minus = + base_coordinate - difference_step * coordinate_gradient(coordinate); + + mapping::compactification::ExteriorMapResult result_plus; + mapping::compactification::ExteriorMapResult result_minus; + + REQUIRE( + evaluate_affine_map( + compactification, reference_plus, affine_jacobian, offset, + compactification_plus, coordinate_gradient, result_plus + ) == mapping::MappingStatus::valid + ); + REQUIRE( + evaluate_affine_map( + compactification, reference_minus, affine_jacobian, offset, + compactification_minus, coordinate_gradient, result_minus + ) == mapping::MappingStatus::valid + ); + + for (int component = 0; component < dimension; ++component) { + const double finite_difference = + (result_plus.physical_position(component) - + result_minus.physical_position(component)) / + (2.0 * difference_step); + CHECK_THAT( + finite_difference, + WithinAbs( + base_result.mapping_jacobian(component, coordinate), + tolerance + ) + ); + } + } +} + +TEST_CASE( + "Kelvin Compactification Variation Matches State Finite Differences", + tags::unit &tags::mapping &tags::kelvin +) { + constexpr double coordinate = 0.46; + constexpr double difference_step = 1.0e-6; + constexpr double tolerance = 2.0e-10; + + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = 1.0, .r_inf_ref = 4.0} + ); + const mfem::Vector reference_position = make_vector(1.3, -0.2, 0.4); + const mfem::Vector displaced_position = make_vector(1.4, -0.1, 0.35); + const mfem::Vector coordinate_gradient = make_vector(0.12, -0.04, 0.08); + const mfem::Vector position_direction = make_vector(0.03, -0.05, 0.02); + + mfem::DenseMatrix displacement_jacobian = make_identity(); + displacement_jacobian(0, 1) = 0.04; + displacement_jacobian(1, 2) = -0.03; + displacement_jacobian(2, 0) = 0.02; + + mfem::DenseMatrix jacobian_direction(dimension); + jacobian_direction(0, 0) = 0.02; + jacobian_direction(0, 1) = -0.01; + jacobian_direction(0, 2) = 0.03; + jacobian_direction(1, 0) = 0.01; + jacobian_direction(1, 1) = -0.02; + jacobian_direction(1, 2) = 0.00; + jacobian_direction(2, 0) = -0.01; + jacobian_direction(2, 1) = 0.02; + jacobian_direction(2, 2) = 0.01; + + const mapping::compactification::ExteriorMapInput input{ + reference_position, displaced_position, displacement_jacobian, + coordinate, coordinate_gradient + }; + const mapping::compactification::ExteriorMapDirection direction{ + position_direction, jacobian_direction + }; + + mapping::compactification::ExteriorMapResult base_result; + mapping::compactification::ExteriorMapVariation variation; + + REQUIRE( + compactification.Evaluate(input, base_result) == + mapping::MappingStatus::valid + ); + REQUIRE( + compactification.EvaluateVariation( + input, base_result, direction, variation + ) == mapping::MappingStatus::valid + ); + + mfem::Vector displaced_plus(displaced_position); + mfem::Vector displaced_minus(displaced_position); + displaced_plus.Add(difference_step, position_direction); + displaced_minus.Add(-difference_step, position_direction); + + mfem::DenseMatrix jacobian_plus(displacement_jacobian); + mfem::DenseMatrix jacobian_minus(displacement_jacobian); + jacobian_plus.Add(difference_step, jacobian_direction); + jacobian_minus.Add(-difference_step, jacobian_direction); + + const mapping::compactification::ExteriorMapInput input_plus{ + reference_position, displaced_plus, jacobian_plus, coordinate, + coordinate_gradient + }; + const mapping::compactification::ExteriorMapInput input_minus{ + reference_position, displaced_minus, jacobian_minus, coordinate, + coordinate_gradient + }; + + mapping::compactification::ExteriorMapResult result_plus; + mapping::compactification::ExteriorMapResult result_minus; + + REQUIRE( + compactification.Evaluate(input_plus, result_plus) == + mapping::MappingStatus::valid + ); + REQUIRE( + compactification.Evaluate(input_minus, result_minus) == + mapping::MappingStatus::valid + ); + + for (int i = 0; i < dimension; ++i) { + const double position_finite_difference = + (result_plus.physical_position(i) - + result_minus.physical_position(i)) / + (2.0 * difference_step); + CHECK_THAT( + position_finite_difference, + WithinAbs(variation.physical_position_variation(i), tolerance) + ); + + for (int j = 0; j < dimension; ++j) { + const double jacobian_finite_difference = + (result_plus.mapping_jacobian(i, j) - + result_minus.mapping_jacobian(i, j)) / + (2.0 * difference_step); + CHECK_THAT( + jacobian_finite_difference, + WithinAbs(variation.mapping_jacobian_variation(i, j), tolerance) + ); + } + } +} + +TEST_CASE( + "Kelvin Compactification Preserves Rotational Covariance", + tags::unit &tags::mapping &tags::kelvin +) { + constexpr double coordinate = 0.31; + constexpr double tolerance = 1.0e-12; + + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = 1.0, .r_inf_ref = 4.0} + ); + const mfem::Vector reference_position = make_vector(1.3, 0.4, -0.2); + const mfem::Vector displaced_position = make_vector(1.4, 0.2, -0.1); + const mfem::Vector coordinate_gradient = make_vector(0.16, -0.08, 0.03); + + mfem::DenseMatrix displacement_jacobian = make_identity(); + displacement_jacobian(0, 1) = 0.05; + displacement_jacobian(1, 0) = -0.02; + displacement_jacobian(2, 1) = 0.03; + + const mapping::compactification::ExteriorMapInput input{ + reference_position, displaced_position, displacement_jacobian, + coordinate, coordinate_gradient + }; + mapping::compactification::ExteriorMapResult result; + REQUIRE( + compactification.Evaluate(input, result) == + mapping::MappingStatus::valid + ); + + mfem::DenseMatrix rotation(dimension); + rotation = 0.0; + rotation(0, 1) = -1.0; + rotation(1, 0) = 1.0; + rotation(2, 2) = 1.0; + + mfem::Vector rotated_reference(dimension); + mfem::Vector rotated_displaced(dimension); + mfem::Vector rotated_coordinate_gradient(dimension); + rotation.Mult(reference_position, rotated_reference); + rotation.Mult(displaced_position, rotated_displaced); + rotation.Mult(coordinate_gradient, rotated_coordinate_gradient); + + mfem::DenseMatrix temporary(dimension); + mfem::DenseMatrix rotated_displacement_jacobian(dimension); + mfem::Mult(rotation, displacement_jacobian, temporary); + mfem::MultABt(temporary, rotation, rotated_displacement_jacobian); + + const mapping::compactification::ExteriorMapInput rotated_input{ + rotated_reference, rotated_displaced, rotated_displacement_jacobian, + coordinate, rotated_coordinate_gradient + }; + mapping::compactification::ExteriorMapResult rotated_result; + REQUIRE( + compactification.Evaluate(rotated_input, rotated_result) == + mapping::MappingStatus::valid + ); + + mfem::Vector expected_position(dimension); + rotation.Mult(result.physical_position, expected_position); + + mfem::DenseMatrix expected_jacobian(dimension); + mfem::Mult(rotation, result.mapping_jacobian, temporary); + mfem::MultABt(temporary, rotation, expected_jacobian); + + check_vector( + rotated_result.physical_position, expected_position, tolerance + ); + check_matrix(rotated_result.mapping_jacobian, expected_jacobian, tolerance); +} + +TEST_CASE( + "Kelvin Compactification Is Continuous At The Mesh Defined Stellar Surface", + tags::unit &tags::mapping &tags::kelvin +) { + constexpr double tolerance = 1.0e-14; + + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = 1.0, .r_inf_ref = 4.0} + ); + const mfem::Vector reference_position = make_vector( + -0.5260553366425769, 0.5260553366425769, -0.6553163792879153 + ); + const mfem::Vector displaced_position = make_vector(-0.55, 0.51, -0.63); + const mfem::Vector coordinate_gradient = make_vector(-0.18, 0.18, -0.22); + const mfem::DenseMatrix displacement_jacobian = make_identity(); + + REQUIRE(reference_position.Norml2() < 1.0); + + const mapping::compactification::ExteriorMapInput input{ + reference_position, displaced_position, displacement_jacobian, 0.0, + coordinate_gradient + }; + mapping::compactification::ExteriorMapResult result; + + REQUIRE( + compactification.Evaluate(input, result) == + mapping::MappingStatus::valid + ); + check_vector(result.physical_position, displaced_position, tolerance); + CHECK(result.mapping_jacobian.Det() > 0.0); +} + +TEST_CASE( + "Kelvin Compactification Has Correct Infinity And Coordinate Bound " + "Behavior", + tags::unit &tags::mapping &tags::kelvin +) { + constexpr double r_star = 1.0; + constexpr double r_inf = 4.0; + constexpr double radial_extent = r_inf - r_star; + constexpr double coordinate_tolerance = 1.0e-12; + constexpr double tolerance = 2.0e-11; + + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = r_star, + .r_inf_ref = r_inf, + .coordinate_tolerance = coordinate_tolerance} + ); + const mfem::DenseMatrix identity = make_identity(); + const mfem::Vector coordinate_gradient = + make_vector(1.0 / radial_extent, 0.0, 0.0); + + for (const double coordinate : + std::array{0.0, 0.25, 0.75, 0.95, 0.99, 0.999}) { + CAPTURE(coordinate); + + const double computational_radius = r_star + coordinate * radial_extent; + const mfem::Vector reference_position = + make_vector(computational_radius, 0.0, 0.0); + const mapping::compactification::ExteriorMapInput input{ + reference_position, reference_position, identity, coordinate, + coordinate_gradient + }; + mapping::compactification::ExteriorMapResult result; + + REQUIRE( + compactification.Evaluate(input, result) == + mapping::MappingStatus::valid + ); + CHECK_THAT( + result.physical_position.Norml2() * (1.0 - coordinate), + WithinAbs(r_star, tolerance) + ); + } + + const mfem::Vector reference_position = make_vector(r_inf, 0.0, 0.0); + mapping::compactification::ExteriorMapResult result; + + CHECK( + compactification.Evaluate( + {reference_position, reference_position, identity, 1.0, + coordinate_gradient}, + result + ) == mapping::MappingStatus::at_compactified_infinity + ); + CHECK( + compactification.Evaluate( + {reference_position, reference_position, identity, + 1.0 - 0.5 * coordinate_tolerance, coordinate_gradient}, + result + ) == mapping::MappingStatus::at_compactified_infinity + ); + CHECK( + compactification.Evaluate( + {reference_position, reference_position, identity, + 1.0 + 0.5 * coordinate_tolerance, coordinate_gradient}, + result + ) == mapping::MappingStatus::at_compactified_infinity + ); + CHECK( + compactification.Evaluate( + {reference_position, reference_position, identity, + 1.0 + 2.0 * coordinate_tolerance, coordinate_gradient}, + result + ) == mapping::MappingStatus::outside_reference_domain + ); + CHECK( + compactification.Evaluate( + {reference_position, reference_position, identity, + -2.0 * coordinate_tolerance, coordinate_gradient}, + result + ) == mapping::MappingStatus::outside_reference_domain + ); + + const mfem::Vector surface_position = make_vector(0.97, 0.0, 0.0); + CHECK( + compactification.Evaluate( + {surface_position, surface_position, identity, + -0.5 * coordinate_tolerance, coordinate_gradient}, + result + ) == mapping::MappingStatus::valid + ); + check_vector(result.physical_position, surface_position, tolerance); +} + +TEST_CASE( + "Kelvin Compactification Rejects Invalid Inputs And Inverted Maps", + tags::unit &tags::mapping &tags::kelvin +) { + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = 1.0, .r_inf_ref = 4.0} + ); + + const mfem::Vector reference_position = make_vector(2.0, 0.0, 0.0); + const mfem::Vector displaced_position(reference_position); + const mfem::Vector coordinate_gradient = make_vector(1.0 / 3.0, 0.0, 0.0); + const mfem::Vector zero_gradient = make_vector(0.0, 0.0, 0.0); + const mfem::DenseMatrix identity = make_identity(); + mapping::compactification::ExteriorMapResult result; + + mfem::Vector wrong_dimension(2); + wrong_dimension = 1.0; + CHECK( + compactification.Evaluate( + {wrong_dimension, displaced_position, identity, 1.0 / 3.0, + coordinate_gradient}, + result + ) == mapping::MappingStatus::invalid_dimension + ); + CHECK( + compactification.Evaluate( + {reference_position, displaced_position, identity, 1.0 / 3.0, + wrong_dimension}, + result + ) == mapping::MappingStatus::invalid_dimension + ); + + mfem::Vector non_finite_position(reference_position); + non_finite_position(1) = std::numeric_limits::quiet_NaN(); + CHECK( + compactification.Evaluate( + {non_finite_position, displaced_position, identity, 1.0 / 3.0, + coordinate_gradient}, + result + ) == mapping::MappingStatus::non_finite_input + ); + + mfem::Vector non_finite_gradient(coordinate_gradient); + non_finite_gradient(2) = std::numeric_limits::infinity(); + CHECK( + compactification.Evaluate( + {reference_position, displaced_position, identity, 1.0 / 3.0, + non_finite_gradient}, + result + ) == mapping::MappingStatus::non_finite_input + ); + CHECK( + compactification.Evaluate( + {reference_position, displaced_position, identity, + std::numeric_limits::quiet_NaN(), coordinate_gradient}, + result + ) == mapping::MappingStatus::non_finite_input + ); + + mfem::DenseMatrix singular_displacement_jacobian(dimension); + singular_displacement_jacobian = 0.0; + CHECK( + compactification.Evaluate( + {reference_position, displaced_position, + singular_displacement_jacobian, 1.0 / 3.0, zero_gradient}, + result + ) == mapping::MappingStatus::non_positive_determinant + ); + + mfem::DenseMatrix inverted_displacement_jacobian = make_identity(); + inverted_displacement_jacobian(0, 0) = -1.0; + CHECK( + compactification.Evaluate( + {reference_position, displaced_position, + inverted_displacement_jacobian, 1.0 / 3.0, zero_gradient}, + result + ) == mapping::MappingStatus::non_positive_determinant + ); +} + +TEST_CASE( + "Kelvin Compactification Variation Rejects Invalid Inputs", + tags::unit &tags::mapping &tags::kelvin +) { + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = 1.0, .r_inf_ref = 4.0} + ); + const mfem::Vector reference_position = make_vector(2.0, 0.0, 0.0); + const mfem::Vector displaced_position(reference_position); + const mfem::Vector coordinate_gradient = make_vector(1.0 / 3.0, 0.0, 0.0); + const mfem::DenseMatrix identity = make_identity(); + const mapping::compactification::ExteriorMapInput input{ + reference_position, displaced_position, identity, 1.0 / 3.0, + coordinate_gradient + }; + + mapping::compactification::ExteriorMapResult result; + REQUIRE( + compactification.Evaluate(input, result) == + mapping::MappingStatus::valid + ); + + const mfem::Vector valid_position_direction = + make_vector(0.01, -0.02, 0.03); + const mfem::DenseMatrix valid_jacobian_direction = make_identity(); + mapping::compactification::ExteriorMapVariation variation; + + mfem::Vector wrong_dimension(2); + wrong_dimension = 0.0; + CHECK( + compactification.EvaluateVariation( + input, result, {wrong_dimension, valid_jacobian_direction}, + variation + ) == mapping::MappingStatus::invalid_dimension + ); + + mfem::DenseMatrix wrong_jacobian_dimension(2); + wrong_jacobian_dimension = 0.0; + CHECK( + compactification.EvaluateVariation( + input, result, {valid_position_direction, wrong_jacobian_dimension}, + variation + ) == mapping::MappingStatus::invalid_dimension + ); + + mfem::Vector non_finite_direction(valid_position_direction); + non_finite_direction(0) = std::numeric_limits::quiet_NaN(); + CHECK( + compactification.EvaluateVariation( + input, result, {non_finite_direction, valid_jacobian_direction}, + variation + ) == mapping::MappingStatus::non_finite_input + ); +} + +TEST_CASE( + "Kelvin Compactification Evaluations Are Independent", + tags::unit &tags::mapping &tags::kelvin +) { + constexpr double tolerance = 0.0; + + mapping::compactification::KelvinCompactification compactification( + {.r_star_ref = 1.0, .r_inf_ref = 4.0} + ); + const mfem::DenseMatrix identity = make_identity(); + const mfem::Vector gradient_a = make_vector(0.12, 0.03, -0.02); + const mfem::Vector gradient_b = make_vector(-0.04, 0.15, 0.01); + const mfem::Vector reference_a = make_vector(1.5, 0.2, 0.1); + const mfem::Vector reference_b = make_vector(2.5, -0.3, 0.4); + + const mapping::compactification::ExteriorMapInput input_a{ + reference_a, reference_a, identity, 0.25, gradient_a + }; + const mapping::compactification::ExteriorMapInput input_b{ + reference_b, reference_b, identity, 0.70, gradient_b + }; + + mapping::compactification::ExteriorMapResult first_a; + mapping::compactification::ExteriorMapResult result_b; + mapping::compactification::ExteriorMapResult second_a; + + REQUIRE( + compactification.Evaluate(input_a, first_a) == + mapping::MappingStatus::valid + ); + REQUIRE( + compactification.Evaluate(input_b, result_b) == + mapping::MappingStatus::valid + ); + REQUIRE( + compactification.Evaluate(input_a, second_a) == + mapping::MappingStatus::valid + ); + + check_vector( + first_a.physical_position, second_a.physical_position, tolerance + ); + check_matrix( + first_a.mapping_jacobian, second_a.mapping_jacobian, tolerance + ); +} \ No newline at end of file diff --git a/tests/mapping/domain_mapper.cpp b/tests/mapping/domain_mapper.cpp new file mode 100644 index 0000000..91d7857 --- /dev/null +++ b/tests/mapping/domain_mapper.cpp @@ -0,0 +1,3486 @@ +#include +#include +#include +#include +#include +#include +#include +#include + +import mean_field; +import test_helpers; +using namespace mean_field; +using Catch::Matchers::WithinAbs; + +namespace { + constexpr int dimension = 3; + constexpr double tolerance = 1.0e-12; + + std::unique_ptr + make_kelvin_compactification() { + return std::make_unique< + mapping::compactification::KelvinCompactification>( + mapping::compactification::options::KelvinCompactificationOptions{ + .r_star_ref = 1.0, .r_inf_ref = 4.0 + } + ); + } + + mfem::DenseMatrix make_identity_matrix(const int size) { + mfem::DenseMatrix matrix(size); + matrix = 0.0; + for (int i = 0; i < size; ++i) + matrix(i, i) = 1.0; + return matrix; + } + + mfem::Vector make_constant_compactification_dofs( + const mfem::FiniteElement &element, + const double value = 0.0 + ) { + mfem::Vector dofs(element.GetDof()); + dofs = value; + return dofs; + } + + template + mfem::Vector make_compactification_element_dofs( + const mfem::FiniteElement &element, + mfem::ElementTransformation &transformation, + Function &&function + ) { + const mfem::IntegrationRule &nodes = element.GetNodes(); + REQUIRE(nodes.GetNPoints() == element.GetDof()); + + mfem::Vector dofs(element.GetDof()); + mfem::Vector reference_position(dimension); + + for (int i = 0; i < element.GetDof(); ++i) { + transformation.Transform(nodes.IntPoint(i), reference_position); + dofs(i) = function(reference_position); + } + + return dofs; + } + + class ElementMappingDataOwner { + public: + explicit ElementMappingDataOwner( + const mapping::ElementDisplacementData &displacement + ) + : m_compactification( + displacement.GetElement(), + make_constant_compactification_dofs(displacement.GetElement()) + ), + m_element_data{ + .displacement = displacement, + .compactification = m_compactification + } { + } + + ElementMappingDataOwner( + const mapping::ElementDisplacementData &displacement, + const mfem::FiniteElement &compactification_element, + const mfem::Vector &compactification_dofs + ) + : m_compactification( + compactification_element, + compactification_dofs + ), + m_element_data{ + .displacement = displacement, + .compactification = m_compactification + } { + } + + ElementMappingDataOwner(const ElementMappingDataOwner &) = delete; + ElementMappingDataOwner & + operator=(const ElementMappingDataOwner &) = delete; + ElementMappingDataOwner(ElementMappingDataOwner &&) = delete; + ElementMappingDataOwner &operator=(ElementMappingDataOwner &&) = delete; + + [[nodiscard]] const mapping::ElementMappingData &Get() const noexcept { + return m_element_data; + } + + private: + mapping::ElementCompactificationData m_compactification; + mapping::ElementMappingData m_element_data; + }; + + void check_vector( + const mfem::Vector &actual, + const mfem::Vector &expected, + const double comparison_tolerance = tolerance + ) { + REQUIRE(actual.Size() == expected.Size()); + for (int i = 0; i < actual.Size(); ++i) + CHECK_THAT(actual(i), WithinAbs(expected(i), comparison_tolerance)); + } + + void check_matrix( + const mfem::DenseMatrix &actual, + const mfem::DenseMatrix &expected, + const double comparison_tolerance = tolerance + ) { + REQUIRE(actual.Height() == expected.Height()); + REQUIRE(actual.Width() == expected.Width()); + + for (int i = 0; i < actual.Height(); ++i) { + for (int j = 0; j < actual.Width(); ++j) + CHECK_THAT( + actual(i, j), + WithinAbs(expected(i, j), comparison_tolerance) + ); + } + } + + struct SingleElementFixture { + mfem::Mesh mesh; + mfem::H1_FECollection displacement_collection; + mfem::FiniteElementSpace displacement_space; + + SingleElementFixture() + : mesh( + mfem::Mesh::MakeCartesian3D( + 1, + 1, + 1, + mfem::Element::HEXAHEDRON, + 2.0, + 3.0, + 4.0 + ) + ), + displacement_collection( + 1, + dimension + ), + displacement_space( + &mesh, + &displacement_collection, + dimension, + mfem::Ordering::byVDIM + ) { + } + + [[nodiscard]] const mfem::FiniteElement &GetElement() const { + return *displacement_space.GetFE(0); + } + + [[nodiscard]] mfem::Vector MakeZeroElementDofs() const { + mfem::Vector element_dofs(GetElement().GetDof() * dimension); + element_dofs = 0.0; + return element_dofs; + } + }; + + mfem::Vector make_vector( + const double x, + const double y, + const double z + ) { + mfem::Vector vector(3); + vector(0) = x; + vector(1) = y; + vector(2) = z; + return vector; + } + + mfem::DenseMatrix make_affine_displacement_gradient() { + mfem::DenseMatrix gradient(3); + gradient(0, 0) = 0.10; + gradient(0, 1) = 0.04; + gradient(0, 2) = -0.02; + gradient(1, 0) = -0.03; + gradient(1, 1) = 0.08; + gradient(1, 2) = 0.01; + gradient(2, 0) = 0.02; + gradient(2, 1) = -0.01; + gradient(2, 2) = -0.05; + return gradient; + } + + mfem::Vector make_affine_element_dofs( + const mfem::FiniteElement &element, + mfem::ElementTransformation &transformation, + const mfem::DenseMatrix &displacement_gradient, + const mfem::Vector &displacement_offset, + const mfem::Ordering::Type ordering + ) { + const int dof_count = element.GetDof(); + const int field_dimension = displacement_offset.Size(); + const mfem::IntegrationRule &nodes = element.GetNodes(); + + REQUIRE(nodes.GetNPoints() == dof_count); + + mfem::Vector element_dofs(dof_count * field_dimension); + mfem::Vector reference_position(field_dimension); + mfem::Vector displacement(field_dimension); + + for (int i = 0; i < dof_count; ++i) { + transformation.Transform(nodes.IntPoint(i), reference_position); + displacement_gradient.Mult(reference_position, displacement); + displacement += displacement_offset; + + for (int component = 0; component < field_dimension; ++component) { + const int index = ordering == mfem::Ordering::byNODES + ? i + component * dof_count + : component + i * field_dimension; + element_dofs(index) = displacement(component); + } + } + + return element_dofs; + } + + mfem::DenseMatrix + make_deformation_jacobian(const mfem::DenseMatrix &displacement_gradient) { + mfem::DenseMatrix deformation_jacobian = + make_identity_matrix(displacement_gradient.Height()); + deformation_jacobian.Add(1.0, displacement_gradient); + return deformation_jacobian; + } + + mfem::Vector evaluate_affine_physical_position( + const mfem::Vector &reference_position, + const mfem::DenseMatrix &displacement_gradient, + const mfem::Vector &displacement_offset + ) { + mfem::Vector physical_position(reference_position); + mfem::Vector displacement(reference_position.Size()); + displacement_gradient.Mult(reference_position, displacement); + physical_position += displacement; + physical_position += displacement_offset; + return physical_position; + } + + void check_point_context( + const mapping::MappingPointContext &actual, + const mapping::MappingPointContext &expected, + const double comparison_tolerance = tolerance + ) { + CHECK(actual.compactified == expected.compactified); + check_vector( + actual.reference_position, expected.reference_position, + comparison_tolerance + ); + check_vector( + actual.displaced_position, expected.displaced_position, + comparison_tolerance + ); + check_vector( + actual.physical_position, expected.physical_position, + comparison_tolerance + ); + check_matrix( + actual.displacement_jacobian, expected.displacement_jacobian, + comparison_tolerance + ); + check_matrix( + actual.mapping_jacobian, expected.mapping_jacobian, + comparison_tolerance + ); + check_matrix( + actual.inverse_mapping_jacobian, expected.inverse_mapping_jacobian, + comparison_tolerance + ); + CHECK_THAT( + actual.mapping_determinant, + WithinAbs(expected.mapping_determinant, comparison_tolerance) + ); + } + + constexpr double polynomial_tolerance = 2.0e-11; + constexpr double difference_step = 2.0e-6; + + struct QuadraticElementFixture { + mfem::Mesh mesh; + mfem::H1_FECollection displacement_collection; + mfem::FiniteElementSpace displacement_space; + + QuadraticElementFixture() + : mesh( + mfem::Mesh::MakeCartesian3D( + 1, + 1, + 1, + mfem::Element::HEXAHEDRON, + 2.0, + 3.0, + 4.0 + ) + ), + displacement_collection( + 2, + dimension + ), + displacement_space( + &mesh, + &displacement_collection, + dimension, + mfem::Ordering::byVDIM + ) { + } + + [[nodiscard]] const mfem::FiniteElement &GetElement() const { + return *displacement_space.GetFE(0); + } + }; + + template + mfem::Vector make_function_element_dofs( + const mfem::FiniteElement &element, + mfem::ElementTransformation &transformation, + Function &&function, + const mfem::Ordering::Type ordering + ) { + const int dof_count = element.GetDof(); + const mfem::IntegrationRule &nodes = element.GetNodes(); + + REQUIRE(nodes.GetNPoints() == dof_count); + + mfem::Vector element_dofs(dof_count * dimension); + mfem::Vector reference_position(dimension); + mfem::Vector value(dimension); + + for (int i = 0; i < dof_count; ++i) { + transformation.Transform(nodes.IntPoint(i), reference_position); + function(reference_position, value); + + for (int component = 0; component < dimension; ++component) { + const int index = ordering == mfem::Ordering::byNODES + ? i + component * dof_count + : component + i * dimension; + element_dofs(index) = value(component); + } + } + + return element_dofs; + } + + void evaluate_quadratic_displacement( + const mfem::Vector &position, + mfem::Vector &displacement + ) { + const double x = position(0); + const double y = position(1); + const double z = position(2); + + displacement.SetSize(dimension); + displacement(0) = 0.01 + 0.010 * x * x + 0.005 * y * z; + displacement(1) = -0.02 - 0.004 * x * y + 0.006 * z * z; + displacement(2) = 0.015 + 0.003 * x * z - 0.002 * y * y; + } + + mfem::DenseMatrix + evaluate_quadratic_displacement_gradient(const mfem::Vector &position) { + const double x = position(0); + const double y = position(1); + const double z = position(2); + + mfem::DenseMatrix gradient(dimension); + gradient(0, 0) = 0.020 * x; + gradient(0, 1) = 0.005 * z; + gradient(0, 2) = 0.005 * y; + gradient(1, 0) = -0.004 * y; + gradient(1, 1) = -0.004 * x; + gradient(1, 2) = 0.012 * z; + gradient(2, 0) = 0.003 * z; + gradient(2, 1) = -0.004 * y; + gradient(2, 2) = 0.003 * x; + return gradient; + } + + void evaluate_quadratic_direction( + const mfem::Vector &position, + mfem::Vector &direction + ) { + const double x = position(0); + const double y = position(1); + const double z = position(2); + + direction.SetSize(dimension); + direction(0) = 0.020 * x - 0.010 * y * z; + direction(1) = -0.015 * y + 0.005 * x * z; + direction(2) = 0.010 * z + 0.004 * x * y; + } + + mfem::DenseMatrix + evaluate_quadratic_direction_gradient(const mfem::Vector &position) { + const double x = position(0); + const double y = position(1); + const double z = position(2); + + mfem::DenseMatrix gradient(dimension); + gradient(0, 0) = 0.020; + gradient(0, 1) = -0.010 * z; + gradient(0, 2) = -0.010 * y; + gradient(1, 0) = 0.005 * z; + gradient(1, 1) = -0.015; + gradient(1, 2) = 0.005 * x; + gradient(2, 0) = 0.004 * y; + gradient(2, 1) = 0.004 * x; + gradient(2, 2) = 0.010; + return gradient; + } + + void check_vector_central_difference( + const mfem::Vector &plus, + const mfem::Vector &minus, + const mfem::Vector &expected, + const double step, + const double comparison_tolerance + ) { + REQUIRE(plus.Size() == minus.Size()); + REQUIRE(plus.Size() == expected.Size()); + + for (int i = 0; i < expected.Size(); ++i) { + const double finite_difference = + (plus(i) - minus(i)) / (2.0 * step); + CHECK_THAT( + finite_difference, WithinAbs(expected(i), comparison_tolerance) + ); + } + } + + void check_matrix_central_difference( + const mfem::DenseMatrix &plus, + const mfem::DenseMatrix &minus, + const mfem::DenseMatrix &expected, + const double step, + const double comparison_tolerance + ) { + REQUIRE(plus.Height() == minus.Height()); + REQUIRE(plus.Width() == minus.Width()); + REQUIRE(plus.Height() == expected.Height()); + REQUIRE(plus.Width() == expected.Width()); + + for (int i = 0; i < expected.Height(); ++i) { + for (int j = 0; j < expected.Width(); ++j) { + const double finite_difference = + (plus(i, j) - minus(i, j)) / (2.0 * step); + CHECK_THAT( + finite_difference, + WithinAbs(expected(i, j), comparison_tolerance) + ); + } + } + } + + struct QuadraticMappingData { + mfem::Vector base_dofs; + mfem::Vector direction_dofs; + mfem::Vector plus_dofs; + mfem::Vector minus_dofs; + + QuadraticMappingData( + const mfem::FiniteElement &element, + mfem::ElementTransformation &transformation + ) { + base_dofs = make_function_element_dofs( + element, transformation, evaluate_quadratic_displacement, + mfem::Ordering::byVDIM + ); + direction_dofs = make_function_element_dofs( + element, transformation, evaluate_quadratic_direction, + mfem::Ordering::byVDIM + ); + plus_dofs = base_dofs; + minus_dofs = base_dofs; + plus_dofs.Add(difference_step, direction_dofs); + minus_dofs.Add(-difference_step, direction_dofs); + } + }; + + void check_scalar_relative( + const double actual, + const double expected, + const double relative_tolerance, + const double absolute_tolerance = 1.0e-11 + ) { + CHECK_THAT( + actual, WithinAbs( + expected, absolute_tolerance + + relative_tolerance * std::abs(expected) + ) + ); + } + + void check_vector_central_difference_relative( + const mfem::Vector &plus, + const mfem::Vector &minus, + const mfem::Vector &expected, + const double step, + const double relative_tolerance + ) { + REQUIRE(plus.Size() == minus.Size()); + REQUIRE(plus.Size() == expected.Size()); + + for (int i = 0; i < expected.Size(); ++i) { + const double finite_difference = + (plus(i) - minus(i)) / (2.0 * step); + check_scalar_relative( + finite_difference, expected(i), relative_tolerance + ); + } + } + + void check_matrix_central_difference_relative( + const mfem::DenseMatrix &plus, + const mfem::DenseMatrix &minus, + const mfem::DenseMatrix &expected, + const double step, + const double relative_tolerance + ) { + REQUIRE(plus.Height() == minus.Height()); + REQUIRE(plus.Width() == minus.Width()); + REQUIRE(plus.Height() == expected.Height()); + REQUIRE(plus.Width() == expected.Width()); + + for (int i = 0; i < expected.Height(); ++i) { + for (int j = 0; j < expected.Width(); ++j) { + const double finite_difference = + (plus(i, j) - minus(i, j)) / (2.0 * step); + check_scalar_relative( + finite_difference, expected(i, j), relative_tolerance + ); + } + } + } + + mfem::Vector evaluate_reference_hdiv_field(const mfem::Vector &position) { + const double x = position(0); + const double y = position(1); + const double z = position(2); + return make_vector(x * x + 0.1 * y, y * y - 0.2 * z, z * z + 0.3 * x); + } + + double evaluate_reference_hdiv_divergence(const mfem::Vector &position) { + return 2.0 * (position(0) + position(1) + position(2)); + } + + mfem::Vector matrix_curl(const mfem::DenseMatrix &gradient) { + return make_vector( + gradient(2, 1) - gradient(1, 2), gradient(0, 2) - gradient(2, 0), + gradient(1, 0) - gradient(0, 1) + ); + } + + void check_centered_difference( + const double analytic, + const double finite_difference, + const double plus_value, + const double minus_value, + const double step, + const double relative_tolerance = 2.0e-6, + const double absolute_tolerance = 1.0e-11 + ) { + const double derivative_scale = + std::max(std::abs(analytic), std::abs(finite_difference)); + const double primal_scale = + std::max(std::abs(plus_value), std::abs(minus_value)); + const double roundoff_tolerance = + 8.0 * std::numeric_limits::epsilon() * primal_scale / step; + const double tolerance = absolute_tolerance + + relative_tolerance * derivative_scale + + roundoff_tolerance; + + CHECK_THAT( + finite_difference, Catch::Matchers::WithinAbs(analytic, tolerance) + ); + } + + double relative_vector_difference( + const mfem::Vector &lhs, + const mfem::Vector &rhs + ) { + mfem::Vector difference(lhs); + difference -= rhs; + + const double scale = std::max({lhs.Norml2(), rhs.Norml2(), 1.0e-12}); + return difference.Norml2() / scale; + } + + double relative_matrix_difference( + const mfem::DenseMatrix &lhs, + const mfem::DenseMatrix &rhs + ) { + mfem::DenseMatrix difference(lhs); + difference -= rhs; + + const double scale = std::max({lhs.FNorm(), rhs.FNorm(), 1.0e-12}); + return difference.FNorm() / scale; + } +} // namespace + +TEST_CASE( + "Element Displacement Data Preserves MFEM Ordering", + tags::unit &tags::mapping +) { + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + const int dof_count = element.GetDof(); + + mfem::Vector by_vdim_dofs(dof_count * dimension); + mfem::Vector by_nodes_dofs(dof_count * dimension); + + for (int i = 0; i < dof_count; ++i) { + for (int component = 0; component < dimension; ++component) { + const double value = 100.0 * component + i + 1.0; + by_vdim_dofs(component + i * dimension) = value; + by_nodes_dofs(i + component * dof_count) = value; + } + } + + const mapping::ElementDisplacementData by_vdim_data( + element, by_vdim_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData by_nodes_data( + element, by_nodes_dofs, mfem::Ordering::byNODES + ); + + REQUIRE(&by_vdim_data.GetElement() == &element); + REQUIRE(&by_nodes_data.GetElement() == &element); + REQUIRE(by_vdim_data.GetDimension() == dimension); + REQUIRE(by_nodes_data.GetDimension() == dimension); + REQUIRE(by_vdim_data.GetDofCount() == dof_count); + REQUIRE(by_nodes_data.GetDofCount() == dof_count); + REQUIRE(by_vdim_data.GetOrdering() == mfem::Ordering::byVDIM); + REQUIRE(by_nodes_data.GetOrdering() == mfem::Ordering::byNODES); + + check_matrix( + by_vdim_data.GetDofMatrix(), by_nodes_data.GetDofMatrix(), 0.0 + ); + + for (int i = 0; i < dof_count; ++i) { + for (int component = 0; component < dimension; ++component) { + CHECK_THAT( + by_vdim_data.GetDofMatrix()(i, component), + WithinAbs(100.0 * component + i + 1.0, 0.0) + ); + } + } +} + +TEST_CASE( + "Element Displacement Data Rejects Invalid Vector Sizes", + tags::unit &tags::mapping +) { + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + const int dof_count = element.GetDof(); + + mfem::Vector empty_dofs; + mfem::Vector incomplete_dofs(dof_count * dimension - 1); + incomplete_dofs = 0.0; + + CHECK_THROWS_AS( + mapping::ElementDisplacementData( + element, empty_dofs, mfem::Ordering::byVDIM + ), + std::invalid_argument + ); + CHECK_THROWS_AS( + mapping::ElementDisplacementData( + element, incomplete_dofs, mfem::Ordering::byVDIM + ), + std::invalid_argument + ); +} + +TEST_CASE( + "Domain Mapping Workspace Tracks Its Dimension", + tags::unit &tags::mapping +) { + mapping::DomainMapperStateless::Workspace workspace(dimension); + + REQUIRE(workspace.GetDimension() == dimension); + + workspace.SetDimension(2); + REQUIRE(workspace.GetDimension() == 2); + + workspace.SetDimension(dimension); + REQUIRE(workspace.GetDimension() == dimension); + + CHECK_THROWS_AS(workspace.SetDimension(0), std::invalid_argument); + CHECK_THROWS_AS(workspace.SetDimension(-1), std::invalid_argument); + CHECK_THROWS_AS( + mapping::DomainMapperStateless::Workspace(0), std::invalid_argument + ); +} + +TEST_CASE( + "Stateless Domain Mapper Validates Its Configuration", + tags::unit &tags::mapping +) { + const utils::DomainMapperStatelessOptions valid_options{ + .dimension = dimension, .vacuum_element_attribute = 3 + }; + mapping::DomainMapperStateless mapper( + valid_options, make_kelvin_compactification() + ); + + REQUIRE(mapper.GetDimension() == dimension); + REQUIRE(mapper.GetVacuumElementAttribute() == 3); + REQUIRE(mapper.GetExteriorMap().GetName() == "KelvinCompactification"); + + const utils::DomainMapperStatelessOptions invalid_dimension{ + .dimension = 0, .vacuum_element_attribute = 3 + }; + const utils::DomainMapperStatelessOptions invalid_attribute{ + .dimension = dimension, .vacuum_element_attribute = 0 + }; + + CHECK_THROWS_AS( + mapping::DomainMapperStateless( + invalid_dimension, make_kelvin_compactification() + ), + std::invalid_argument + ); + CHECK_THROWS_AS( + mapping::DomainMapperStateless( + invalid_attribute, make_kelvin_compactification() + ), + std::invalid_argument + ); + + std::unique_ptr + null_exterior_map; + CHECK_THROWS_AS( + mapping::DomainMapperStateless( + valid_options, std::move(null_exterior_map) + ), + std::invalid_argument + ); +} + +TEST_CASE( + "Stateless Domain Mapper Preserves Identity Point Geometry", + tags::unit &tags::mapping +) { + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + const mfem::Vector zero_dofs = fixture.MakeZeroElementDofs(); + const mapping::ElementDisplacementData displacement( + element, zero_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner element_data(displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + mapping::MappingPointContext context; + + mfem::ElementTransformation *transformation = + fixture.mesh.GetElementTransformation(0); + REQUIRE_FALSE(mapper.IsCompactifiedElement(*transformation)); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 4); + const mfem::DenseMatrix identity = make_identity_matrix(dimension); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + mfem::Vector expected_position(dimension); + transformation->Transform(integration_point, expected_position); + + REQUIRE( + mapper.EvaluatePoint( + element_data.Get(), *transformation, integration_point, + workspace, context + ) == mapping::MappingStatus::valid + ); + + CAPTURE(q); + REQUIRE_FALSE(context.compactified); + check_vector(context.reference_position, expected_position); + check_vector(context.displaced_position, expected_position); + check_vector(context.physical_position, expected_position); + check_matrix(context.displacement_jacobian, identity); + check_matrix(context.mapping_jacobian, identity); + check_matrix(context.inverse_mapping_jacobian, identity); + CHECK_THAT(context.mapping_determinant, WithinAbs(1.0, tolerance)); + } +} + +TEST_CASE( + "Stateless Domain Mapper Preserves Identity Volume Geometry", + tags::unit &tags::mapping +) { + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + const mfem::Vector zero_dofs = fixture.MakeZeroElementDofs(); + const mapping::ElementDisplacementData displacement( + element, zero_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner element_data(displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + mapping::VolumeMappingContext context; + + mfem::ElementTransformation *transformation = + fixture.mesh.GetElementTransformation(0); + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 4); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + + REQUIRE( + mapper.EvaluateVolume( + element_data.Get(), *transformation, integration_point, + workspace, context + ) == mapping::MappingStatus::valid + ); + + transformation->SetIntPoint(&integration_point); + + mfem::DenseMatrix expected_inverse(dimension); + mfem::CalcInverse(transformation->Jacobian(), expected_inverse); + + const double expected_weight = + integration_point.weight * transformation->Weight(); + + CAPTURE(q); + REQUIRE_FALSE(context.mapping.compactified); + check_matrix(context.quadrature.J_inv, expected_inverse); + CHECK_THAT(context.quadrature.detJ, WithinAbs(1.0, tolerance)); + CHECK_THAT( + context.quadrature.weight, WithinAbs(expected_weight, tolerance) + ); + CHECK(context.quadrature.weight > 0.0); + } +} + +TEST_CASE( + "Stateless Domain Mapper Preserves Identity Face Geometry", + tags::unit &tags::mapping +) { + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + const mfem::Vector zero_dofs = fixture.MakeZeroElementDofs(); + const mapping::ElementDisplacementData displacement( + element, zero_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner element_data(displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + mapping::FaceMappingContext context; + + for (int boundary_element = 0; boundary_element < fixture.mesh.GetNBE(); + ++boundary_element) { + mfem::FaceElementTransformations *transformation = + fixture.mesh.GetBdrFaceTransformations(boundary_element); + REQUIRE(transformation != nullptr); + REQUIRE(transformation->Elem1 != nullptr); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 4); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + + REQUIRE( + mapper.EvaluateFace( + element_data.Get(), *transformation, + mapping::FaceElementSide::element_1, integration_point, + workspace, context + ) == mapping::MappingStatus::valid + ); + + transformation->SetAllIntPoints(&integration_point); + + mfem::Vector raw_normal(dimension); + mfem::CalcOrtho(transformation->Jacobian(), raw_normal); + + const double raw_normal_magnitude = raw_normal.Norml2(); + mfem::Vector expected_normal(raw_normal); + expected_normal /= raw_normal_magnitude; + + const double expected_surface_weight = + integration_point.weight * raw_normal_magnitude; + + const mfem::IntegrationPoint element_integration_point = + transformation->Elem1->GetIntPoint(); + + mfem::Vector expected_position(dimension); + transformation->Elem1->Transform( + element_integration_point, expected_position + ); + + CAPTURE(boundary_element, q); + REQUIRE_FALSE(context.mapping.compactified); + check_vector(context.mapping.reference_position, expected_position); + check_vector(context.mapping.displaced_position, expected_position); + check_vector(context.mapping.physical_position, expected_position); + check_vector(context.reference_normal, expected_normal); + check_vector(context.quadrature.normal, expected_normal); + CHECK_THAT( + context.reference_surface_weight, + WithinAbs(expected_surface_weight, tolerance) + ); + CHECK_THAT( + context.physical_surface_weight, + WithinAbs(expected_surface_weight, tolerance) + ); + CHECK_THAT( + context.quadrature.ds, + WithinAbs(expected_surface_weight, tolerance) + ); + CHECK_THAT( + context.quadrature.v_dot_n_scale, WithinAbs(1.0, tolerance) + ); + } + } +} + +TEST_CASE( + "Stateless Domain Mapper Matches Exact Affine Point Mapping", + tags::unit &tags::mapping +) { + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *transformation = + fixture.mesh.GetElementTransformation(0); + + const mfem::DenseMatrix displacement_gradient = + make_affine_displacement_gradient(); + const mfem::DenseMatrix deformation_jacobian = + make_deformation_jacobian(displacement_gradient); + const mfem::Vector displacement_offset = make_vector(0.07, -0.04, 0.03); + const mfem::Vector element_dofs = make_affine_element_dofs( + element, *transformation, displacement_gradient, displacement_offset, + mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData displacement( + element, element_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner element_data(displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + mapping::MappingPointContext context; + + mfem::DenseMatrix inverse_deformation_jacobian(dimension); + mfem::CalcInverse(deformation_jacobian, inverse_deformation_jacobian); + const double deformation_determinant = deformation_jacobian.Det(); + + REQUIRE(deformation_determinant > 0.0); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 6); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + mfem::Vector reference_position(dimension); + transformation->Transform(integration_point, reference_position); + + const mfem::Vector expected_position = + evaluate_affine_physical_position( + reference_position, displacement_gradient, displacement_offset + ); + + REQUIRE( + mapper.EvaluatePoint( + element_data.Get(), *transformation, integration_point, + workspace, context + ) == mapping::MappingStatus::valid + ); + + CAPTURE(q); + REQUIRE_FALSE(context.compactified); + check_vector(context.reference_position, reference_position); + check_vector(context.displaced_position, expected_position); + check_vector(context.physical_position, expected_position); + check_matrix(context.displacement_jacobian, deformation_jacobian); + check_matrix(context.mapping_jacobian, deformation_jacobian); + check_matrix( + context.inverse_mapping_jacobian, inverse_deformation_jacobian + ); + CHECK_THAT( + context.mapping_determinant, + WithinAbs(deformation_determinant, tolerance) + ); + } +} + +TEST_CASE( + "Stateless Domain Mapper Produces Equivalent Results For Both MFEM " + "Orderings", + tags::unit &tags::mapping +) { + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *transformation = + fixture.mesh.GetElementTransformation(0); + + const mfem::DenseMatrix displacement_gradient = + make_affine_displacement_gradient(); + const mfem::Vector displacement_offset = make_vector(0.07, -0.04, 0.03); + + const mfem::Vector by_vdim_dofs = make_affine_element_dofs( + element, *transformation, displacement_gradient, displacement_offset, + mfem::Ordering::byVDIM + ); + const mfem::Vector by_nodes_dofs = make_affine_element_dofs( + element, *transformation, displacement_gradient, displacement_offset, + mfem::Ordering::byNODES + ); + + const mapping::ElementDisplacementData by_vdim_displacement( + element, by_vdim_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData by_nodes_displacement( + element, by_nodes_dofs, mfem::Ordering::byNODES + ); + const ElementMappingDataOwner by_vdim_data(by_vdim_displacement); + const ElementMappingDataOwner by_nodes_data(by_nodes_displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + + mapping::VolumeMappingContext by_vdim_context; + mapping::VolumeMappingContext by_nodes_context; + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 6); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + + REQUIRE( + mapper.EvaluateVolume( + by_vdim_data.Get(), *transformation, integration_point, + workspace, by_vdim_context + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateVolume( + by_nodes_data.Get(), *transformation, integration_point, + workspace, by_nodes_context + ) == mapping::MappingStatus::valid + ); + + CAPTURE(q); + check_point_context(by_vdim_context.mapping, by_nodes_context.mapping); + check_matrix( + by_vdim_context.quadrature.J_inv, by_nodes_context.quadrature.J_inv + ); + CHECK_THAT( + by_vdim_context.quadrature.detJ, + WithinAbs(by_nodes_context.quadrature.detJ, tolerance) + ); + CHECK_THAT( + by_vdim_context.quadrature.weight, + WithinAbs(by_nodes_context.quadrature.weight, tolerance) + ); + } +} + +TEST_CASE( + "Stateless Domain Mapper Composes Affine Volume Jacobians", + tags::unit &tags::mapping +) { + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *transformation = + fixture.mesh.GetElementTransformation(0); + + const mfem::DenseMatrix displacement_gradient = + make_affine_displacement_gradient(); + const mfem::DenseMatrix mapping_jacobian = + make_deformation_jacobian(displacement_gradient); + const mfem::Vector displacement_offset = make_vector(0.07, -0.04, 0.03); + const mfem::Vector element_dofs = make_affine_element_dofs( + element, *transformation, displacement_gradient, displacement_offset, + mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData displacement( + element, element_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner element_data(displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + mapping::VolumeMappingContext context; + + const double mapping_determinant = mapping_jacobian.Det(); + REQUIRE(mapping_determinant > 0.0); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 6); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + transformation->SetIntPoint(&integration_point); + + mfem::DenseMatrix full_element_jacobian(dimension); + mfem::DenseMatrix expected_inverse(dimension); + mfem::Mult( + mapping_jacobian, transformation->Jacobian(), full_element_jacobian + ); + mfem::CalcInverse(full_element_jacobian, expected_inverse); + + const double expected_weight = integration_point.weight * + transformation->Weight() * + mapping_determinant; + + REQUIRE( + mapper.EvaluateVolume( + element_data.Get(), *transformation, integration_point, + workspace, context + ) == mapping::MappingStatus::valid + ); + + CAPTURE(q); + check_matrix(context.mapping.mapping_jacobian, mapping_jacobian); + check_matrix(context.quadrature.J_inv, expected_inverse); + CHECK_THAT( + context.quadrature.detJ, WithinAbs(mapping_determinant, tolerance) + ); + CHECK_THAT( + context.quadrature.weight, WithinAbs(expected_weight, tolerance) + ); + } +} + +TEST_CASE( + "Stateless Domain Mapper Applies Nanson Formula On Affine Faces", + tags::unit &tags::mapping +) { + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *element_transformation = + fixture.mesh.GetElementTransformation(0); + + const mfem::DenseMatrix displacement_gradient = + make_affine_displacement_gradient(); + const mfem::DenseMatrix mapping_jacobian = + make_deformation_jacobian(displacement_gradient); + const mfem::Vector displacement_offset = make_vector(0.07, -0.04, 0.03); + const mfem::Vector element_dofs = make_affine_element_dofs( + element, *element_transformation, displacement_gradient, + displacement_offset, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData displacement( + element, element_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner element_data(displacement); + + mfem::DenseMatrix inverse_mapping_jacobian(dimension); + mfem::CalcInverse(mapping_jacobian, inverse_mapping_jacobian); + const double mapping_determinant = mapping_jacobian.Det(); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + mapping::FaceMappingContext context; + + for (int boundary_element = 0; boundary_element < fixture.mesh.GetNBE(); + ++boundary_element) { + mfem::FaceElementTransformations *transformation = + fixture.mesh.GetBdrFaceTransformations(boundary_element); + REQUIRE(transformation != nullptr); + REQUIRE(transformation->Elem1 != nullptr); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 6); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + transformation->SetAllIntPoints(&integration_point); + + mfem::Vector raw_normal(dimension); + mfem::Vector mapped_normal(dimension); + mfem::CalcOrtho(transformation->Jacobian(), raw_normal); + + inverse_mapping_jacobian.MultTranspose(raw_normal, mapped_normal); + mapped_normal *= mapping_determinant; + + const double raw_normal_magnitude = raw_normal.Norml2(); + const double mapped_normal_magnitude = mapped_normal.Norml2(); + + mfem::Vector expected_reference_normal(raw_normal); + mfem::Vector expected_physical_normal(mapped_normal); + expected_reference_normal /= raw_normal_magnitude; + expected_physical_normal /= mapped_normal_magnitude; + + const double expected_reference_weight = + integration_point.weight * raw_normal_magnitude; + const double expected_physical_weight = + integration_point.weight * mapped_normal_magnitude; + const double expected_normal_scale = + mapped_normal_magnitude / raw_normal_magnitude; + + REQUIRE( + mapper.EvaluateFace( + element_data.Get(), *transformation, + mapping::FaceElementSide::element_1, integration_point, + workspace, context + ) == mapping::MappingStatus::valid + ); + + CAPTURE(boundary_element, q); + check_matrix(context.mapping.mapping_jacobian, mapping_jacobian); + check_vector(context.reference_normal, expected_reference_normal); + check_vector(context.quadrature.normal, expected_physical_normal); + CHECK_THAT( + context.reference_surface_weight, + WithinAbs(expected_reference_weight, tolerance) + ); + CHECK_THAT( + context.physical_surface_weight, + WithinAbs(expected_physical_weight, tolerance) + ); + CHECK_THAT( + context.quadrature.ds, + WithinAbs(expected_reference_weight, tolerance) + ); + CHECK_THAT( + context.quadrature.v_dot_n_scale, + WithinAbs(expected_normal_scale, tolerance) + ); + } + } +} + +TEST_CASE( + "Stateless Domain Mapper Has No Cross State Contamination", + tags::unit &tags::mapping +) { + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *transformation = + fixture.mesh.GetElementTransformation(0); + + const mfem::DenseMatrix gradient_a = make_affine_displacement_gradient(); + mfem::DenseMatrix gradient_b(3); + gradient_b = 0.0; + gradient_b(0, 0) = -0.06; + gradient_b(0, 2) = 0.03; + gradient_b(1, 0) = 0.02; + gradient_b(1, 1) = 0.12; + gradient_b(2, 1) = -0.04; + gradient_b(2, 2) = 0.07; + + const mfem::Vector offset_a = make_vector(0.07, -0.04, 0.03); + const mfem::Vector offset_b = make_vector(-0.05, 0.08, -0.02); + + const mfem::Vector dofs_a = make_affine_element_dofs( + element, *transformation, gradient_a, offset_a, mfem::Ordering::byVDIM + ); + const mfem::Vector dofs_b = make_affine_element_dofs( + element, *transformation, gradient_b, offset_b, mfem::Ordering::byVDIM + ); + + const mapping::ElementDisplacementData displacement_a( + element, dofs_a, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData displacement_b( + element, dofs_b, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner element_data_a(displacement_a); + const ElementMappingDataOwner element_data_b(displacement_b); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + + const mfem::IntegrationPoint &integration_point = + mfem::Geometries.GetCenter(transformation->GetGeometryType()); + + mapping::MappingPointContext first_a; + mapping::MappingPointContext result_b; + mapping::MappingPointContext second_a; + + REQUIRE( + mapper.EvaluatePoint( + element_data_a.Get(), *transformation, integration_point, workspace, + first_a + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluatePoint( + element_data_b.Get(), *transformation, integration_point, workspace, + result_b + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluatePoint( + element_data_a.Get(), *transformation, integration_point, workspace, + second_a + ) == mapping::MappingStatus::valid + ); + + check_point_context(first_a, second_a, 0.0); + + mfem::Vector state_difference(result_b.physical_position); + state_difference -= first_a.physical_position; + CHECK(state_difference.Norml2() > 1.0e-3); +} + +TEST_CASE( + "Stateless Domain Mapper Reports Invalid Element States", + tags::unit &tags::mapping +) { + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *transformation = + fixture.mesh.GetElementTransformation(0); + const mfem::IntegrationPoint &integration_point = + mfem::Geometries.GetCenter(transformation->GetGeometryType()); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + mapping::MappingPointContext context; + + mfem::Vector non_finite_dofs = fixture.MakeZeroElementDofs(); + non_finite_dofs(0) = std::numeric_limits::quiet_NaN(); + const mapping::ElementDisplacementData non_finite_displacement( + element, non_finite_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner non_finite_data(non_finite_displacement); + + CHECK( + mapper.EvaluatePoint( + non_finite_data.Get(), *transformation, integration_point, + workspace, context + ) == mapping::MappingStatus::non_finite_input + ); + + mfem::DenseMatrix singular_gradient(dimension); + singular_gradient = 0.0; + for (int i = 0; i < dimension; ++i) + singular_gradient(i, i) = -1.0; + + const mfem::Vector zero_offset(dimension); + const mfem::Vector singular_dofs = make_affine_element_dofs( + element, *transformation, singular_gradient, zero_offset, + mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData singular_displacement( + element, singular_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner singular_data(singular_displacement); + + CHECK( + mapper.EvaluatePoint( + singular_data.Get(), *transformation, integration_point, workspace, + context + ) == mapping::MappingStatus::non_positive_determinant + ); + + mfem::DenseMatrix inverted_gradient(dimension); + inverted_gradient = 0.0; + for (int i = 0; i < dimension; ++i) + inverted_gradient(i, i) = -2.0; + + const mfem::Vector inverted_dofs = make_affine_element_dofs( + element, *transformation, inverted_gradient, zero_offset, + mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData inverted_displacement( + element, inverted_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner inverted_data(inverted_displacement); + + CHECK( + mapper.EvaluatePoint( + inverted_data.Get(), *transformation, integration_point, workspace, + context + ) == mapping::MappingStatus::non_positive_determinant + ); + + mapping::DomainMapperStateless::Workspace wrong_workspace(2); + CHECK_THROWS_AS( + mapper.EvaluatePoint( + singular_data.Get(), *transformation, integration_point, + wrong_workspace, context + ), + std::invalid_argument + ); + + mfem::Vector two_dimensional_dofs(element.GetDof() * 2); + two_dimensional_dofs = 0.0; + const mapping::ElementDisplacementData two_dimensional_displacement( + element, two_dimensional_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner two_dimensional_data( + two_dimensional_displacement + ); + + CHECK_THROWS_AS( + mapper.EvaluatePoint( + two_dimensional_data.Get(), *transformation, integration_point, + workspace, context + ), + std::invalid_argument + ); +} + +TEST_CASE( + "Stateless Domain Mapper Matches Exact Quadratic Point Mapping", + tags::unit &tags::mapping +) { + QuadraticElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *transformation = + fixture.mesh.GetElementTransformation(0); + + const mfem::Vector element_dofs = make_function_element_dofs( + element, *transformation, evaluate_quadratic_displacement, + mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData displacement( + element, element_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner element_data(displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + mapping::MappingPointContext context; + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 6); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + + mfem::Vector reference_position(dimension); + mfem::Vector expected_displacement(dimension); + transformation->Transform(integration_point, reference_position); + evaluate_quadratic_displacement( + reference_position, expected_displacement + ); + + mfem::Vector expected_position(reference_position); + expected_position += expected_displacement; + + const mfem::DenseMatrix displacement_gradient = + evaluate_quadratic_displacement_gradient(reference_position); + mfem::DenseMatrix expected_jacobian = make_identity_matrix(dimension); + expected_jacobian.Add(1.0, displacement_gradient); + + mfem::DenseMatrix expected_inverse(dimension); + mfem::CalcInverse(expected_jacobian, expected_inverse); + const double expected_determinant = expected_jacobian.Det(); + + REQUIRE(expected_determinant > 0.0); + REQUIRE( + mapper.EvaluatePoint( + element_data.Get(), *transformation, integration_point, + workspace, context + ) == mapping::MappingStatus::valid + ); + + CAPTURE(q); + REQUIRE_FALSE(context.compactified); + check_vector( + context.reference_position, reference_position, polynomial_tolerance + ); + check_vector( + context.displaced_position, expected_position, polynomial_tolerance + ); + check_vector( + context.physical_position, expected_position, polynomial_tolerance + ); + check_matrix( + context.displacement_jacobian, expected_jacobian, + polynomial_tolerance + ); + check_matrix( + context.mapping_jacobian, expected_jacobian, polynomial_tolerance + ); + check_matrix( + context.inverse_mapping_jacobian, expected_inverse, + polynomial_tolerance + ); + CHECK_THAT( + context.mapping_determinant, + WithinAbs(expected_determinant, polynomial_tolerance) + ); + } +} + +TEST_CASE( + "Stateless Domain Mapper Point Linearization Matches Centered Differences", + tags::unit &tags::mapping +) { + constexpr double linearization_tolerance = 2.0e-9; + + QuadraticElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *transformation = + fixture.mesh.GetElementTransformation(0); + const QuadraticMappingData mapping_data(element, *transformation); + + const mapping::ElementDisplacementData base_displacement( + element, mapping_data.base_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData direction( + element, mapping_data.direction_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData plus_displacement( + element, mapping_data.plus_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData minus_displacement( + element, mapping_data.minus_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner base_data(base_displacement); + const ElementMappingDataOwner plus_data(plus_displacement); + const ElementMappingDataOwner minus_data(minus_displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 6); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + + mapping::MappingPointContext base_context; + mapping::MappingPointContext plus_context; + mapping::MappingPointContext minus_context; + mapping::MappingPointVariation variation; + + REQUIRE( + mapper.EvaluatePoint( + base_data.Get(), *transformation, integration_point, workspace, + base_context + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluatePointVariation( + base_data.Get(), direction, *transformation, integration_point, + base_context, workspace, variation + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluatePoint( + plus_data.Get(), *transformation, integration_point, workspace, + plus_context + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluatePoint( + minus_data.Get(), *transformation, integration_point, workspace, + minus_context + ) == mapping::MappingStatus::valid + ); + + mfem::Vector reference_position(dimension); + mfem::Vector expected_direction(dimension); + transformation->Transform(integration_point, reference_position); + evaluate_quadratic_direction(reference_position, expected_direction); + + const mfem::DenseMatrix expected_direction_gradient = + evaluate_quadratic_direction_gradient(reference_position); + + CAPTURE(q); + check_vector( + variation.displacement_variation, expected_direction, + polynomial_tolerance + ); + check_vector( + variation.physical_position_variation, expected_direction, + polynomial_tolerance + ); + check_matrix( + variation.displacement_jacobian_variation, + expected_direction_gradient, polynomial_tolerance + ); + check_matrix( + variation.mapping_jacobian_variation, expected_direction_gradient, + polynomial_tolerance + ); + + check_vector_central_difference( + plus_context.physical_position, minus_context.physical_position, + variation.physical_position_variation, difference_step, + linearization_tolerance + ); + check_matrix_central_difference( + plus_context.mapping_jacobian, minus_context.mapping_jacobian, + variation.mapping_jacobian_variation, difference_step, + linearization_tolerance + ); + check_matrix_central_difference( + plus_context.inverse_mapping_jacobian, + minus_context.inverse_mapping_jacobian, + variation.inverse_mapping_jacobian_variation, difference_step, + linearization_tolerance + ); + + const double determinant_finite_difference = + (plus_context.mapping_determinant - + minus_context.mapping_determinant) / + (2.0 * difference_step); + CHECK_THAT( + determinant_finite_difference, + WithinAbs( + variation.mapping_determinant_variation, linearization_tolerance + ) + ); + } +} + +TEST_CASE( + "Stateless Domain Mapper Volume Linearization Matches Centered Differences", + tags::unit &tags::mapping +) { + constexpr double linearization_tolerance = 5.0e-9; + + QuadraticElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *transformation = + fixture.mesh.GetElementTransformation(0); + const QuadraticMappingData mapping_data(element, *transformation); + + const mapping::ElementDisplacementData base_displacement( + element, mapping_data.base_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData direction( + element, mapping_data.direction_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData plus_displacement( + element, mapping_data.plus_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData minus_displacement( + element, mapping_data.minus_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner base_data(base_displacement); + const ElementMappingDataOwner plus_data(plus_displacement); + const ElementMappingDataOwner minus_data(minus_displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 6); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + + mapping::VolumeMappingContext base_context; + mapping::VolumeMappingContext plus_context; + mapping::VolumeMappingContext minus_context; + mapping::VolumeMappingVariation variation; + + REQUIRE( + mapper.EvaluateVolume( + base_data.Get(), *transformation, integration_point, workspace, + base_context + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateVolumeVariation( + base_data.Get(), direction, *transformation, integration_point, + base_context, workspace, variation + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateVolume( + plus_data.Get(), *transformation, integration_point, workspace, + plus_context + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateVolume( + minus_data.Get(), *transformation, integration_point, workspace, + minus_context + ) == mapping::MappingStatus::valid + ); + + CAPTURE(q); + check_matrix_central_difference( + plus_context.quadrature.J_inv, minus_context.quadrature.J_inv, + variation.inverse_element_jacobian_variation, difference_step, + linearization_tolerance + ); + + const double determinant_finite_difference = + (plus_context.quadrature.detJ - minus_context.quadrature.detJ) / + (2.0 * difference_step); + const double weight_finite_difference = + (plus_context.quadrature.weight - minus_context.quadrature.weight) / + (2.0 * difference_step); + + CHECK_THAT( + determinant_finite_difference, + WithinAbs( + variation.mapping.mapping_determinant_variation, + linearization_tolerance + ) + ); + CHECK_THAT( + weight_finite_difference, + WithinAbs(variation.weight_variation, linearization_tolerance) + ); + } +} + +TEST_CASE( + "Stateless Domain Mapper Face Linearization Matches Centered Differences", + tags::unit &tags::mapping +) { + constexpr double normal_tolerance = 2.0e-8; + constexpr double measure_tolerance = 2.0e-8; + + QuadraticElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *element_transformation = + fixture.mesh.GetElementTransformation(0); + const QuadraticMappingData mapping_data(element, *element_transformation); + + const mapping::ElementDisplacementData base_displacement( + element, mapping_data.base_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData direction( + element, mapping_data.direction_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData plus_displacement( + element, mapping_data.plus_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData minus_displacement( + element, mapping_data.minus_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner base_data(base_displacement); + const ElementMappingDataOwner plus_data(plus_displacement); + const ElementMappingDataOwner minus_data(minus_displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + + for (int boundary_element = 0; boundary_element < fixture.mesh.GetNBE(); + ++boundary_element) { + mfem::FaceElementTransformations *transformation = + fixture.mesh.GetBdrFaceTransformations(boundary_element); + REQUIRE(transformation != nullptr); + REQUIRE(transformation->Elem1 != nullptr); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 4); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + + mapping::FaceMappingContext base_context; + mapping::FaceMappingContext plus_context; + mapping::FaceMappingContext minus_context; + mapping::FaceMappingVariation variation; + + REQUIRE( + mapper.EvaluateFace( + base_data.Get(), *transformation, + mapping::FaceElementSide::element_1, integration_point, + workspace, base_context + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateFaceVariation( + base_data.Get(), direction, *transformation, + mapping::FaceElementSide::element_1, integration_point, + base_context, workspace, variation + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateFace( + plus_data.Get(), *transformation, + mapping::FaceElementSide::element_1, integration_point, + workspace, plus_context + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateFace( + minus_data.Get(), *transformation, + mapping::FaceElementSide::element_1, integration_point, + workspace, minus_context + ) == mapping::MappingStatus::valid + ); + + CAPTURE(boundary_element, q); + check_vector_central_difference( + plus_context.quadrature.normal, minus_context.quadrature.normal, + variation.physical_normal_variation, difference_step, + normal_tolerance + ); + + const double surface_weight_finite_difference = + (plus_context.physical_surface_weight - + minus_context.physical_surface_weight) / + (2.0 * difference_step); + const double normal_scale_finite_difference = + (plus_context.quadrature.v_dot_n_scale - + minus_context.quadrature.v_dot_n_scale) / + (2.0 * difference_step); + + CHECK_THAT( + surface_weight_finite_difference, + WithinAbs( + variation.physical_surface_weight_variation, + measure_tolerance + ) + ); + CHECK_THAT( + normal_scale_finite_difference, + WithinAbs( + variation.normal_flux_scale_variation, measure_tolerance + ) + ); + } + } +} + +TEST_CASE( + "Stateless Domain Mapper Rejects Invalid Linearization Directions", + tags::unit &tags::mapping +) { + QuadraticElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *transformation = + fixture.mesh.GetElementTransformation(0); + const mfem::IntegrationPoint &integration_point = + mfem::Geometries.GetCenter(transformation->GetGeometryType()); + const QuadraticMappingData mapping_data(element, *transformation); + + const mapping::ElementDisplacementData base_displacement( + element, mapping_data.base_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner base_data(base_displacement); + + mfem::Vector non_finite_direction_dofs(mapping_data.direction_dofs); + non_finite_direction_dofs(0) = std::numeric_limits::quiet_NaN(); + const mapping::ElementDisplacementData non_finite_direction( + element, non_finite_direction_dofs, mfem::Ordering::byVDIM + ); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + + mapping::MappingPointContext base_context; + mapping::MappingPointVariation variation; + + REQUIRE( + mapper.EvaluatePoint( + base_data.Get(), *transformation, integration_point, workspace, + base_context + ) == mapping::MappingStatus::valid + ); + CHECK( + mapper.EvaluatePointVariation( + base_data.Get(), non_finite_direction, *transformation, + integration_point, base_context, workspace, variation + ) == mapping::MappingStatus::non_finite_input + ); + + SingleElementFixture linear_fixture; + const mfem::FiniteElement &linear_element = linear_fixture.GetElement(); + const mfem::Vector linear_direction_dofs = + linear_fixture.MakeZeroElementDofs(); + const mapping::ElementDisplacementData incompatible_direction( + linear_element, linear_direction_dofs, mfem::Ordering::byVDIM + ); + + CHECK_THROWS_AS( + mapper.EvaluatePointVariation( + base_data.Get(), incompatible_direction, *transformation, + integration_point, base_context, workspace, variation + ), + std::invalid_argument + ); +} + +TEST_CASE( + "Mapping Field Transforms Satisfy Piola And Gradient Identities", + tags::unit &tags::mapping +) { + constexpr double transform_tolerance = 1.0e-12; + + mapping::MappingPointContext context; + context.mapping_jacobian.SetSize(3); + context.mapping_jacobian(0, 0) = 1.20; + context.mapping_jacobian(0, 1) = 0.15; + context.mapping_jacobian(0, 2) = -0.05; + context.mapping_jacobian(1, 0) = -0.08; + context.mapping_jacobian(1, 1) = 0.95; + context.mapping_jacobian(1, 2) = 0.12; + context.mapping_jacobian(2, 0) = 0.04; + context.mapping_jacobian(2, 1) = -0.10; + context.mapping_jacobian(2, 2) = 1.10; + + context.mapping_determinant = context.mapping_jacobian.Det(); + REQUIRE(context.mapping_determinant > 0.0); + + context.inverse_mapping_jacobian.SetSize(3); + mfem::CalcInverse( + context.mapping_jacobian, context.inverse_mapping_jacobian + ); + + const mfem::Vector reference_flux = make_vector(0.7, -0.4, 1.1); + const mfem::Vector reference_test_flux = make_vector(-0.2, 0.9, 0.5); + const mfem::Vector reference_gradient = make_vector(0.3, -0.6, 0.8); + const mfem::Vector reference_test_gradient = make_vector(-0.7, 0.2, 0.4); + + mfem::Vector physical_flux; + mfem::Vector recovered_flux; + mfem::Vector physical_test_flux; + mfem::Vector physical_gradient; + mfem::Vector recovered_gradient; + mfem::Vector physical_test_gradient; + + mapping::MapHDivFluxToPhysical(context, reference_flux, physical_flux); + mapping::MapPhysicalFluxToHDivReference( + context, physical_flux, recovered_flux + ); + mapping::MapHDivFluxToPhysical( + context, reference_test_flux, physical_test_flux + ); + + mapping::MapReferenceGradientToPhysical( + context, reference_gradient, physical_gradient + ); + mapping::MapPhysicalGradientToReference( + context, physical_gradient, recovered_gradient + ); + mapping::MapReferenceGradientToPhysical( + context, reference_test_gradient, physical_test_gradient + ); + + check_vector(recovered_flux, reference_flux, transform_tolerance); + check_vector(recovered_gradient, reference_gradient, transform_tolerance); + + mfem::DenseMatrix reference_vector_gradient(3); + reference_vector_gradient(0, 0) = 0.20; + reference_vector_gradient(0, 1) = -0.10; + reference_vector_gradient(0, 2) = 0.04; + reference_vector_gradient(1, 0) = 0.03; + reference_vector_gradient(1, 1) = 0.15; + reference_vector_gradient(1, 2) = -0.08; + reference_vector_gradient(2, 0) = -0.05; + reference_vector_gradient(2, 1) = 0.02; + reference_vector_gradient(2, 2) = 0.11; + + mfem::DenseMatrix physical_vector_gradient; + mfem::DenseMatrix recovered_vector_gradient; + + mapping::MapReferenceVectorGradientToPhysical( + context, reference_vector_gradient, physical_vector_gradient + ); + mapping::MapPhysicalVectorGradientToReference( + context, physical_vector_gradient, recovered_vector_gradient + ); + check_matrix( + recovered_vector_gradient, reference_vector_gradient, + transform_tolerance + ); + + mfem::DenseMatrix hdiv_mass_tensor; + mfem::DenseMatrix diffusion_tensor; + mapping::ComputeHDivMassTensor(context, hdiv_mass_tensor); + mapping::ComputeScalarDiffusionTensor(context, diffusion_tensor); + + mfem::Vector mass_action(3); + mfem::Vector diffusion_action(3); + hdiv_mass_tensor.Mult(reference_test_flux, mass_action); + diffusion_tensor.Mult(reference_test_gradient, diffusion_action); + + const double physical_hdiv_inner_product = + context.mapping_determinant * (physical_flux * physical_test_flux); + const double reference_hdiv_inner_product = reference_flux * mass_action; + const double physical_gradient_inner_product = + context.mapping_determinant * + (physical_gradient * physical_test_gradient); + const double reference_gradient_inner_product = + reference_gradient * diffusion_action; + + CHECK_THAT( + physical_hdiv_inner_product, + WithinAbs(reference_hdiv_inner_product, transform_tolerance) + ); + CHECK_THAT( + physical_gradient_inner_product, + WithinAbs(reference_gradient_inner_product, transform_tolerance) + ); + + const double reference_divergence = 0.73; + const double physical_divergence = + mapping::MapHDivDivergenceToPhysical(context, reference_divergence); + CHECK_THAT( + physical_divergence, + WithinAbs( + reference_divergence / context.mapping_determinant, + transform_tolerance + ) + ); +} + +TEST_CASE( + "Mapped Hdiv Flux Preserves Physical Face Flux", + tags::unit &tags::mapping +) { + constexpr double flux_tolerance = 2.0e-11; + + SingleElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *element_transformation = + fixture.mesh.GetElementTransformation(0); + + const mfem::DenseMatrix displacement_gradient = + make_affine_displacement_gradient(); + const mfem::Vector displacement_offset = make_vector(0.07, -0.04, 0.03); + const mfem::Vector element_dofs = make_affine_element_dofs( + element, *element_transformation, displacement_gradient, + displacement_offset, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData displacement( + element, element_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner element_data(displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + + const mfem::Vector reference_flux = make_vector(0.7, -0.4, 1.1); + + for (int boundary_element = 0; boundary_element < fixture.mesh.GetNBE(); + ++boundary_element) { + mfem::FaceElementTransformations *transformation = + fixture.mesh.GetBdrFaceTransformations(boundary_element); + REQUIRE(transformation != nullptr); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 6); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + mapping::FaceMappingContext context; + mfem::Vector physical_flux; + + REQUIRE( + mapper.EvaluateFace( + element_data.Get(), *transformation, + mapping::FaceElementSide::element_1, integration_point, + workspace, context + ) == mapping::MappingStatus::valid + ); + + mapping::MapHDivFluxToPhysical( + context.mapping, reference_flux, physical_flux + ); + + const double reference_integrated_flux = + (reference_flux * context.reference_normal) * + context.reference_surface_weight; + const double physical_integrated_flux = + (physical_flux * context.quadrature.normal) * + context.physical_surface_weight; + + CAPTURE(boundary_element, q); + CHECK_THAT( + physical_integrated_flux, + WithinAbs(reference_integrated_flux, flux_tolerance) + ); + } + } +} + +TEST_CASE( + "Stateless Domain Mapper Represents Strong Rotating Star Geometry", + tags::integration &tags::mapping +) { + constexpr double r_star = 1.0; + constexpr double r_infinity = 4.0; + constexpr double transform_tolerance = 2.0e-10; + + stroid::config::MeshConfig mesh_config; + mesh_config.refinement_levels = 0; + mesh_config.order = 2; + mesh_config.include_external_domain = true; + mesh_config.r_core = 0.25; + mesh_config.r_star = r_star; + mesh_config.r_infinity = r_infinity; + mesh_config.flattening = 0.0; + mesh_config.optimization_methods = + stroid::config::OptimizationMethods{false, true}; + + stroid::StroidMesh stroid_mesh = stroid::GenerateMesh(mesh_config); + mfem::Mesh &mesh = *stroid_mesh.mesh; + REQUIRE(stroid_mesh.exterior_coordinate != nullptr); + REQUIRE(stroid_mesh.exterior_coordinate->space != nullptr); + REQUIRE(stroid_mesh.exterior_coordinate->values != nullptr); + + mfem::FiniteElementSpace &compactification_space = + *stroid_mesh.exterior_coordinate->space; + mfem::GridFunction &compactification_coordinate = + *stroid_mesh.exterior_coordinate->values; + + mfem::H1_FECollection displacement_collection(3, dimension); + mfem::FiniteElementSpace displacement_space( + &mesh, &displacement_collection, dimension, mfem::Ordering::byVDIM + ); + mfem::GridFunction displacement(&displacement_space); + + auto rotating_displacement = [r_star, r_infinity]( + const mfem::Vector &reference_position, + mfem::Vector &displacement_value + ) { + const double x = reference_position(0); + const double y = reference_position(1); + const double z = reference_position(2); + const double radius_squared = x * x + y * y + z * z; + const double radius = std::sqrt(radius_squared); + + displacement_value.SetSize(3); + displacement_value = 0.0; + + if (radius <= 1.0e-14) + return; + + const double cylindrical_fraction = (x * x + y * y) / radius_squared; + const double angular_deformation = + 0.20 * cylindrical_fraction + + 0.12 * cylindrical_fraction * cylindrical_fraction; + + double radial_extension = 0.0; + if (radius <= r_star) { + radial_extension = radius_squared / (r_star * r_star); + } else { + radial_extension = + std::max(0.0, (r_infinity - radius) / (r_infinity - r_star)); + } + + const double scale = radial_extension * angular_deformation; + displacement_value(0) = scale * x; + displacement_value(1) = scale * y; + displacement_value(2) = scale * z; + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + dimension, rotating_displacement + ); + displacement.ProjectCoefficient(displacement_coefficient); + + std::unique_ptr + exterior_map = std::make_unique< + mapping::compactification::KelvinCompactification>( + mapping::compactification::options::KelvinCompactificationOptions{ + .r_star_ref = r_star, .r_inf_ref = r_infinity + } + ); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + std::move(exterior_map) + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + + double minimum_mapping_determinant = + std::numeric_limits::infinity(); + double maximum_mapping_determinant = 0.0; + double stellar_volume = 0.0; + double moment_x = 0.0; + double moment_y = 0.0; + double moment_z = 0.0; + + int stellar_elements = 0; + int vacuum_elements = 0; + + for (int element_id = 0; element_id < mesh.GetNE(); ++element_id) { + mfem::ElementTransformation *transformation = + mesh.GetElementTransformation(element_id); + const mfem::FiniteElement *element = + displacement_space.GetFE(element_id); + + mfem::Array element_vdofs; + mfem::Vector element_dofs; + displacement_space.GetElementVDofs(element_id, element_vdofs); + displacement.GetSubVector(element_vdofs, element_dofs); + + const mapping::ElementDisplacementData element_displacement = + mapping::ElementDisplacementDataFromElementVDofs( + *element, element_dofs + ); + + mfem::Array compactification_dof_indices; + mfem::Vector compactification_dofs; + compactification_space.GetElementDofs( + element_id, compactification_dof_indices + ); + compactification_coordinate.GetSubVector( + compactification_dof_indices, compactification_dofs + ); + + const ElementMappingDataOwner element_data( + element_displacement, *compactification_space.GetFE(element_id), + compactification_dofs + ); + const int quadrature_order = 2 * element->GetOrder() + 6; + const mfem::IntegrationRule &integration_rule = mfem::IntRules.Get( + transformation->GetGeometryType(), quadrature_order + ); + + if (transformation->Attribute == 3) { + ++vacuum_elements; + } else { + ++stellar_elements; + } + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + mapping::VolumeMappingContext context; + + REQUIRE( + mapper.EvaluateVolume( + element_data.Get(), *transformation, integration_point, + workspace, context + ) == mapping::MappingStatus::valid + ); + + minimum_mapping_determinant = std::min( + minimum_mapping_determinant, context.mapping.mapping_determinant + ); + maximum_mapping_determinant = std::max( + maximum_mapping_determinant, context.mapping.mapping_determinant + ); + + REQUIRE(context.mapping.mapping_determinant > 0.0); + REQUIRE(context.quadrature.weight > 0.0); + + mfem::Vector reference_flux = make_vector( + 0.4 + context.mapping.reference_position(0), + -0.3 + 0.5 * context.mapping.reference_position(1), + 0.7 - 0.2 * context.mapping.reference_position(2) + ); + + mfem::Vector physical_flux; + mfem::Vector recovered_flux; + mapping::MapHDivFluxToPhysical( + context.mapping, reference_flux, physical_flux + ); + mapping::MapPhysicalFluxToHDivReference( + context.mapping, physical_flux, recovered_flux + ); + check_vector(recovered_flux, reference_flux, transform_tolerance); + + const mfem::Vector reference_gradient = make_vector(0.3, -0.5, 0.8); + mfem::Vector physical_gradient; + mfem::Vector recovered_gradient; + mapping::MapReferenceGradientToPhysical( + context.mapping, reference_gradient, physical_gradient + ); + mapping::MapPhysicalGradientToReference( + context.mapping, physical_gradient, recovered_gradient + ); + check_vector( + recovered_gradient, reference_gradient, transform_tolerance + ); + + if (transformation->Attribute == 3) { + transformation->SetIntPoint(&integration_point); + + mfem::Vector compactification_gradient(dimension); + const double coordinate = compactification_coordinate.GetValue( + element_id, integration_point + ); + compactification_coordinate.GetGradient( + *transformation, compactification_gradient + ); + + mapping::compactification::ExteriorMapResult direct_result; + const mapping::compactification::ExteriorMapInput direct_input{ + .reference_position = context.mapping.reference_position, + .displaced_position = context.mapping.displaced_position, + .displacement_jacobian = + context.mapping.displacement_jacobian, + .compactification_coordinate = coordinate, + .compactification_coordinate_gradient = + compactification_gradient + }; + + REQUIRE( + mapper.GetExteriorMap().Evaluate( + direct_input, direct_result + ) == mapping::MappingStatus::valid + ); + check_vector( + context.mapping.physical_position, + direct_result.physical_position, transform_tolerance + ); + check_matrix( + context.mapping.mapping_jacobian, + direct_result.mapping_jacobian, transform_tolerance + ); + } else { + check_vector( + context.mapping.physical_position, + context.mapping.displaced_position, transform_tolerance + ); + + const double x = context.mapping.physical_position(0); + const double y = context.mapping.physical_position(1); + const double z = context.mapping.physical_position(2); + const double weight = context.quadrature.weight; + + stellar_volume += weight; + moment_x += x * x * weight; + moment_y += y * y * weight; + moment_z += z * z * weight; + } + } + } + + REQUIRE(stellar_elements > 0); + REQUIRE(vacuum_elements > 0); + REQUIRE(stellar_volume > 0.0); + REQUIRE(std::isfinite(minimum_mapping_determinant)); + REQUIRE(minimum_mapping_determinant > 0.0); + + const double moment_trace = moment_x + moment_y + moment_z; + const double quadrupole_x = 3.0 * moment_x - moment_trace; + const double quadrupole_y = 3.0 * moment_y - moment_trace; + const double quadrupole_z = 3.0 * moment_z - moment_trace; + const double normalized_quadrupole = + std::sqrt( + quadrupole_x * quadrupole_x + quadrupole_y * quadrupole_y + + quadrupole_z * quadrupole_z + ) / + moment_trace; + const double axisymmetry_error = + std::abs(moment_x - moment_y) / (0.5 * (moment_x + moment_y)); + + INFO("Stellar volume = " << stellar_volume); + INFO("Minimum mapping determinant = " << minimum_mapping_determinant); + INFO("Maximum mapping determinant = " << maximum_mapping_determinant); + INFO("Normalized geometric quadrupole = " << normalized_quadrupole); + INFO("Axisymmetry error = " << axisymmetry_error); + + CHECK(moment_x > moment_z); + CHECK(moment_y > moment_z); + CHECK(normalized_quadrupole > 1.0e-2); + CHECK(axisymmetry_error < 5.0e-2); +} + +TEST_CASE( + "Kelvin Composed Domain Mapping Linearization Matches Centered Differences", + tags::unit &tags::mapping +) { + constexpr double relative_tolerance = 2.0e-6; + constexpr double kelvin_difference_step = 2.0e-4; + + mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D( + 1, 1, 1, mfem::Element::HEXAHEDRON, 2.98, 0.02, 0.02 + ); + + for (int vertex_id = 0; vertex_id < mesh.GetNV(); ++vertex_id) { + double *vertex = mesh.GetVertex(vertex_id); + vertex[0] += 1.0; + vertex[1] -= 0.01; + vertex[2] -= 0.01; + } + + mesh.GetElement(0)->SetAttribute(3); + mesh.SetAttributes(); + + mfem::H1_FECollection displacement_collection(2, dimension); + mfem::FiniteElementSpace displacement_space( + &mesh, &displacement_collection, dimension, mfem::Ordering::byVDIM + ); + + const mfem::FiniteElement &element = *displacement_space.GetFE(0); + mfem::ElementTransformation *transformation = + mesh.GetElementTransformation(0); + + const mfem::Vector base_dofs = make_function_element_dofs( + element, *transformation, evaluate_quadratic_displacement, + mfem::Ordering::byVDIM + ); + const mfem::Vector direction_dofs = make_function_element_dofs( + element, *transformation, evaluate_quadratic_direction, + mfem::Ordering::byVDIM + ); + + mfem::Vector plus_dofs(base_dofs); + mfem::Vector minus_dofs(base_dofs); + plus_dofs.Add(kelvin_difference_step, direction_dofs); + minus_dofs.Add(-kelvin_difference_step, direction_dofs); + + const mapping::ElementDisplacementData base_displacement( + element, base_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData direction( + element, direction_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData plus_displacement( + element, plus_dofs, mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData minus_displacement( + element, minus_dofs, mfem::Ordering::byVDIM + ); + + const mfem::Vector compactification_dofs = + make_compactification_element_dofs( + element, *transformation, + [](const mfem::Vector &reference_position) { + return (reference_position(0) - 1.0) / 3.0; + } + ); + + const ElementMappingDataOwner base_data( + base_displacement, element, compactification_dofs + ); + const ElementMappingDataOwner plus_data( + plus_displacement, element, compactification_dofs + ); + const ElementMappingDataOwner minus_data( + minus_displacement, element, compactification_dofs + ); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + + auto vector_central_difference = [](const mfem::Vector &plus_value, + const mfem::Vector &minus_value) { + mfem::Vector difference(plus_value); + difference -= minus_value; + difference *= 1.0 / (2.0 * kelvin_difference_step); + return difference; + }; + + auto matrix_central_difference = [](const mfem::DenseMatrix &plus_value, + const mfem::DenseMatrix &minus_value) { + mfem::DenseMatrix difference(plus_value); + difference -= minus_value; + difference *= 1.0 / (2.0 * kelvin_difference_step); + return difference; + }; + + for (const double xi : std::array{0.0, 0.25, 0.75, 0.95, 0.99}) { + mfem::IntegrationPoint integration_point; + integration_point.x = 3.0 * xi / 2.98; + integration_point.y = 0.5; + integration_point.z = 0.5; + integration_point.weight = 0.73; + + mapping::VolumeMappingContext base_context; + mapping::VolumeMappingContext plus_context; + mapping::VolumeMappingContext minus_context; + mapping::VolumeMappingVariation variation; + + REQUIRE( + mapper.EvaluateVolume( + base_data.Get(), *transformation, integration_point, workspace, + base_context + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateVolumeVariation( + base_data.Get(), direction, *transformation, integration_point, + base_context, workspace, variation + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateVolume( + plus_data.Get(), *transformation, integration_point, workspace, + plus_context + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateVolume( + minus_data.Get(), *transformation, integration_point, workspace, + minus_context + ) == mapping::MappingStatus::valid + ); + + CAPTURE(xi); + REQUIRE(base_context.mapping.compactified); + + const mfem::Vector physical_position_difference = + vector_central_difference( + plus_context.mapping.physical_position, + minus_context.mapping.physical_position + ); + const mfem::DenseMatrix mapping_jacobian_difference = + matrix_central_difference( + plus_context.mapping.mapping_jacobian, + minus_context.mapping.mapping_jacobian + ); + const mfem::DenseMatrix inverse_mapping_jacobian_difference = + matrix_central_difference( + plus_context.mapping.inverse_mapping_jacobian, + minus_context.mapping.inverse_mapping_jacobian + ); + const mfem::DenseMatrix inverse_element_jacobian_difference = + matrix_central_difference( + plus_context.quadrature.J_inv, minus_context.quadrature.J_inv + ); + + CHECK_THAT( + relative_vector_difference( + physical_position_difference, + variation.mapping.physical_position_variation + ), + Catch::Matchers::WithinAbs(0.0, relative_tolerance) + ); + CHECK_THAT( + relative_matrix_difference( + mapping_jacobian_difference, + variation.mapping.mapping_jacobian_variation + ), + Catch::Matchers::WithinAbs(0.0, relative_tolerance) + ); + CHECK_THAT( + relative_matrix_difference( + inverse_mapping_jacobian_difference, + variation.mapping.inverse_mapping_jacobian_variation + ), + Catch::Matchers::WithinAbs(0.0, relative_tolerance) + ); + CHECK_THAT( + relative_matrix_difference( + inverse_element_jacobian_difference, + variation.inverse_element_jacobian_variation + ), + Catch::Matchers::WithinAbs(0.0, relative_tolerance) + ); + + const double determinant_difference = + (plus_context.mapping.mapping_determinant - + minus_context.mapping.mapping_determinant) / + (2.0 * kelvin_difference_step); + const double weight_difference = + (plus_context.quadrature.weight - minus_context.quadrature.weight) / + (2.0 * kelvin_difference_step); + + check_centered_difference( + variation.mapping.mapping_determinant_variation, + determinant_difference, plus_context.mapping.mapping_determinant, + minus_context.mapping.mapping_determinant, kelvin_difference_step, + relative_tolerance + ); + check_centered_difference( + variation.weight_variation, weight_difference, + plus_context.quadrature.weight, minus_context.quadrature.weight, + kelvin_difference_step, relative_tolerance + ); + } + + for (int boundary_element = 0; boundary_element < mesh.GetNBE(); + ++boundary_element) { + mfem::FaceElementTransformations *face_transformation = + mesh.GetBdrFaceTransformations(boundary_element); + REQUIRE(face_transformation != nullptr); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(face_transformation->GetGeometryType(), 4); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + + mapping::FaceMappingContext base_context; + mapping::FaceMappingContext plus_context; + mapping::FaceMappingContext minus_context; + mapping::FaceMappingVariation variation; + + REQUIRE( + mapper.EvaluateFace( + base_data.Get(), *face_transformation, + mapping::FaceElementSide::element_1, integration_point, + workspace, base_context + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateFaceVariation( + base_data.Get(), direction, *face_transformation, + mapping::FaceElementSide::element_1, integration_point, + base_context, workspace, variation + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateFace( + plus_data.Get(), *face_transformation, + mapping::FaceElementSide::element_1, integration_point, + workspace, plus_context + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateFace( + minus_data.Get(), *face_transformation, + mapping::FaceElementSide::element_1, integration_point, + workspace, minus_context + ) == mapping::MappingStatus::valid + ); + + CAPTURE(boundary_element, q); + + const mfem::Vector normal_difference = vector_central_difference( + plus_context.quadrature.normal, minus_context.quadrature.normal + ); + + REQUIRE( + normal_difference.Size() == + variation.physical_normal_variation.Size() + ); + for (int i = 0; i < normal_difference.Size(); ++i) { + check_centered_difference( + variation.physical_normal_variation(i), + normal_difference(i), plus_context.quadrature.normal(i), + minus_context.quadrature.normal(i), kelvin_difference_step, + relative_tolerance + ); + } + + const double surface_weight_difference = + (plus_context.physical_surface_weight - + minus_context.physical_surface_weight) / + (2.0 * kelvin_difference_step); + const double normal_scale_difference = + (plus_context.quadrature.v_dot_n_scale - + minus_context.quadrature.v_dot_n_scale) / + (2.0 * kelvin_difference_step); + + check_centered_difference( + variation.physical_surface_weight_variation, + surface_weight_difference, plus_context.physical_surface_weight, + minus_context.physical_surface_weight, kelvin_difference_step, + relative_tolerance + ); + check_centered_difference( + variation.normal_flux_scale_variation, normal_scale_difference, + plus_context.quadrature.v_dot_n_scale, + minus_context.quadrature.v_dot_n_scale, kelvin_difference_step, + relative_tolerance + ); + } + } +} +TEST_CASE( + "Stateless Domain Mapper Produces Consistent Two Sided Interface Geometry", + tags::integration &tags::mapping +) { + constexpr double r_star = 1.0; + constexpr double r_infinity = 4.0; + constexpr double interface_tolerance = 2.0e-7; + + stroid::config::MeshConfig mesh_config; + mesh_config.refinement_levels = 0; + mesh_config.order = 2; + mesh_config.include_external_domain = true; + mesh_config.r_core = 0.25; + mesh_config.r_star = r_star; + mesh_config.r_infinity = r_infinity; + mesh_config.flattening = 0.0; + mesh_config.optimization_methods = + stroid::config::OptimizationMethods{false, true}; + + stroid::StroidMesh stroid_mesh = stroid::GenerateMesh(mesh_config); + mfem::Mesh &mesh = *stroid_mesh.mesh; + REQUIRE(stroid_mesh.exterior_coordinate != nullptr); + REQUIRE(stroid_mesh.exterior_coordinate->space != nullptr); + REQUIRE(stroid_mesh.exterior_coordinate->values != nullptr); + + mfem::FiniteElementSpace &compactification_space = + *stroid_mesh.exterior_coordinate->space; + mfem::GridFunction &compactification_coordinate = + *stroid_mesh.exterior_coordinate->values; + + mfem::H1_FECollection displacement_collection(2, dimension); + mfem::FiniteElementSpace displacement_space( + &mesh, &displacement_collection, dimension, mfem::Ordering::byVDIM + ); + + auto displacement_function = [](const mfem::Vector &position, + mfem::Vector &value) { + value.SetSize(3); + value(0) = 0.08 * position(0) + 0.02 * position(1); + value(1) = -0.03 * position(0) - 0.02 * position(1); + value(2) = 0.04 * position(2); + }; + + auto direction_function = [](const mfem::Vector &position, + mfem::Vector &value) { + value.SetSize(3); + value(0) = 0.02 * position(0); + value(1) = -0.01 * position(1) + 0.005 * position(2); + value(2) = 0.015 * position(2); + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + dimension, displacement_function + ); + mfem::VectorFunctionCoefficient direction_coefficient( + dimension, direction_function + ); + + mfem::GridFunction displacement(&displacement_space); + mfem::GridFunction direction(&displacement_space); + displacement.ProjectCoefficient(displacement_coefficient); + direction.ProjectCoefficient(direction_coefficient); + + std::unique_ptr + exterior_map = std::make_unique< + mapping::compactification::KelvinCompactification>( + mapping::compactification::options::KelvinCompactificationOptions{ + .r_star_ref = r_star, .r_inf_ref = r_infinity + } + ); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + std::move(exterior_map) + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + + int core_envelope_faces = 0; + int stellar_vacuum_faces = 0; + + for (int face_id = 0; face_id < mesh.GetNumFaces(); ++face_id) { + mfem::FaceElementTransformations *transformation = + mesh.GetFaceElementTransformations(face_id); + if (transformation == nullptr || transformation->Elem1 == nullptr || + transformation->Elem2 == nullptr) + continue; + + const int attribute_1 = transformation->Elem1->Attribute; + const int attribute_2 = transformation->Elem2->Attribute; + const bool core_envelope_interface = + (attribute_1 == 1 && attribute_2 == 2) || + (attribute_1 == 2 && attribute_2 == 1); + const bool stellar_vacuum_interface = + (attribute_1 == 3) != (attribute_2 == 3); + + if (!core_envelope_interface && !stellar_vacuum_interface) + continue; + + if (core_envelope_interface) + ++core_envelope_faces; + if (stellar_vacuum_interface) + ++stellar_vacuum_faces; + + const int element_1 = transformation->Elem1->ElementNo; + const int element_2 = transformation->Elem2->ElementNo; + + mfem::Array vdofs_1; + mfem::Array vdofs_2; + mfem::Vector displacement_dofs_1; + mfem::Vector displacement_dofs_2; + mfem::Vector direction_dofs_1; + mfem::Vector direction_dofs_2; + mfem::Array compactification_dof_indices_1; + mfem::Array compactification_dof_indices_2; + mfem::Vector compactification_dofs_1; + mfem::Vector compactification_dofs_2; + + displacement_space.GetElementVDofs(element_1, vdofs_1); + displacement_space.GetElementVDofs(element_2, vdofs_2); + displacement.GetSubVector(vdofs_1, displacement_dofs_1); + displacement.GetSubVector(vdofs_2, displacement_dofs_2); + direction.GetSubVector(vdofs_1, direction_dofs_1); + direction.GetSubVector(vdofs_2, direction_dofs_2); + compactification_space.GetElementDofs( + element_1, compactification_dof_indices_1 + ); + compactification_space.GetElementDofs( + element_2, compactification_dof_indices_2 + ); + compactification_coordinate.GetSubVector( + compactification_dof_indices_1, compactification_dofs_1 + ); + compactification_coordinate.GetSubVector( + compactification_dof_indices_2, compactification_dofs_2 + ); + + const mapping::ElementDisplacementData displacement_1 = + mapping::ElementDisplacementDataFromElementVDofs( + *displacement_space.GetFE(element_1), displacement_dofs_1 + ); + const mapping::ElementDisplacementData displacement_2 = + mapping::ElementDisplacementDataFromElementVDofs( + *displacement_space.GetFE(element_2), displacement_dofs_2 + ); + const mapping::ElementDisplacementData direction_1 = + mapping::ElementDisplacementDataFromElementVDofs( + *displacement_space.GetFE(element_1), direction_dofs_1 + ); + const mapping::ElementDisplacementData direction_2 = + mapping::ElementDisplacementDataFromElementVDofs( + *displacement_space.GetFE(element_2), direction_dofs_2 + ); + + const ElementMappingDataOwner element_data_1( + displacement_1, *compactification_space.GetFE(element_1), + compactification_dofs_1 + ); + const ElementMappingDataOwner element_data_2( + displacement_2, *compactification_space.GetFE(element_2), + compactification_dofs_2 + ); + + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 6); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + + mapping::FaceMappingContext context_1; + mapping::FaceMappingContext context_2; + mapping::FaceMappingVariation variation_1; + mapping::FaceMappingVariation variation_2; + + auto status_1 = mapper.EvaluateFace( + element_data_1.Get(), *transformation, + mapping::FaceElementSide::element_1, integration_point, + workspace, context_1 + ); + auto status_2 = mapper.EvaluateFace( + element_data_2.Get(), *transformation, + mapping::FaceElementSide::element_2, integration_point, + workspace, context_2 + ); + INFO("Element 1 ID = " << transformation->Elem1No); + INFO("Element 2 ID = " << transformation->Elem2No); + INFO("Element 1 attribute = " << transformation->Elem1->Attribute); + INFO("Element 2 attribute = " << transformation->Elem2->Attribute); + INFO("Element 2 status = " << static_cast(status_2)); + + mfem::Vector reference_position(dimension); + transformation->Elem2->Transform( + transformation->Elem2->GetIntPoint(), reference_position + ); + INFO( + std::format( + "Reference position = <{},{},{}>", reference_position(0), + reference_position(1), reference_position(2) + ) + ); + INFO( + std::format( + "Reference radius = {}", reference_position.Norml2() + ) + ); + INFO( + std::format( + "Reference radius minus r_star = {}", + reference_position.Norml2() - r_star + ) + ); + REQUIRE(status_1 == mapping::MappingStatus::valid); + REQUIRE(status_2 == mapping::MappingStatus::valid); + REQUIRE( + mapper.EvaluateFaceVariation( + element_data_1.Get(), direction_1, *transformation, + mapping::FaceElementSide::element_1, integration_point, + context_1, workspace, variation_1 + ) == mapping::MappingStatus::valid + ); + REQUIRE( + mapper.EvaluateFaceVariation( + element_data_2.Get(), direction_2, *transformation, + mapping::FaceElementSide::element_2, integration_point, + context_2, workspace, variation_2 + ) == mapping::MappingStatus::valid + ); + + CAPTURE(face_id, q, attribute_1, attribute_2); + check_vector( + context_1.mapping.physical_position, + context_2.mapping.physical_position, interface_tolerance + ); + check_scalar_relative( + context_1.physical_surface_weight, + context_2.physical_surface_weight, interface_tolerance + ); + + mfem::Vector normal_sum(context_1.quadrature.normal); + normal_sum += context_2.quadrature.normal; + CHECK(normal_sum.Norml2() < interface_tolerance); + + check_vector( + variation_1.mapping.physical_position_variation, + variation_2.mapping.physical_position_variation, + interface_tolerance + ); + check_scalar_relative( + variation_1.physical_surface_weight_variation, + variation_2.physical_surface_weight_variation, + interface_tolerance + ); + + mfem::Vector normal_variation_sum( + variation_1.physical_normal_variation + ); + normal_variation_sum += variation_2.physical_normal_variation; + CHECK(normal_variation_sum.Norml2() < interface_tolerance); + + const mfem::Vector physical_flux = make_vector(0.7, -0.4, 0.9); + mfem::Vector reference_flux_1; + mfem::Vector reference_flux_2; + + mapping::MapPhysicalFluxToHDivReference( + context_1.mapping, physical_flux, reference_flux_1 + ); + mapping::MapPhysicalFluxToHDivReference( + context_2.mapping, physical_flux, reference_flux_2 + ); + + const double flux_1 = + (reference_flux_1 * context_1.reference_normal) * + context_1.reference_surface_weight; + const double flux_2 = + (reference_flux_2 * context_2.reference_normal) * + context_2.reference_surface_weight; + + CHECK_THAT(flux_1 + flux_2, WithinAbs(0.0, interface_tolerance)); + } + } + + INFO("Core-envelope interface faces = " << core_envelope_faces); + INFO("Stellar-vacuum interface faces = " << stellar_vacuum_faces); + + REQUIRE(core_envelope_faces > 0); + REQUIRE(stellar_vacuum_faces > 0); +} + +TEST_CASE( + "Mapped Hdiv Field Satisfies The Divergence Theorem", + tags::unit &tags::mapping +) { + constexpr double divergence_tolerance = 2.0e-9; + + QuadraticElementFixture fixture; + + const mfem::FiniteElement &element = fixture.GetElement(); + mfem::ElementTransformation *element_transformation = + fixture.mesh.GetElementTransformation(0); + + const mfem::Vector displacement_dofs = make_function_element_dofs( + element, *element_transformation, evaluate_quadratic_displacement, + mfem::Ordering::byVDIM + ); + const mapping::ElementDisplacementData displacement( + element, displacement_dofs, mfem::Ordering::byVDIM + ); + const ElementMappingDataOwner element_data(displacement); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + mapping::DomainMapperStateless::Workspace workspace(dimension); + + double reference_divergence_integral = 0.0; + double physical_divergence_integral = 0.0; + double physical_boundary_flux = 0.0; + + const mfem::IntegrationRule &volume_rule = + mfem::IntRules.Get(element_transformation->GetGeometryType(), 10); + + for (int q = 0; q < volume_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + volume_rule.IntPoint(q); + mapping::VolumeMappingContext context; + + REQUIRE( + mapper.EvaluateVolume( + element_data.Get(), *element_transformation, integration_point, + workspace, context + ) == mapping::MappingStatus::valid + ); + + element_transformation->SetIntPoint(&integration_point); + + const double reference_divergence = evaluate_reference_hdiv_divergence( + context.mapping.reference_position + ); + const double physical_divergence = mapping::MapHDivDivergenceToPhysical( + context.mapping, reference_divergence + ); + const double reference_weight = + integration_point.weight * element_transformation->Weight(); + + reference_divergence_integral += + reference_divergence * reference_weight; + physical_divergence_integral += + physical_divergence * context.quadrature.weight; + } + + for (int boundary_element = 0; boundary_element < fixture.mesh.GetNBE(); + ++boundary_element) { + mfem::FaceElementTransformations *transformation = + fixture.mesh.GetBdrFaceTransformations(boundary_element); + REQUIRE(transformation != nullptr); + + const mfem::IntegrationRule &face_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 10); + + for (int q = 0; q < face_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + face_rule.IntPoint(q); + mapping::FaceMappingContext context; + + REQUIRE( + mapper.EvaluateFace( + element_data.Get(), *transformation, + mapping::FaceElementSide::element_1, integration_point, + workspace, context + ) == mapping::MappingStatus::valid + ); + + const mfem::Vector reference_flux = evaluate_reference_hdiv_field( + context.mapping.reference_position + ); + mfem::Vector physical_flux; + mapping::MapHDivFluxToPhysical( + context.mapping, reference_flux, physical_flux + ); + + physical_boundary_flux += + (physical_flux * context.quadrature.normal) * + context.physical_surface_weight; + } + } + + constexpr double analytic_reference_integral = 216.0; + + INFO( + "Analytic reference divergence integral = " + << analytic_reference_integral + ); + INFO( + "Computed reference divergence integral = " + << reference_divergence_integral + ); + INFO( + "Computed physical divergence integral = " + << physical_divergence_integral + ); + INFO("Computed physical boundary flux = " << physical_boundary_flux); + + CHECK_THAT( + reference_divergence_integral, + WithinAbs(analytic_reference_integral, divergence_tolerance) + ); + CHECK_THAT( + physical_divergence_integral, + WithinAbs(analytic_reference_integral, divergence_tolerance) + ); + CHECK_THAT( + physical_boundary_flux, + WithinAbs(analytic_reference_integral, divergence_tolerance) + ); +} + +TEST_CASE( + "Mapped Hcurl Fields Preserve Covariant Piola Identities", + tags::unit &tags::mapping +) { + constexpr double curl_tolerance = 2.0e-12; + + mapping::MappingPointContext context; + context.mapping_jacobian.SetSize(3); + context.mapping_jacobian(0, 0) = 1.20; + context.mapping_jacobian(0, 1) = 0.15; + context.mapping_jacobian(0, 2) = -0.05; + context.mapping_jacobian(1, 0) = -0.08; + context.mapping_jacobian(1, 1) = 0.95; + context.mapping_jacobian(1, 2) = 0.12; + context.mapping_jacobian(2, 0) = 0.04; + context.mapping_jacobian(2, 1) = -0.10; + context.mapping_jacobian(2, 2) = 1.10; + + context.mapping_determinant = context.mapping_jacobian.Det(); + REQUIRE(context.mapping_determinant > 0.0); + + context.inverse_mapping_jacobian.SetSize(3); + mfem::CalcInverse( + context.mapping_jacobian, context.inverse_mapping_jacobian + ); + + const mfem::Vector reference_field = make_vector(0.7, -0.4, 1.1); + const mfem::Vector reference_test_field = make_vector(-0.2, 0.9, 0.5); + + mfem::DenseMatrix reference_gradient(3); + reference_gradient(0, 0) = 0.20; + reference_gradient(0, 1) = -0.10; + reference_gradient(0, 2) = 0.04; + reference_gradient(1, 0) = 0.03; + reference_gradient(1, 1) = 0.15; + reference_gradient(1, 2) = -0.08; + reference_gradient(2, 0) = -0.05; + reference_gradient(2, 1) = 0.02; + reference_gradient(2, 2) = 0.11; + + const mfem::Vector reference_curl = matrix_curl(reference_gradient); + + mfem::Vector physical_field; + mfem::Vector recovered_field; + mfem::Vector physical_test_field; + mfem::Vector physical_curl; + mfem::Vector recovered_curl; + + mapping::MapHCurlFieldToPhysical(context, reference_field, physical_field); + mapping::MapPhysicalFieldToHCurlReference( + context, physical_field, recovered_field + ); + mapping::MapHCurlFieldToPhysical( + context, reference_test_field, physical_test_field + ); + mapping::MapHCurlCurlToPhysical(context, reference_curl, physical_curl); + mapping::MapPhysicalCurlToHCurlReference( + context, physical_curl, recovered_curl + ); + + check_vector(recovered_field, reference_field, curl_tolerance); + check_vector(recovered_curl, reference_curl, curl_tolerance); + + mfem::DenseMatrix temporary(3); + mfem::DenseMatrix physical_gradient(3); + mfem::MultAtB( + context.inverse_mapping_jacobian, reference_gradient, temporary + ); + mfem::Mult(temporary, context.inverse_mapping_jacobian, physical_gradient); + + const mfem::Vector directly_computed_physical_curl = + matrix_curl(physical_gradient); + check_vector( + directly_computed_physical_curl, physical_curl, curl_tolerance + ); + + mfem::DenseMatrix mass_tensor; + mfem::DenseMatrix curl_tensor; + mapping::ComputeHCurlMassTensor(context, mass_tensor); + mapping::ComputeHCurlCurlTensor(context, curl_tensor); + + mfem::Vector mass_action(3); + mass_tensor.Mult(reference_test_field, mass_action); + + const double physical_mass_inner_product = + context.mapping_determinant * (physical_field * physical_test_field); + const double reference_mass_inner_product = reference_field * mass_action; + + CHECK_THAT( + physical_mass_inner_product, + WithinAbs(reference_mass_inner_product, curl_tolerance) + ); + + const mfem::Vector reference_test_curl = make_vector(-0.3, 0.6, 0.2); + mfem::Vector physical_test_curl; + mfem::Vector curl_action(3); + + mapping::MapHCurlCurlToPhysical( + context, reference_test_curl, physical_test_curl + ); + curl_tensor.Mult(reference_test_curl, curl_action); + + const double physical_curl_inner_product = + context.mapping_determinant * (physical_curl * physical_test_curl); + const double reference_curl_inner_product = reference_curl * curl_action; + + CHECK_THAT( + physical_curl_inner_product, + WithinAbs(reference_curl_inner_product, curl_tolerance) + ); +} + +TEST_CASE( + "Element Displacement Data Matches MFEM GridFunction Evaluation", + tags::unit &tags::mapping +) { + constexpr int displacement_order = 2; + constexpr int quadrature_order = 6; + constexpr double value_tolerance = 5.0e-13; + constexpr double gradient_tolerance = 2.0e-12; + constexpr double mapping_tolerance = 3.0e-12; + + auto check_space_ordering = [](const mfem::Ordering::Type space_ordering) { + mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D( + 2, 1, 1, mfem::Element::HEXAHEDRON, 2.0, 1.5, 1.25 + ); + + mfem::H1_FECollection displacement_collection( + displacement_order, dimension + ); + + mfem::FiniteElementSpace displacement_space( + &mesh, &displacement_collection, dimension, space_ordering + ); + + mfem::GridFunction displacement(&displacement_space); + + auto displacement_function = [](const mfem::Vector &position, + mfem::Vector &value) { + const double x = position(0); + const double y = position(1); + const double z = position(2); + + value.SetSize(dimension); + + value(0) = 0.17 + 0.11 * x - 0.07 * y + 0.03 * y * z; + + value(1) = -0.23 + 0.05 * y + 0.09 * z + 0.02 * x * z; + + value(2) = 0.31 - 0.04 * x + 0.08 * z - 0.015 * x * y; + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + dimension, displacement_function + ); + + displacement.ProjectCoefficient(displacement_coefficient); + + mapping::DomainMapperStateless mapper( + {.dimension = dimension, .vacuum_element_attribute = 3}, + make_kelvin_compactification() + ); + + mapping::DomainMapperStateless::Workspace workspace(dimension); + + REQUIRE(displacement_space.GetOrdering() == space_ordering); + REQUIRE(displacement.VectorDim() == dimension); + + for (int element_id = 0; element_id < mesh.GetNE(); ++element_id) { + mfem::ElementTransformation *transformation = + mesh.GetElementTransformation(element_id); + + REQUIRE(transformation != nullptr); + + const mfem::FiniteElement &displacement_element = + *displacement_space.GetFE(element_id); + + mfem::Array element_vdofs; + + mfem::DofTransformation *dof_transformation = + displacement_space.GetElementVDofs(element_id, element_vdofs); + + mfem::Vector element_displacement; + + displacement.GetSubVector(element_vdofs, element_displacement); + + if (dof_transformation != nullptr) { + dof_transformation->InvTransformPrimal(element_displacement); + } + + const mapping::ElementDisplacementData displacement_data = + mapping::ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement + ); + + REQUIRE(displacement_data.GetOrdering() == mfem::Ordering::byNODES); + + const ElementMappingDataOwner element_data(displacement_data); + + const mfem::IntegrationRule &integration_rule = mfem::IntRules.Get( + transformation->GetGeometryType(), quadrature_order + ); + + mfem::Vector shape(displacement_element.GetDof()); + + mfem::DenseMatrix physical_dshape( + displacement_element.GetDof(), dimension + ); + + mfem::Vector computed_value(dimension); + mfem::Vector expected_value(dimension); + + mfem::DenseMatrix computed_gradient(dimension, dimension); + + mfem::DenseMatrix expected_gradient(dimension, dimension); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + + CAPTURE(static_cast(space_ordering), element_id, q); + + transformation->SetIntPoint(&integration_point); + + displacement_element.CalcShape(integration_point, shape); + + displacement_element.CalcPhysDShape( + *transformation, physical_dshape + ); + + displacement_data.GetDofMatrix().MultTranspose( + shape, computed_value + ); + + mfem::MultAtB( + displacement_data.GetDofMatrix(), physical_dshape, + computed_gradient + ); + + /* + * Use MFEM's native evaluation as the authoritative + * interpretation of the GridFunction. + */ + transformation->SetIntPoint(&integration_point); + + displacement.GetVectorValue( + *transformation, integration_point, expected_value + ); + + transformation->SetIntPoint(&integration_point); + + displacement.GetVectorGradient( + *transformation, expected_gradient + ); + + check_vector(computed_value, expected_value, value_tolerance); + + check_matrix( + computed_gradient, expected_gradient, gradient_tolerance + ); + + /* + * Also exercise the complete stateless-mapper path. + * The Cartesian elements are stellar-domain elements, + * so the mapper should produce x + u and I + grad(u). + */ + mapping::MappingPointContext context; + + const mapping::MappingStatus status = mapper.EvaluatePoint( + element_data.Get(), *transformation, integration_point, + workspace, context + ); + + REQUIRE(status == mean_field::mapping::MappingStatus::valid); + + REQUIRE_FALSE(context.compactified); + + mfem::Vector expected_displaced_position( + context.reference_position + ); + + expected_displaced_position += expected_value; + + mfem::DenseMatrix expected_displacement_jacobian( + expected_gradient + ); + + for (int d = 0; d < dimension; ++d) { + expected_displacement_jacobian(d, d) += 1.0; + } + + check_vector( + context.displaced_position, expected_displaced_position, + mapping_tolerance + ); + + check_vector( + context.physical_position, expected_displaced_position, + mapping_tolerance + ); + + check_matrix( + context.displacement_jacobian, + expected_displacement_jacobian, mapping_tolerance + ); + + check_matrix( + context.mapping_jacobian, expected_displacement_jacobian, + mapping_tolerance + ); + + const double expected_determinant = + expected_displacement_jacobian.Det(); + + CHECK_THAT( + context.mapping_determinant, + Catch::Matchers::WithinAbs( + expected_determinant, mapping_tolerance + ) + ); + + REQUIRE(context.mapping_determinant > 0.0); + } + } + }; + + SECTION("Global finite-element-space ordering is byNODES") { + check_space_ordering(mfem::Ordering::byNODES); + } + + SECTION("Global finite-element-space ordering is byVDIM") { + check_space_ordering(mfem::Ordering::byVDIM); + } +} \ No newline at end of file diff --git a/tests/mapping/hdiv_mass_tensor.cpp b/tests/mapping/hdiv_mass_tensor.cpp new file mode 100644 index 0000000..1f82693 --- /dev/null +++ b/tests/mapping/hdiv_mass_tensor.cpp @@ -0,0 +1,454 @@ +#include +#include +#include +#include +#include +#include +#include +#include + +import mean_field; +import test_helpers; +using namespace mean_field; +using Catch::Matchers::WithinAbs; + +namespace { + constexpr int dimension = 3; + + mfem::DenseMatrix make_matrix( + const std::array< + double, + 9> &values + ) { + mfem::DenseMatrix matrix(dimension); + + for (int row = 0; row < dimension; ++row) { + for (int column = 0; column < dimension; ++column) + matrix(row, column) = values[row * dimension + column]; + } + + return matrix; + } + + mfem::DenseMatrix make_identity_matrix() { + mfem::DenseMatrix identity(dimension); + identity = 0.0; + for (int i = 0; i < dimension; ++i) + identity(i, i) = 1.0; + return identity; + } + + mapping::MappingPointContext + make_context(const mfem::DenseMatrix &jacobian) { + mapping::MappingPointContext context; + context.mapping_jacobian = jacobian; + context.mapping_determinant = jacobian.Det(); + context.inverse_mapping_jacobian.SetSize(dimension); + mfem::CalcInverse(jacobian, context.inverse_mapping_jacobian); + context.physical_position.SetSize(dimension); + context.physical_position = 0.0; + return context; + } + + double determinant_variation( + const mfem::DenseMatrix &jacobian, + const mfem::DenseMatrix &jacobian_variation + ) { + mfem::DenseMatrix inverse_jacobian(dimension); + mfem::DenseMatrix product(dimension); + mfem::CalcInverse(jacobian, inverse_jacobian); + mfem::Mult(inverse_jacobian, jacobian_variation, product); + + double trace = 0.0; + for (int i = 0; i < dimension; ++i) + trace += product(i, i); + return jacobian.Det() * trace; + } + + mapping::MappingPointVariation make_variation( + const mfem::DenseMatrix &jacobian, + const mfem::DenseMatrix &jacobian_variation + ) { + mapping::MappingPointVariation variation; + variation.mapping_jacobian_variation = jacobian_variation; + variation.mapping_determinant_variation = + determinant_variation(jacobian, jacobian_variation); + variation.physical_position_variation.SetSize(dimension); + variation.physical_position_variation = 0.0; + return variation; + } + + double matrix_norm(const mfem::DenseMatrix &matrix) { + double norm_squared = 0.0; + + for (int row = 0; row < matrix.Height(); ++row) { + for (int column = 0; column < matrix.Width(); ++column) + norm_squared += matrix(row, column) * matrix(row, column); + } + + return std::sqrt(norm_squared); + } + + double relative_matrix_error( + const mfem::DenseMatrix &computed, + const mfem::DenseMatrix &reference + ) { + REQUIRE(computed.Height() == reference.Height()); + REQUIRE(computed.Width() == reference.Width()); + + mfem::DenseMatrix difference(computed); + difference -= reference; + + return matrix_norm(difference) / + std::max( + matrix_norm(reference), + std::numeric_limits::epsilon() + ); + } + + double matrix_asymmetry(const mfem::DenseMatrix &matrix) { + double asymmetry_squared = 0.0; + + for (int row = 0; row < matrix.Height(); ++row) { + for (int column = 0; column < matrix.Width(); ++column) { + const double difference = + matrix(row, column) - matrix(column, row); + asymmetry_squared += difference * difference; + } + } + + return std::sqrt(asymmetry_squared); + } + + mfem::DenseMatrix centered_mass_tensor_difference( + const mfem::DenseMatrix &jacobian, + const mfem::DenseMatrix &jacobian_variation, + const double step + ) { + mfem::DenseMatrix plus_jacobian(jacobian); + mfem::DenseMatrix minus_jacobian(jacobian); + + for (int row = 0; row < dimension; ++row) { + for (int column = 0; column < dimension; ++column) { + plus_jacobian(row, column) += + step * jacobian_variation(row, column); + minus_jacobian(row, column) -= + step * jacobian_variation(row, column); + } + } + + REQUIRE(plus_jacobian.Det() > 0.0); + REQUIRE(minus_jacobian.Det() > 0.0); + + const mapping::MappingPointContext plus_context = + make_context(plus_jacobian); + const mapping::MappingPointContext minus_context = + make_context(minus_jacobian); + + mfem::DenseMatrix plus_tensor; + mfem::DenseMatrix minus_tensor; + mapping::ComputeHDivMassTensor(plus_context, plus_tensor); + mapping::ComputeHDivMassTensor(minus_context, minus_tensor); + + plus_tensor -= minus_tensor; + plus_tensor *= 1 / (2.0 * step); + return plus_tensor; + } + + void check_zero_matrix( + const mfem::DenseMatrix &matrix, + const double tolerance + ) { + for (int row = 0; row < matrix.Height(); ++row) { + for (int column = 0; column < matrix.Width(); ++column) + CHECK_THAT(matrix(row, column), WithinAbs(0.0, tolerance)); + } + } + + struct TensorVariationCase { + std::string name; + mfem::DenseMatrix jacobian; + mfem::DenseMatrix jacobian_variation; + }; +} // namespace + +TEST_CASE( + "Hdiv Mass Tensor Variation Matches Centered Differences", + tags::unit &tags::transformations +) { + std::vector cases; + + cases.push_back( + {"identity with general variation", make_identity_matrix(), + make_matrix({0.12, -0.07, 0.03, 0.05, -0.09, 0.04, -0.02, 0.08, 0.06})} + ); + + cases.push_back( + {"anisotropic stretch", + make_matrix({1.20, 0.00, 0.00, 0.00, 0.85, 0.00, 0.00, 0.00, 1.10}), + make_matrix({0.08, 0.01, -0.03, 0.02, -0.05, 0.04, 0.01, -0.02, 0.07})} + ); + + cases.push_back( + {"sheared mapping", + make_matrix({1.10, 0.20, -0.05, 0.04, 0.90, 0.12, -0.03, 0.08, 1.15}), + make_matrix( + {0.06, -0.04, 0.02, 0.03, 0.05, -0.07, -0.01, 0.04, -0.02} + )} + ); + + cases.push_back( + {"strong general mapping", + make_matrix({1.35, 0.31, -0.18, -0.12, 0.78, 0.22, 0.09, -0.16, 1.27}), + make_matrix({-0.11, 0.08, 0.05, 0.07, 0.09, -0.04, -0.06, 0.03, 0.12})} + ); + + for (const TensorVariationCase &test_case : cases) { + DYNAMIC_SECTION(test_case.name) { + REQUIRE(test_case.jacobian.Det() > 0.0); + + const mapping::MappingPointContext context = + make_context(test_case.jacobian); + const mapping::MappingPointVariation variation = make_variation( + test_case.jacobian, test_case.jacobian_variation + ); + + mfem::DenseMatrix analytic_variation; + mapping::ComputeHDivMassTensorVariation( + context, variation, analytic_variation + ); + + const mfem::DenseMatrix finite_difference = + centered_mass_tensor_difference( + test_case.jacobian, test_case.jacobian_variation, 1.0e-6 + ); + const double relative_error = + relative_matrix_error(analytic_variation, finite_difference); + const double asymmetry = matrix_asymmetry(analytic_variation); + + INFO("Mapping determinant = " << context.mapping_determinant); + INFO( + "Determinant variation = " + << variation.mapping_determinant_variation + ); + INFO( + "Analytic variation norm = " << matrix_norm(analytic_variation) + ); + INFO( + "Finite-difference variation norm = " + << matrix_norm(finite_difference) + ); + INFO("Relative tensor-variation error = " << relative_error); + INFO("Tensor-variation asymmetry = " << asymmetry); + + CHECK(relative_error < 2.0e-9); + CHECK(asymmetry < 2.0e-14); + } + } +} + +TEST_CASE( + "Hdiv Mass Tensor Variation Has Second Order Centered Difference " + "Convergence", + tags::unit &tags::transformations &tags::convergence +) { + const mfem::DenseMatrix jacobian = + make_matrix({1.18, 0.17, -0.09, -0.04, 0.92, 0.14, 0.07, -0.11, 1.23}); + + const mfem::DenseMatrix jacobian_variation = + make_matrix({0.09, -0.06, 0.04, 0.03, 0.07, -0.05, -0.02, 0.08, -0.03}); + + const mapping::MappingPointContext context = make_context(jacobian); + const mapping::MappingPointVariation variation = + make_variation(jacobian, jacobian_variation); + + mfem::DenseMatrix analytic_variation; + mapping::ComputeHDivMassTensorVariation( + context, variation, analytic_variation + ); + + const std::array steps{4.0e-2, 2.0e-2, 1.0e-2}; + std::array errors{}; + + for (int i = 0; i < static_cast(steps.size()); ++i) { + const mfem::DenseMatrix finite_difference = + centered_mass_tensor_difference( + jacobian, jacobian_variation, steps[i] + ); + errors[i] = + relative_matrix_error(finite_difference, analytic_variation); + INFO("Step = " << steps[i] << ", relative error = " << errors[i]); + } + + const double first_reduction = errors[1] / errors[0]; + const double second_reduction = errors[2] / errors[1]; + + INFO("First error-reduction ratio = " << first_reduction); + INFO("Second error-reduction ratio = " << second_reduction); + + CHECK(first_reduction < 0.30); + CHECK(second_reduction < 0.30); + CHECK(errors[2] < 1.0e-5); +} + +TEST_CASE( + "Hdiv Mass Tensor Variation Vanishes For Translation", + tags::unit &tags::transformations +) { + const mfem::DenseMatrix jacobian = + make_matrix({1.12, 0.08, -0.03, 0.02, 0.94, 0.07, -0.01, 0.05, 1.09}); + + mfem::DenseMatrix zero_jacobian_variation(dimension); + zero_jacobian_variation = 0.0; + + mapping::MappingPointContext context = make_context(jacobian); + mapping::MappingPointVariation variation = + make_variation(jacobian, zero_jacobian_variation); + variation.physical_position_variation.SetSize(dimension); + variation.physical_position_variation(0) = 0.7; + variation.physical_position_variation(1) = -0.4; + variation.physical_position_variation(2) = 0.9; + + mfem::DenseMatrix tensor_variation; + mapping::ComputeHDivMassTensorVariation( + context, variation, tensor_variation + ); + + CHECK_THAT(variation.mapping_determinant_variation, WithinAbs(0.0, 0.0)); + check_zero_matrix(tensor_variation, 1.0e-14); +} + +TEST_CASE( + "Hdiv Mass Tensor Variation Vanishes For Infinitesimal Rotation At " + "Identity", + tags::unit &tags::transformations +) { + const mfem::DenseMatrix identity = make_identity_matrix(); + + const mfem::DenseMatrix rotation_variation = + make_matrix({0.0, -0.30, 0.20, 0.30, 0.0, -0.15, -0.20, 0.15, 0.0}); + + const mapping::MappingPointContext context = make_context(identity); + const mapping::MappingPointVariation variation = + make_variation(identity, rotation_variation); + + mfem::DenseMatrix tensor_variation; + mapping::ComputeHDivMassTensorVariation( + context, variation, tensor_variation + ); + + CHECK_THAT( + variation.mapping_determinant_variation, WithinAbs(0.0, 1.0e-15) + ); + check_zero_matrix(tensor_variation, 1.0e-14); +} + +TEST_CASE( + "Hdiv Mass Tensor Variation Matches Isotropic Scaling At Identity", + tags::unit &tags::transformations +) { + constexpr double scaling_variation = 0.17; + + const mfem::DenseMatrix identity = make_identity_matrix(); + mfem::DenseMatrix jacobian_variation(dimension); + jacobian_variation = 0.0; + for (int i = 0; i < dimension; ++i) + jacobian_variation(i, i) = scaling_variation; + + const mapping::MappingPointContext context = make_context(identity); + const mapping::MappingPointVariation variation = + make_variation(identity, jacobian_variation); + + mfem::DenseMatrix tensor_variation; + mapping::ComputeHDivMassTensorVariation( + context, variation, tensor_variation + ); + + CHECK_THAT( + variation.mapping_determinant_variation, + WithinAbs(3.0 * scaling_variation, 1.0e-14) + ); + + for (int row = 0; row < dimension; ++row) { + for (int column = 0; column < dimension; ++column) { + const double expected = row == column ? -scaling_variation : 0.0; + CHECK_THAT( + tensor_variation(row, column), WithinAbs(expected, 1.0e-14) + ); + } + } +} + +TEST_CASE( + "Hdiv Mass Tensor Variation Symmetrizes Simple Shear At Identity", + tags::unit &tags::transformations +) { + constexpr double shear_variation = 0.23; + + const mfem::DenseMatrix identity = make_identity_matrix(); + mfem::DenseMatrix jacobian_variation(dimension); + jacobian_variation = 0.0; + jacobian_variation(0, 1) = shear_variation; + + const mapping::MappingPointContext context = make_context(identity); + const mapping::MappingPointVariation variation = + make_variation(identity, jacobian_variation); + + mfem::DenseMatrix tensor_variation; + mapping::ComputeHDivMassTensorVariation( + context, variation, tensor_variation + ); + + CHECK_THAT( + variation.mapping_determinant_variation, WithinAbs(0.0, 1.0e-15) + ); + CHECK_THAT(tensor_variation(0, 1), WithinAbs(shear_variation, 1.0e-14)); + CHECK_THAT(tensor_variation(1, 0), WithinAbs(shear_variation, 1.0e-14)); + + for (int row = 0; row < dimension; ++row) { + for (int column = 0; column < dimension; ++column) { + if ((row == 0 && column == 1) || (row == 1 && column == 0)) + continue; + CHECK_THAT(tensor_variation(row, column), WithinAbs(0.0, 1.0e-14)); + } + } +} + +TEST_CASE( + "Mapping Determinant Variation Matches Jacobi Formula", + tags::unit &tags::transformations +) { + const mfem::DenseMatrix jacobian = + make_matrix({1.24, 0.19, -0.07, -0.06, 0.88, 0.16, 0.04, -0.12, 1.19}); + + const mfem::DenseMatrix jacobian_variation = + make_matrix({0.08, -0.03, 0.05, 0.02, 0.06, -0.04, -0.01, 0.07, -0.02}); + + const mapping::MappingPointContext context = make_context(jacobian); + const mapping::MappingPointVariation variation = + make_variation(jacobian, jacobian_variation); + constexpr double difference_step = 1.0e-3; + + mfem::DenseMatrix plus_one(context.mapping_jacobian); + mfem::DenseMatrix plus_two(context.mapping_jacobian); + mfem::DenseMatrix minus_one(context.mapping_jacobian); + mfem::DenseMatrix minus_two(context.mapping_jacobian); + + plus_one.Add(difference_step, variation.mapping_jacobian_variation); + plus_two.Add(2.0 * difference_step, variation.mapping_jacobian_variation); + minus_one.Add(-difference_step, variation.mapping_jacobian_variation); + minus_two.Add(-2.0 * difference_step, variation.mapping_jacobian_variation); + + const double finite_difference = (minus_two.Det() - 8.0 * minus_one.Det() + + 8.0 * plus_one.Det() - plus_two.Det()) / + (12.0 * difference_step); + const double analytic = variation.mapping_determinant_variation; + const double relative_error = std::abs(finite_difference - analytic) / + std::max(std::abs(analytic), 1.0e-14); + + INFO("Analytic determinant variation = " << analytic); + INFO("Finite-difference determinant variation = " << finite_difference); + INFO("Relative determinant-variation error = " << relative_error); + + CHECK(relative_error < 2.0e-11); +} \ No newline at end of file diff --git a/tests/operators/contexts/barotropic_closure_linearization_context.cpp b/tests/operators/contexts/barotropic_closure_linearization_context.cpp new file mode 100644 index 0000000..e6d9ec0 --- /dev/null +++ b/tests/operators/contexts/barotropic_closure_linearization_context.cpp @@ -0,0 +1,297 @@ +#include + +#include +#include + +import mean_field; +import test_helpers; + +namespace barotropic_closure_context_test_utils { + mfem::Vector project_field( + mfem::ParFiniteElementSpace &finiteElementSpace, + mfem::Coefficient &coefficient + ) { + mfem::ParGridFunction field(&finiteElementSpace); + + field.ProjectCoefficient(coefficient); + + mfem::Vector trueVector; + field.GetTrueDofs(trueVector); + + return trueVector; + } + + mfem::Vector make_density(const mean_field::fem::FEM &f) { + mfem::FunctionCoefficient coefficient([](const mfem::Vector &position) { + return 0.55 + 0.025 * position(0) - 0.010 * position(1); + }); + + return project_field(*f.densityFes, coefficient); + } + + mfem::Vector make_enthalpy(const mean_field::fem::FEM &f) { + mfem::FunctionCoefficient coefficient([](const mfem::Vector &position) { + return 0.90 + 0.020 * position(0) - 0.010 * position(1) + + 0.005 * position(2); + }); + + return project_field(*f.enthalpyFes, coefficient); + } +} // namespace barotropic_closure_context_test_utils + +TEST_CASE( + "Barotropic Closure Context Tracks Independent Revisions", + tags::barotrope &tags::closure &tags::hydro &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + mean_field::operators::context::barotropic:: + BarotropicClosureLinearizationContext context( + f, *f.domainMapperStateless, barotrope + ); + + mfem::Vector density = + barotropic_closure_context_test_utils::make_density(f); + + mfem::Vector enthalpy = + barotropic_closure_context_test_utils::make_enthalpy(f); + + mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.0); + + mean_field::operators::context::barotropic::BarotropicClosureRevisions + revisions{.density = 3, .enthalpy = 5, .displacement = 7}; + + CHECK_FALSE(context.IsPrepared()); + CHECK(context.GetPreparationCount() == 0); + + context.Prepare(density, enthalpy, displacement, revisions); + + REQUIRE(context.IsPrepared()); + + CHECK(context.MatchesRevisions(revisions)); + CHECK(context.GetRevisions() == revisions); + CHECK(context.GetPreparationCount() == 1); + + CHECK(context.GetOperator().GetPreparationCount() == 1); + + context.Prepare(density, enthalpy, displacement, revisions); + + CHECK(context.GetPreparationCount() == 1); + + const double frozenDensityValue = context.GetBaseDensityTrue()(0); + + density(0) += 0.125; + + CHECK(context.GetBaseDensityTrue()(0) == frozenDensityValue); + + context.Prepare(density, enthalpy, displacement, revisions); + + CHECK(context.GetPreparationCount() == 1); + CHECK(context.GetBaseDensityTrue()(0) == frozenDensityValue); + + ++revisions.density; + + context.Prepare(density, enthalpy, displacement, revisions); + + CHECK(context.GetPreparationCount() == 2); + CHECK(context.GetBaseDensityTrue()(0) == density(0)); + + enthalpy(0) += 0.050; + ++revisions.enthalpy; + + context.Prepare(density, enthalpy, displacement, revisions); + + CHECK(context.GetPreparationCount() == 3); + CHECK(context.GetBaseEnthalpyTrue()(0) == enthalpy(0)); + + displacement = gravity_prepared_test_utils::make_displacement(f, 1.0); + + ++revisions.displacement; + + context.Prepare(density, enthalpy, displacement, revisions); + + CHECK(context.GetPreparationCount() == 4); + CHECK(context.GetRevisions() == revisions); + CHECK(context.MatchesRevisions(revisions)); + + CHECK(context.GetOperator().GetPreparationCount() == 4); +} + +TEST_CASE( + "Barotropic Closure Context Reprepares A Consistent Frozen State", + tags::barotrope &tags::closure &tags::hydro &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + mean_field::operators::context::barotropic:: + BarotropicClosureLinearizationContext context( + f, *f.domainMapperStateless, barotrope + ); + + const mfem::Vector density = + barotropic_closure_context_test_utils::make_density(f); + + const mfem::Vector enthalpy = + barotropic_closure_context_test_utils::make_enthalpy(f); + + const mfem::Vector identityDisplacement = + gravity_prepared_test_utils::make_displacement(f, 0.0); + + const mfem::Vector densityVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.37 + ); + + const mfem::Vector enthalpyVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), 0.71 + ); + + const mfem::Vector displacementVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.displacementFes->GetTrueVSize(), 0.37 + ); + + mean_field::operators::context::barotropic::BarotropicClosureRevisions + revisions{.density = 11, .enthalpy = 13, .displacement = 17}; + + context.Prepare(density, enthalpy, identityDisplacement, revisions); + + mfem::Vector initialResidual; + mfem::Vector initialAction; + + context.BuildResidual(initialResidual); + + context.GetOperator().Mult( + densityVariation, enthalpyVariation, displacementVariation, + initialAction + ); + + mfem::Vector changedDensity(density); + changedDensity.Add(0.025, densityVariation); + + mfem::Vector changedEnthalpy(enthalpy); + changedEnthalpy.Add(0.015, enthalpyVariation); + + const mfem::Vector deformedDisplacement = + gravity_prepared_test_utils::make_displacement(f, 1.0); + + context.Prepare( + changedDensity, changedEnthalpy, deformedDisplacement, revisions + ); + + mfem::Vector unchangedResidual; + mfem::Vector unchangedAction; + + context.BuildResidual(unchangedResidual); + + context.GetOperator().Mult( + densityVariation, enthalpyVariation, displacementVariation, + unchangedAction + ); + + const MPI_Comm communicator = f.mesh->GetComm(); + + CHECK(context.GetPreparationCount() == 1); + + CHECK( + gravity_prepared_test_utils::relative_error( + unchangedResidual, initialResidual, communicator + ) < 5.0e-15 + ); + + CHECK( + gravity_prepared_test_utils::relative_error( + unchangedAction, initialAction, communicator + ) < 5.0e-15 + ); + + ++revisions.density; + ++revisions.enthalpy; + ++revisions.displacement; + + context.Prepare( + changedDensity, changedEnthalpy, deformedDisplacement, revisions + ); + + mfem::Vector preparedResidual; + mfem::Vector preparedAction; + + context.BuildResidual(preparedResidual); + + context.GetOperator().Mult( + densityVariation, enthalpyVariation, displacementVariation, + preparedAction + ); + + mfem::Vector referenceResidual; + mfem::Vector referenceDensityAction; + mfem::Vector referenceEnthalpyAction; + mfem::Vector referenceDisplacementAction; + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, changedDensity, changedEnthalpy, + deformedDisplacement, referenceResidual + ); + + mean_field::operators::kernels::apply_barotropic_closure_density_action( + f, *f.domainMapperStateless, barotrope, densityVariation, + deformedDisplacement, referenceDensityAction + ); + + mean_field::operators::kernels::apply_barotropic_closure_enthalpy_action( + f, *f.domainMapperStateless, barotrope, changedEnthalpy, + enthalpyVariation, deformedDisplacement, referenceEnthalpyAction + ); + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, changedDensity, + changedEnthalpy, deformedDisplacement, displacementVariation, + referenceDisplacementAction + ); + + mfem::Vector referenceAction(referenceDensityAction); + referenceAction += referenceEnthalpyAction; + referenceAction += referenceDisplacementAction; + const double residualError = gravity_prepared_test_utils::relative_error( + preparedResidual, referenceResidual, communicator + ); + + const double actionError = gravity_prepared_test_utils::relative_error( + preparedAction, referenceAction, communicator + ); + + const double residualChange = gravity_prepared_test_utils::relative_error( + preparedResidual, initialResidual, communicator + ); + + const double actionChange = gravity_prepared_test_utils::relative_error( + preparedAction, initialAction, communicator + ); + + INFO("Prepared-context residual error = " << residualError); + + INFO("Prepared-context Jacobian error = " << actionError); + + INFO("Residual change after valid revision = " << residualChange); + + INFO("Jacobian change after valid revision = " << actionChange); + + CHECK(context.GetPreparationCount() == 2); + CHECK(residualError < 5.0e-12); + CHECK(actionError < 5.0e-12); + CHECK(residualChange > 1.0e-6); + CHECK(actionChange > 1.0e-6); +} \ No newline at end of file diff --git a/tests/operators/contexts/gravity_field_context.cpp b/tests/operators/contexts/gravity_field_context.cpp new file mode 100644 index 0000000..10218ba --- /dev/null +++ b/tests/operators/contexts/gravity_field_context.cpp @@ -0,0 +1,306 @@ +#include +#include + +import mean_field; +import test_helpers; + +using namespace mean_field; +namespace prepared_test = gravity_prepared_test_utils; +namespace gravity_context = operators::context::gravity_field; + +TEST_CASE( + "Gravity Field Linearization Context Applies Selective Invalidation", + tags::integration &tags::gravity &tags::contexts +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + gravity_context::GravityFieldLinearizationContext context( + f, *f.domainMapperStateless + ); + + mfem::Vector density = prepared_test::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.11 + ); + mfem::Vector displacement = prepared_test::make_displacement(f, 0.0); + mfem::Vector gravity_gradient = prepared_test::make_deterministic_vector( + f.gravityFluxFes->GetTrueVSize(), 0.37 + ); + mfem::Vector gravity_potential = prepared_test::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), 0.63 + ); + + gravity_context::GravityFieldRevisions revisions; + + auto make_state = [&]() { + return gravity_context::GravityFieldStateView{ + .density = density, + .displacement = displacement, + .gravity_gradient = gravity_gradient, + .gravity_potential = gravity_potential + }; + }; + + REQUIRE_FALSE(context.IsPrepared()); + + const gravity_context::GravityFieldPreparationReport initial_report = + context.Prepare(make_state(), revisions); + + REQUIRE(context.IsPrepared()); + CHECK(initial_report.geometry.reconstructed_operators); + CHECK(initial_report.geometry.rebuilt_mass_operator); + CHECK(initial_report.geometry.rebuilt_source_operator); + CHECK(initial_report.geometry.refreshed_variation_state); + CHECK(initial_report.updated_density); + CHECK(initial_report.updated_gravity_gradient); + CHECK(initial_report.DidAnyWork()); + + const auto initial_mass_preparations = + context.GetGeometryContext().GetMassOperator().GetPreparationCount(); + const auto initial_source_preparations = + context.GetGeometryContext().GetSourceOperator().GetPreparationCount(); + + const gravity_context::GravityFieldPreparationReport repeated_report = + context.Prepare(make_state(), revisions); + + CHECK_FALSE(repeated_report.DidAnyWork()); + CHECK( + context.GetGeometryContext().GetMassOperator().GetPreparationCount() == + initial_mass_preparations + ); + CHECK( + context.GetGeometryContext() + .GetSourceOperator() + .GetPreparationCount() == initial_source_preparations + ); + + gravity_potential(0) += 0.25; + ++revisions.gravity_potential.value; + + const gravity_context::GravityFieldPreparationReport potential_report = + context.Prepare(make_state(), revisions); + + CHECK_FALSE(potential_report.DidAnyWork()); + CHECK( + context.GetRevisions().gravity_potential == revisions.gravity_potential + ); + + density(0) += 0.5; + ++revisions.density.value; + + const gravity_context::GravityFieldPreparationReport density_report = + context.Prepare(make_state(), revisions); + + CHECK(density_report.updated_density); + CHECK_FALSE(density_report.updated_gravity_gradient); + CHECK_FALSE(density_report.geometry.DidAnyWork()); + CHECK(context.GetDensity()(0) == density(0)); + + gravity_gradient(0) -= 0.4; + ++revisions.gravity_gradient.value; + + const gravity_context::GravityFieldPreparationReport gradient_report = + context.Prepare(make_state(), revisions); + + CHECK_FALSE(gradient_report.updated_density); + CHECK(gradient_report.updated_gravity_gradient); + CHECK_FALSE(gradient_report.geometry.DidAnyWork()); + CHECK(context.GetGravityGradient()(0) == gravity_gradient(0)); + + displacement = prepared_test::make_displacement(f, 1.0); + ++revisions.displacement.value; + + const gravity_context::GravityFieldPreparationReport displacement_report = + context.Prepare(make_state(), revisions); + + CHECK_FALSE(displacement_report.geometry.reconstructed_operators); + CHECK(displacement_report.geometry.rebuilt_mass_operator); + CHECK(displacement_report.geometry.rebuilt_source_operator); + CHECK(displacement_report.geometry.refreshed_variation_state); + CHECK_FALSE(displacement_report.updated_density); + CHECK_FALSE(displacement_report.updated_gravity_gradient); + CHECK( + context.GetGeometryContext().GetMassOperator().GetPreparationCount() == + initial_mass_preparations + 1 + ); + CHECK( + context.GetGeometryContext() + .GetSourceOperator() + .GetPreparationCount() == initial_source_preparations + 1 + ); + + ++revisions.discretization.value; + + const gravity_context::GravityFieldPreparationReport discretization_report = + context.Prepare(make_state(), revisions); + + CHECK(discretization_report.geometry.reconstructed_operators); + CHECK(discretization_report.geometry.rebuilt_mass_operator); + CHECK(discretization_report.geometry.rebuilt_source_operator); + CHECK(discretization_report.updated_density); + CHECK(discretization_report.updated_gravity_gradient); + CHECK( + context.GetGeometryContext().GetMassOperator().GetPreparationCount() == + 1 + ); + CHECK( + context.GetGeometryContext() + .GetSourceOperator() + .GetPreparationCount() == 1 + ); +} + +TEST_CASE( + "Gravity Field Linearization Context Owns Frozen Base Fields", + tags::integration &tags::gravity &tags::contexts +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + gravity_context::GravityFieldLinearizationContext context( + f, *f.domainMapperStateless + ); + + mfem::Vector density = prepared_test::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.13 + ); + mfem::Vector displacement = prepared_test::make_displacement(f, 0.4); + mfem::Vector gravity_gradient = prepared_test::make_deterministic_vector( + f.gravityFluxFes->GetTrueVSize(), 0.47 + ); + mfem::Vector gravity_potential = prepared_test::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), 0.71 + ); + + gravity_context::GravityFieldRevisions revisions; + + context.Prepare( + {.density = density, + .displacement = displacement, + .gravity_gradient = gravity_gradient, + .gravity_potential = gravity_potential}, + revisions + ); + + const mfem::Vector frozen_density = context.GetDensity(); + const mfem::Vector frozen_displacement = + context.GetGeometryContext().GetDisplacement(); + const mfem::Vector frozen_gravity_gradient = context.GetGravityGradient(); + + density = 0.0; + displacement = 0.0; + gravity_gradient = 0.0; + gravity_potential = 0.0; + + CHECK( + prepared_test::relative_error( + context.GetDensity(), frozen_density, f.mesh->GetComm() + ) == 0.0 + ); + CHECK( + prepared_test::relative_error( + context.GetGeometryContext().GetDisplacement(), frozen_displacement, + f.displacementFes->GetComm() + ) == 0.0 + ); + CHECK( + prepared_test::relative_error( + context.GetGravityGradient(), frozen_gravity_gradient, + f.gravityFluxFes->GetComm() + ) == 0.0 + ); + + const gravity_context::GravityFieldPreparationReport + unchanged_revision_report = context.Prepare( + {.density = density, + .displacement = displacement, + .gravity_gradient = gravity_gradient, + .gravity_potential = gravity_potential}, + revisions + ); + + CHECK_FALSE(unchanged_revision_report.DidAnyWork()); + CHECK( + prepared_test::relative_error( + context.GetDensity(), frozen_density, f.mesh->GetComm() + ) == 0.0 + ); + CHECK( + prepared_test::relative_error( + context.GetGeometryContext().GetDisplacement(), frozen_displacement, + f.displacementFes->GetComm() + ) == 0.0 + ); + CHECK( + prepared_test::relative_error( + context.GetGravityGradient(), frozen_gravity_gradient, + f.gravityFluxFes->GetComm() + ) == 0.0 + ); +} + +TEST_CASE( + "Gravity Field Geometry Contexts Have Independent Prepared State", + tags::integration &tags::gravity &tags::contexts +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + gravity_context::GravityFieldGeometryContext first_context( + f, *f.domainMapperStateless + ); + gravity_context::GravityFieldGeometryContext second_context( + f, *f.domainMapperStateless + ); + + const mfem::Vector first_displacement = + prepared_test::make_displacement(f, 0.0); + const mfem::Vector second_displacement = + prepared_test::make_displacement(f, 1.0); + const mfem::Vector gravity_gradient = + prepared_test::make_deterministic_vector( + f.gravityFluxFes->GetTrueVSize(), 0.35 + ); + + first_context.Prepare(first_displacement, {.value = 0}, {.value = 0}); + second_context.Prepare(second_displacement, {.value = 0}, {.value = 0}); + + mfem::Vector first_action; + mfem::Vector second_action_before; + mfem::Vector second_action_after; + + first_context.GetMassOperator().Mult(gravity_gradient, first_action); + second_context.GetMassOperator().Mult( + gravity_gradient, second_action_before + ); + + const mfem::Vector updated_first_displacement = + prepared_test::make_displacement(f, 0.6); + first_context.Prepare( + updated_first_displacement, {.value = 0}, {.value = 1} + ); + + second_context.GetMassOperator().Mult( + gravity_gradient, second_action_after + ); + + const MPI_Comm communicator = f.gravityFluxFes->GetComm(); + const double independent_context_error = prepared_test::relative_error( + second_action_after, second_action_before, communicator + ); + const double distinct_geometry_difference = prepared_test::relative_error( + first_action, second_action_before, communicator + ); + + INFO( + "Second-context change after preparing first context = " + << independent_context_error + ); + INFO( + "Difference between independently prepared geometries = " + << distinct_geometry_difference + ); + + CHECK(independent_context_error < 2.0e-14); + CHECK(distinct_geometry_difference > 1.0e-5); +} diff --git a/tests/operators/contexts/hydrostatic_equilibrium_context.cpp b/tests/operators/contexts/hydrostatic_equilibrium_context.cpp new file mode 100644 index 0000000..ce8a580 --- /dev/null +++ b/tests/operators/contexts/hydrostatic_equilibrium_context.cpp @@ -0,0 +1,382 @@ +#include +#include + +import mean_field; +import test_helpers; + +namespace hydrostatic_context_test_utils { + mean_field::operators::context::hydrostatic:: + HydrostaticEquilibriumDependencies + make_dependencies() { + return { + .discretization = {.identity = 101, .revision = 2}, + .enthalpy = {.identity = 103, .revision = 3}, + .gravityPotential = {.identity = 107, .revision = 5}, + .displacement = {.identity = 109, .revision = 7}, + .rotation = {.identity = 113, .revision = 11}, + .bernoulliConstant = {.identity = 127, .revision = 13} + }; + } + + mean_field::operators::context::hydrostatic::HydrostaticEquilibriumStateView + make_state( + const mfem::Vector &enthalpy, + const mfem::Vector &gravityPotential, + const mfem::Vector &displacement, + const double bernoulliConstant + ) { + return { + .enthalpy = enthalpy, + .gravityPotential = gravityPotential, + .displacement = displacement, + .bernoulliConstant = bernoulliConstant + }; + } + + void check_base_only( + const mean_field::operators::context::hydrostatic:: + HydrostaticPreparationReport &report + ) { + CHECK_FALSE(report.preparedStaticDependencies); + CHECK_FALSE(report.preparedGeometryState); + CHECK_FALSE(report.preparedRotationDependencies); + CHECK(report.preparedBaseState); + } +} // namespace hydrostatic_context_test_utils + +TEST_CASE( + "Hydrostatic Context Applies Selective Invalidation", + tags::barotrope &tags::contexts &tags::hydro &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + mean_field::operators::context::hydrostatic::HydrostaticEquilibriumContext + context(f, *f.domainMapperStateless); + + mfem::Vector enthalpy = + gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), 0.17 + ); + + mfem::Vector gravityPotential = + gravity_prepared_test_utils::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), 0.31 + ); + + mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.35); + + double bernoulliConstant = 0.73; + + mean_field::operators::context::hydrostatic:: + HydrostaticEquilibriumDependencies dependencies = + hydrostatic_context_test_utils::make_dependencies(); + + CHECK_FALSE(context.IsPrepared()); + CHECK_FALSE(context.MatchesDependencies(dependencies)); + + const auto initialStatistics = context.GetPreparationStatistics(); + + CHECK(initialStatistics.staticPreparations == 0); + CHECK(initialStatistics.geometryPreparations == 0); + CHECK(initialStatistics.rotationPreparations == 0); + CHECK(initialStatistics.baseStatePreparations == 0); + + const auto initialReport = context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + REQUIRE(context.IsPrepared()); + CHECK(context.MatchesDependencies(dependencies)); + CHECK(context.GetDependencies() == dependencies); + + CHECK(initialReport.preparedStaticDependencies); + CHECK(initialReport.preparedGeometryState); + CHECK(initialReport.preparedRotationDependencies); + CHECK(initialReport.preparedBaseState); + CHECK(initialReport.updatedEnthalpy); + CHECK(initialReport.updatedGravityPotential); + CHECK(initialReport.updatedDisplacement); + CHECK(initialReport.updatedBernoulliConstant); + CHECK(initialReport.DidAnyWork()); + + const mfem::Vector frozenEnthalpy = context.GetBaseEnthalpyTrue(); + + const mfem::Vector frozenGravityPotential = + context.GetBaseGravityPotentialTrue(); + + const mfem::Vector frozenDisplacement = context.GetDisplacementTrue(); + + const double frozenBernoulliConstant = context.GetBernoulliConstant(); + + enthalpy(0) += 0.125; + gravityPotential(0) -= 0.075; + displacement(0) += 0.050; + bernoulliConstant += 0.20; + + const auto repeatedReport = context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + CHECK_FALSE(repeatedReport.DidAnyWork()); + CHECK_FALSE(repeatedReport.updatedEnthalpy); + CHECK_FALSE(repeatedReport.updatedGravityPotential); + CHECK_FALSE(repeatedReport.updatedDisplacement); + CHECK_FALSE(repeatedReport.updatedBernoulliConstant); + + const MPI_Comm communicator = f.mesh->GetComm(); + + CHECK( + gravity_prepared_test_utils::relative_error( + context.GetBaseEnthalpyTrue(), frozenEnthalpy, communicator + ) == 0.0 + ); + + CHECK( + gravity_prepared_test_utils::relative_error( + context.GetBaseGravityPotentialTrue(), frozenGravityPotential, + communicator + ) == 0.0 + ); + + CHECK( + gravity_prepared_test_utils::relative_error( + context.GetDisplacementTrue(), frozenDisplacement, communicator + ) == 0.0 + ); + + CHECK(context.GetBernoulliConstant() == frozenBernoulliConstant); + + ++dependencies.enthalpy.revision; + + const auto enthalpyReport = context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + hydrostatic_context_test_utils::check_base_only(enthalpyReport); + + CHECK(enthalpyReport.updatedEnthalpy); + CHECK_FALSE(enthalpyReport.updatedGravityPotential); + CHECK_FALSE(enthalpyReport.updatedDisplacement); + CHECK_FALSE(enthalpyReport.updatedBernoulliConstant); + CHECK(context.GetBaseEnthalpyTrue()(0) == enthalpy(0)); + + ++dependencies.gravityPotential.revision; + + const auto gravityPotentialReport = context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + hydrostatic_context_test_utils::check_base_only(gravityPotentialReport); + + CHECK_FALSE(gravityPotentialReport.updatedEnthalpy); + CHECK(gravityPotentialReport.updatedGravityPotential); + CHECK_FALSE(gravityPotentialReport.updatedDisplacement); + CHECK_FALSE(gravityPotentialReport.updatedBernoulliConstant); + + CHECK(context.GetBaseGravityPotentialTrue()(0) == gravityPotential(0)); + + ++dependencies.bernoulliConstant.revision; + + const auto bernoulliReport = context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + hydrostatic_context_test_utils::check_base_only(bernoulliReport); + + CHECK_FALSE(bernoulliReport.updatedEnthalpy); + CHECK_FALSE(bernoulliReport.updatedGravityPotential); + CHECK_FALSE(bernoulliReport.updatedDisplacement); + CHECK(bernoulliReport.updatedBernoulliConstant); + + CHECK(context.GetBernoulliConstant() == bernoulliConstant); + + ++dependencies.rotation.revision; + + const auto rotationReport = context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + CHECK_FALSE(rotationReport.preparedStaticDependencies); + CHECK_FALSE(rotationReport.preparedGeometryState); + CHECK(rotationReport.preparedRotationDependencies); + CHECK(rotationReport.preparedBaseState); + CHECK_FALSE(rotationReport.updatedEnthalpy); + CHECK_FALSE(rotationReport.updatedGravityPotential); + CHECK_FALSE(rotationReport.updatedDisplacement); + CHECK_FALSE(rotationReport.updatedBernoulliConstant); + + ++dependencies.displacement.revision; + + const auto displacementReport = context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + CHECK_FALSE(displacementReport.preparedStaticDependencies); + + CHECK(displacementReport.preparedGeometryState); + CHECK(displacementReport.preparedRotationDependencies); + CHECK(displacementReport.preparedBaseState); + CHECK_FALSE(displacementReport.updatedEnthalpy); + CHECK_FALSE(displacementReport.updatedGravityPotential); + CHECK(displacementReport.updatedDisplacement); + CHECK_FALSE(displacementReport.updatedBernoulliConstant); + + CHECK(context.GetDisplacementTrue()(0) == displacement(0)); + + ++dependencies.discretization.revision; + + const auto discretizationReport = context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + CHECK(discretizationReport.preparedStaticDependencies); + CHECK(discretizationReport.preparedGeometryState); + CHECK(discretizationReport.preparedRotationDependencies); + CHECK(discretizationReport.preparedBaseState); + CHECK(discretizationReport.updatedEnthalpy); + CHECK(discretizationReport.updatedGravityPotential); + CHECK(discretizationReport.updatedDisplacement); + CHECK(discretizationReport.updatedBernoulliConstant); + + const auto finalStatistics = context.GetPreparationStatistics(); + + CHECK(finalStatistics.staticPreparations == 2); + CHECK(finalStatistics.geometryPreparations == 3); + CHECK(finalStatistics.rotationPreparations == 4); + CHECK(finalStatistics.baseStatePreparations == 7); +} + +TEST_CASE( + "Hydrostatic Context Uses Identity In Every Dependency", + tags::barotrope &tags::contexts &tags::hydro &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + mean_field::operators::context::hydrostatic::HydrostaticEquilibriumContext + context(f, *f.domainMapperStateless); + + mfem::Vector enthalpy = + gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), 0.23 + ); + + const mfem::Vector gravityPotential = + gravity_prepared_test_utils::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), 0.41 + ); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.60); + + constexpr double bernoulliConstant = 0.81; + + mean_field::operators::context::hydrostatic:: + HydrostaticEquilibriumDependencies dependencies = + hydrostatic_context_test_utils::make_dependencies(); + + const auto preparedEnthalpyDependency = dependencies.enthalpy; + + auto olderSameIdentity = preparedEnthalpyDependency; + --olderSameIdentity.revision; + + auto resetNewIdentity = preparedEnthalpyDependency; + ++resetNewIdentity.identity; + resetNewIdentity.revision = 0; + + CHECK_FALSE(olderSameIdentity.CanFollow(preparedEnthalpyDependency)); + + CHECK(resetNewIdentity.CanFollow(preparedEnthalpyDependency)); + + context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + const mfem::Vector firstFrozenEnthalpy = context.GetBaseEnthalpyTrue(); + + enthalpy(0) += 0.33; + + const auto sameStampReport = context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + CHECK_FALSE(sameStampReport.DidAnyWork()); + CHECK(context.GetBaseEnthalpyTrue()(0) == firstFrozenEnthalpy(0)); + + ++dependencies.enthalpy.identity; + dependencies.enthalpy.revision = 0; + + const auto newIdentityReport = context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + hydrostatic_context_test_utils::check_base_only(newIdentityReport); + + CHECK(newIdentityReport.updatedEnthalpy); + CHECK(context.GetBaseEnthalpyTrue()(0) == enthalpy(0)); + CHECK(context.MatchesDependencies(dependencies)); + + ++dependencies.rotation.identity; + dependencies.rotation.revision = 0; + + const auto newRotationIdentityReport = context.Prepare( + hydrostatic_context_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies + ); + + CHECK_FALSE(newRotationIdentityReport.preparedStaticDependencies); + + CHECK_FALSE(newRotationIdentityReport.preparedGeometryState); + + CHECK(newRotationIdentityReport.preparedRotationDependencies); + + CHECK(newRotationIdentityReport.preparedBaseState); + + const auto statistics = context.GetPreparationStatistics(); + + CHECK(statistics.staticPreparations == 1); + CHECK(statistics.geometryPreparations == 1); + CHECK(statistics.rotationPreparations == 2); + CHECK(statistics.baseStatePreparations == 3); +} diff --git a/tests/operators/gravity_field.cpp b/tests/operators/gravity_field.cpp new file mode 100644 index 0000000..c3049e8 --- /dev/null +++ b/tests/operators/gravity_field.cpp @@ -0,0 +1,4483 @@ +#include "profile.h" +#include +#include +#include +#include +#include + +import mean_field; +import test_helpers; + +using namespace mean_field; +using Catch::Matchers::WithinAbs; + +namespace { + namespace blocks = utils::blocks; + using form = blocks::gravity_field_form; + + constexpr auto density_block = + blocks::get_value_block(blocks::density_field.mass_term); + constexpr auto displacement_block = + blocks::get_value_block(blocks::displacement_field.geometry_term); + constexpr auto gravity_gradient_block = + blocks::get_value_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_potential_block = + blocks::get_value_block(blocks::gravity_field.poisson_term); + constexpr auto gravity_gradient_residual_block = + blocks::get_residual_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_poisson_residual_block = + blocks::get_residual_block(blocks::gravity_field.poisson_term); + + blocks::form_layout make_gravity_layout(const fem::FEM &f) { + const std::array value_sizes{ + f.densityFes->GetTrueVSize(), f.displacementFes->GetTrueVSize(), + f.gravityFluxFes->GetTrueVSize(), + f.gravityPotentialFes->GetTrueVSize() + }; + + const std::array residual_sizes{ + f.gravityFluxFes->GetTrueVSize(), + f.gravityPotentialFes->GetTrueVSize() + }; + + return blocks::form_layout(value_sizes, residual_sizes); + } + + template + void set_block( + mfem::Vector &vector, + const mfem::Array &offsets, + const Block block, + const mfem::Vector &values + ) { + const int block_id = block; + const int begin = offsets[block_id]; + const int size = offsets[block_id + 1] - begin; + + REQUIRE(values.Size() == size); + for (int i = 0; i < size; ++i) + vector(begin + i) = values(i); + } + + template + mfem::Vector get_block( + const mfem::Vector &vector, + const mfem::Array &offsets, + const Block block + ) { + const int block_id = block; + const int begin = offsets[block_id]; + const int size = offsets[block_id + 1] - begin; + + mfem::Vector result(size); + for (int i = 0; i < size; ++i) + result(i) = vector(begin + i); + return result; + } + + mfem::Vector make_test_vector( + const int size, + const double phase + ) { + mfem::Vector vector(size); + for (int i = 0; i < size; ++i) + vector(i) = + 0.4 * std::sin(0.37 * static_cast(i + 1) + phase) + + 0.2 * std::cos(0.19 * static_cast(i + 1) - phase); + return vector; + } + + mfem::Vector make_displacement(const fem::FEM &f) { + auto displacement_function = [](const mfem::Vector &position, + mfem::Vector &value) { + value.SetSize(3); + value(0) = 0.015 * position(0) + 0.004 * position(1); + value(1) = -0.003 * position(0) + 0.012 * position(1); + value(2) = -0.008 * position(2); + }; + + mfem::VectorFunctionCoefficient coefficient(3, displacement_function); + mfem::ParGridFunction displacement(f.displacementFes.get()); + mfem::Vector displacement_true; + + displacement.ProjectCoefficient(coefficient); + displacement.GetTrueDofs(displacement_true); + return displacement_true; + } + + mfem::Vector make_constant_density( + const fem::FEM &f, + const double value + ) { + mfem::ConstantCoefficient coefficient(value); + mfem::ParGridFunction density(f.densityFes.get()); + mfem::Vector density_true; + + density.ProjectCoefficient(coefficient); + density.GetTrueDofs(density_true); + return density_true; + } + + mfem::Vector make_vacuum_density( + const fem::FEM &f, + const double value + ) { + mfem::ParGridFunction density(f.densityFes.get()); + density = 0.0; + + mfem::Array element_dofs; + mfem::Vector element_values; + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + if (f.mesh->GetAttribute(element_id) != + f.domainMapperStateless->GetVacuumElementAttribute()) + continue; + + f.densityFes->GetElementDofs(element_id, element_dofs); + element_values.SetSize(element_dofs.Size()); + element_values = value; + density.SetSubVector(element_dofs, element_values); + } + + mfem::Vector density_true; + density.GetTrueDofs(density_true); + return density_true; + } + + double relative_difference( + const mfem::Vector &lhs, + const mfem::Vector &rhs + ) { + REQUIRE(lhs.Size() == rhs.Size()); + + mfem::Vector difference(lhs); + difference -= rhs; + + return difference.Norml2() / + std::max({lhs.Norml2(), rhs.Norml2(), 1.0e-14}); + } + + mfem::Vector make_core_supported_gravity_gradient(const fem::FEM &f) { + constexpr double support_radius = 0.15 * utils::RADIUS; + constexpr double support_radius_squared = + support_radius * support_radius; + + auto field_function = [](const mfem::Vector &position, + mfem::Vector &value) { + const double radius_squared = position * position; + + value.SetSize(3); + value = 0.0; + + if (radius_squared >= support_radius_squared) + return; + + const double normalized_radius_squared = + radius_squared / support_radius_squared; + const double envelope = + std::pow(1.0 - normalized_radius_squared, 3.0); + + value(0) = envelope; + value(1) = -0.4 * envelope; + value(2) = 0.7 * envelope; + }; + + mfem::VectorFunctionCoefficient coefficient(3, field_function); + mfem::ParGridFunction gravity_gradient(f.gravityFluxFes.get()); + mfem::Vector gravity_gradient_true; + + gravity_gradient.ProjectCoefficient(coefficient); + gravity_gradient.GetTrueDofs(gravity_gradient_true); + return gravity_gradient_true; + } + + double global_norm( + const mfem::Vector &vector, + MPI_Comm communicator + ) { + REQUIRE(vector.Size() > 0); + const double local_norm_squared = vector * vector; + double global_norm_squared = 0.0; + + MPI_Allreduce( + &local_norm_squared, &global_norm_squared, 1, MPI_DOUBLE, MPI_SUM, + communicator + ); + return std::sqrt(global_norm_squared); + } + + double global_relative_difference( + const mfem::Vector &lhs, + const mfem::Vector &rhs, + MPI_Comm communicator + ) { + REQUIRE(lhs.Size() == rhs.Size()); + + mfem::Vector difference(lhs); + difference -= rhs; + + const double difference_norm = global_norm(difference, communicator); + const double lhs_norm = global_norm(lhs, communicator); + const double rhs_norm = global_norm(rhs, communicator); + + return difference_norm / std::max({lhs_norm, rhs_norm, 1.0e-14}); + } + + struct StatelessHDivMassReference { + mfem::Vector total_action; + mfem::Vector stellar_action; + mfem::Vector vacuum_action; + long long stellar_elements{0}; + long long vacuum_elements{0}; + long long stellar_quadrature_points{0}; + long long vacuum_quadrature_points{0}; + double minimum_stellar_determinant{ + std::numeric_limits::infinity() + }; + double maximum_stellar_determinant{0.0}; + double minimum_vacuum_determinant{ + std::numeric_limits::infinity() + }; + double maximum_vacuum_determinant{0.0}; + }; + + void reference_true_to_local( + const mfem::ParFiniteElementSpace &fes, + const mfem::Vector &true_vector, + mfem::Vector &local_vector + ) { + local_vector.SetSize(fes.GetVSize()); + + const mfem::Operator *prolongation = fes.GetProlongationMatrix(); + if (prolongation != nullptr) { + prolongation->Mult(true_vector, local_vector); + } else { + local_vector = true_vector; + } + } + + void reference_local_to_true( + const mfem::ParFiniteElementSpace &fes, + const mfem::Vector &local_vector, + mfem::Vector &true_vector + ) { + true_vector.SetSize(fes.GetTrueVSize()); + true_vector = 0.0; + + const mfem::Operator *prolongation = fes.GetProlongationMatrix(); + if (prolongation != nullptr) { + prolongation->MultTranspose(local_vector, true_vector); + } else { + true_vector = local_vector; + } + } + + double global_vector_norm( + const mfem::Vector &vector, + MPI_Comm communicator + ) { + const double local_norm_squared = vector * vector; + double global_norm_squared = 0.0; + MPI_Allreduce( + &local_norm_squared, &global_norm_squared, 1, MPI_DOUBLE, MPI_SUM, + communicator + ); + return std::sqrt(global_norm_squared); + } + + double global_vector_dot( + const mfem::Vector &lhs, + const mfem::Vector &rhs, + MPI_Comm communicator + ) { + const double local_dot = lhs * rhs; + double global_dot = 0.0; + MPI_Allreduce( + &local_dot, &global_dot, 1, MPI_DOUBLE, MPI_SUM, communicator + ); + return global_dot; + } + + double global_relative_vector_error( + const mfem::Vector &computed, + const mfem::Vector &reference, + MPI_Comm communicator + ) { + mfem::Vector difference(computed); + difference -= reference; + return global_vector_norm(difference, communicator) / + std::max( + global_vector_norm(reference, communicator), + std::numeric_limits::epsilon() + ); + } + + const mfem::IntegrationRule &get_stateless_hdiv_reference_rule( + const fem::FEM &f, + const mfem::FiniteElement &element, + const mfem::ElementTransformation &transformation + ) { + const bool is_vacuum = + transformation.Attribute == + f.domainMapperStateless->GetVacuumElementAttribute(); + + const quadrature::Query query{ + .term = quadrature::Term::gravity_hdiv_mass, + .role = quadrature::QuadratureRole::discretization, + .domain = utils::DOMAINS::ALL, + .mapping = is_vacuum ? quadrature::MappingKind::kelvin + : quadrature::MappingKind::general, + .trial_order = element.GetOrder(), + .test_order = element.GetOrder(), + .coefficient_order = 0, + .geometry_weight_order = transformation.OrderW() + }; + + return *f.quadratureFactory + ->get(query, transformation.GetGeometryType()) + .integration_rule; + } + + mfem::Vector make_full_support_gravity_gradient(const fem::FEM &f) { + mfem::Vector gravity_gradient(f.gravityFluxFes->GetTrueVSize()); + + for (int i = 0; i < gravity_gradient.Size(); ++i) { + const double index = static_cast(i + 1); + gravity_gradient(i) = + std::sin(0.37 * index) + 0.31 * std::cos(0.19 * index); + } + + return gravity_gradient; + } + + mfem::Vector make_stateless_reference_displacement( + const fem::FEM &f, + const bool deformed + ) { + mfem::ParGridFunction displacement(f.displacementFes.get()); + displacement = 0.0; + + if (deformed) { + auto displacement_function = [](const mfem::Vector &position, + mfem::Vector &value) { + value.SetSize(3); + value(0) = + 0.04 * position(0) + 0.01 * position(1) * position(2); + value(1) = + -0.03 * position(1) + 0.008 * position(0) * position(2); + value(2) = + 0.02 * position(2) - 0.006 * position(0) * position(1); + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + 3, displacement_function + ); + displacement.ProjectCoefficient(displacement_coefficient); + } + + mfem::Vector displacement_true; + displacement.GetTrueDofs(displacement_true); + return displacement_true; + } + + std::string_view mapping_status_name(const mapping::MappingStatus status) { + switch (status) { + case mapping::MappingStatus::valid: + return "valid"; + case mapping::MappingStatus::invalid_dimension: + return "invalid_dimension"; + case mapping::MappingStatus::non_finite_input: + return "non_finite_input"; + case mapping::MappingStatus::invalid_reference_radius: + return "invalid_reference_radius"; + case mapping::MappingStatus::at_compactified_infinity: + return "at_compactified_infinity"; + case mapping::MappingStatus::outside_reference_domain: + return "outside_reference_domain"; + case mapping::MappingStatus::non_finite_result: + return "non_finite_result"; + case mapping::MappingStatus::non_positive_determinant: + return "non_positive_determinant"; + } + + return "unknown"; + } + + StatelessHDivMassReference + evaluate_stateless_hdiv_mass_quadrature_reference( + const fem::FEM &fem, + const mfem::Vector &gravity_gradient_true, + const mfem::Vector &displacement_true + ) { + MFEM_VERIFY( + fem.domainMapperStateless != nullptr, + "The stateless domain mapper is unavailable." + ); + + MFEM_VERIFY( + fem.compactificationFes != nullptr, + "The compactification finite-element space is unavailable." + ); + + MFEM_VERIFY( + fem.compactificationCoordinate != nullptr, + "The compactification coordinate is unavailable." + ); + + MFEM_VERIFY( + gravity_gradient_true.Size() == fem.gravityFluxFes->GetTrueVSize(), + "The gravity-gradient vector has the wrong size." + ); + + MFEM_VERIFY( + displacement_true.Size() == fem.displacementFes->GetTrueVSize(), + "The displacement vector has the wrong size." + ); + + mfem::Vector gravity_gradient_local; + mfem::Vector displacement_local; + + reference_true_to_local( + *fem.gravityFluxFes, gravity_gradient_true, gravity_gradient_local + ); + + reference_true_to_local( + *fem.displacementFes, displacement_true, displacement_local + ); + + mfem::Vector total_local(fem.gravityFluxFes->GetVSize()); + + mfem::Vector stellar_local(fem.gravityFluxFes->GetVSize()); + + mfem::Vector vacuum_local(fem.gravityFluxFes->GetVSize()); + + total_local = 0.0; + stellar_local = 0.0; + vacuum_local = 0.0; + + StatelessHDivMassReference reference; + + mapping::DomainMapperStateless::Workspace workspace( + fem.mesh->Dimension() + ); + + mapping::VolumeMappingContext mapping_context; + + mfem::Array gravity_dofs; + mfem::Array displacement_dofs; + mfem::Array compactification_dofs; + + mfem::Vector element_gravity_gradient; + mfem::Vector element_displacement; + mfem::Vector element_compactification; + mfem::Vector element_action; + mfem::Vector quadrature_flux; + mfem::Vector mapped_quadrature_flux; + + mfem::DenseMatrix vector_shape; + mfem::DenseMatrix mapped_mass_tensor; + + const int vacuum_attribute = + fem.domainMapperStateless->GetVacuumElementAttribute(); + + for (int element_id = 0; element_id < fem.mesh->GetNE(); ++element_id) { + const mfem::FiniteElement &gravity_element = + *fem.gravityFluxFes->GetFE(element_id); + + const mfem::FiniteElement &displacement_element = + *fem.displacementFes->GetFE(element_id); + + const mfem::FiniteElement &compactification_element = + *fem.compactificationFes->GetFE(element_id); + + mfem::ElementTransformation &transformation = + *fem.mesh->GetElementTransformation(element_id); + + const bool is_vacuum = transformation.Attribute == vacuum_attribute; + + mfem::DofTransformation *gravity_dof_transformation = + fem.gravityFluxFes->GetElementVDofs(element_id, gravity_dofs); + + mfem::DofTransformation *displacement_dof_transformation = + fem.displacementFes->GetElementVDofs( + element_id, displacement_dofs + ); + + mfem::DofTransformation *compactification_dof_transformation = + fem.compactificationFes->GetElementDofs( + element_id, compactification_dofs + ); + + gravity_gradient_local.GetSubVector( + gravity_dofs, element_gravity_gradient + ); + + displacement_local.GetSubVector( + displacement_dofs, element_displacement + ); + + fem.compactificationCoordinate->GetSubVector( + compactification_dofs, element_compactification + ); + + if (gravity_dof_transformation != nullptr) { + gravity_dof_transformation->InvTransformPrimal( + element_gravity_gradient + ); + } + + if (displacement_dof_transformation != nullptr) { + displacement_dof_transformation->InvTransformPrimal( + element_displacement + ); + } + + if (compactification_dof_transformation != nullptr) { + compactification_dof_transformation->InvTransformPrimal( + element_compactification + ); + } + + const mapping::ElementDisplacementData displacement_data = + mapping::ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement + ); + + const mapping::ElementCompactificationData compactification_data( + compactification_element, element_compactification + ); + + const mapping::ElementMappingData mapping_data{ + .displacement = displacement_data, + .compactification = compactification_data + }; + + const int gravity_dof_count = gravity_element.GetDof(); + + const int dimension = transformation.GetSpaceDim(); + + element_action.SetSize(gravity_dof_count); + element_action = 0.0; + + quadrature_flux.SetSize(dimension); + mapped_quadrature_flux.SetSize(dimension); + + vector_shape.SetSize(gravity_dof_count, dimension); + + mapped_mass_tensor.SetSize(dimension, dimension); + + const mfem::IntegrationRule &integration_rule = + get_stateless_hdiv_reference_rule( + fem, gravity_element, transformation + ); + + for (int quadrature_point = 0; + quadrature_point < integration_rule.GetNPoints(); + ++quadrature_point) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(quadrature_point); + + transformation.SetIntPoint(&integration_point); + + const mapping::MappingStatus status = + fem.domainMapperStateless->EvaluateVolume( + mapping_data, transformation, integration_point, + workspace, mapping_context + ); + + MFEM_VERIFY( + status == mean_field::mapping::MappingStatus::valid, + "Stateless mapping failed while evaluating the H(div) " + "quadrature reference." + << "\nElement ID = " << element_id + << "\nElement attribute = " << transformation.Attribute + << "\nQuadrature point = " << quadrature_point + << "\nMapping status = " << mapping_status_name(status) + ); + + gravity_element.CalcVShape(transformation, vector_shape); + + mean_field::mapping::ComputeHDivMassTensor( + mapping_context.mapping, mapped_mass_tensor + ); + + // Evaluate B*x at this quadrature point. + vector_shape.MultTranspose( + element_gravity_gradient, quadrature_flux + ); + + // Apply the mapped H(div) mass tensor. + mapped_mass_tensor.Mult( + quadrature_flux, mapped_quadrature_flux + ); + + const double weight = + integration_point.weight * transformation.Weight(); + + // Accumulate B^T*D*B*x directly. + for (int dof = 0; dof < gravity_dof_count; ++dof) { + double contribution = 0.0; + + for (int component = 0; component < dimension; + ++component) { + contribution += vector_shape(dof, component) * + mapped_quadrature_flux(component); + } + + element_action(dof) += weight * contribution; + } + + const double mapping_determinant = + mapping_context.mapping.mapping_determinant; + + MFEM_VERIFY( + std::isfinite(mapping_determinant) && + mapping_determinant > 0.0, + "The quadrature reference encountered an invalid mapping " + "determinant." + ); + + if (is_vacuum) { + reference.minimum_vacuum_determinant = std::min( + reference.minimum_vacuum_determinant, + mapping_determinant + ); + + reference.maximum_vacuum_determinant = std::max( + reference.maximum_vacuum_determinant, + mapping_determinant + ); + + ++reference.vacuum_quadrature_points; + } else { + reference.minimum_stellar_determinant = std::min( + reference.minimum_stellar_determinant, + mapping_determinant + ); + + reference.maximum_stellar_determinant = std::max( + reference.maximum_stellar_determinant, + mapping_determinant + ); + + ++reference.stellar_quadrature_points; + } + } + + if (gravity_dof_transformation != nullptr) { + gravity_dof_transformation->TransformDual(element_action); + } + + total_local.AddElementVector(gravity_dofs, element_action); + + if (is_vacuum) { + vacuum_local.AddElementVector(gravity_dofs, element_action); + + ++reference.vacuum_elements; + } else { + stellar_local.AddElementVector(gravity_dofs, element_action); + + ++reference.stellar_elements; + } + } + + reference_local_to_true( + *fem.gravityFluxFes, total_local, reference.total_action + ); + + reference_local_to_true( + *fem.gravityFluxFes, stellar_local, reference.stellar_action + ); + + reference_local_to_true( + *fem.gravityFluxFes, vacuum_local, reference.vacuum_action + ); + + const MPI_Comm communicator = fem.gravityFluxFes->GetComm(); + + const long long local_counts[4]{ + reference.stellar_elements, reference.vacuum_elements, + reference.stellar_quadrature_points, + reference.vacuum_quadrature_points + }; + + long long global_counts[4]{}; + + MPI_Allreduce( + local_counts, global_counts, 4, MPI_LONG_LONG, MPI_SUM, communicator + ); + + reference.stellar_elements = global_counts[0]; + + reference.vacuum_elements = global_counts[1]; + + reference.stellar_quadrature_points = global_counts[2]; + + reference.vacuum_quadrature_points = global_counts[3]; + + const double local_minimums[2]{ + reference.minimum_stellar_determinant, + reference.minimum_vacuum_determinant + }; + + const double local_maximums[2]{ + reference.maximum_stellar_determinant, + reference.maximum_vacuum_determinant + }; + + double global_minimums[2]{}; + double global_maximums[2]{}; + + MPI_Allreduce( + local_minimums, global_minimums, 2, MPI_DOUBLE, MPI_MIN, + communicator + ); + + MPI_Allreduce( + local_maximums, global_maximums, 2, MPI_DOUBLE, MPI_MAX, + communicator + ); + + reference.minimum_stellar_determinant = global_minimums[0]; + + reference.minimum_vacuum_determinant = global_minimums[1]; + + reference.maximum_stellar_determinant = global_maximums[0]; + + reference.maximum_vacuum_determinant = global_maximums[1]; + + return reference; + } + + using gravity_form = blocks::gravity_field_form; + using gravity_layout = blocks::form_layout; + gravity_layout make_gravity_jacobian_layout(const fem::FEM &f) { + const std::array value_sizes{ + f.densityFes->GetTrueVSize(), f.displacementFes->GetTrueVSize(), + f.gravityFluxFes->GetTrueVSize(), + f.gravityPotentialFes->GetTrueVSize() + }; + + const std::array + residual_sizes{ + f.gravityFluxFes->GetTrueVSize(), + f.gravityPotentialFes->GetTrueVSize() + }; + + return gravity_layout(value_sizes, residual_sizes); + } + + template + void set_value_block( + mfem::Vector &vector, + const gravity_layout &layout, + const blocks::value_block block, + const mfem::Vector &values + ) { + REQUIRE(values.Size() == layout.size(block)); + for (int i = 0; i < values.Size(); ++i) + vector(layout.offset(block) + i) = values(i); + } + + template + mfem::Vector get_value_block( + const mfem::Vector &vector, + const gravity_layout &layout, + const blocks::value_block block + ) { + mfem::Vector values(layout.size(block)); + for (int i = 0; i < values.Size(); ++i) + values(i) = vector(layout.offset(block) + i); + return values; + } + + template + mfem::Vector get_residual_block( + const mfem::Vector &vector, + const gravity_layout &layout, + const blocks::residual_block block + ) { + mfem::Vector values(layout.size(block)); + for (int i = 0; i < values.Size(); ++i) + values(i) = vector(layout.offset(block) + i); + return values; + } + + template + void fill_value_block( + mfem::Vector &vector, + const gravity_layout &layout, + const blocks::value_block block, + const double scale, + const double phase + ) { + for (int i = 0; i < layout.size(block); ++i) { + const double index_value = static_cast(i + 1); + vector(layout.offset(block) + i) = + scale * (std::sin(0.31 * index_value + phase) + + 0.37 * std::cos(0.17 * index_value - phase)); + } + } + + mfem::Vector make_gravity_jacobian_state( + const fem::FEM &f, + const gravity_layout &layout, + const bool deformed + ) { + mfem::Vector state(layout.value_offsets().Last()); + state = 0.0; + + fill_value_block(state, layout, density_block, 0.7, 0.11); + fill_value_block(state, layout, gravity_gradient_block, 0.4, 0.23); + fill_value_block(state, layout, gravity_potential_block, 0.3, 0.37); + + const mfem::Vector displacement = + make_stateless_reference_displacement(f, deformed); + set_value_block(state, layout, displacement_block, displacement); + + return state; + } + + mfem::Vector make_density_direction(const gravity_layout &layout) { + mfem::Vector direction(layout.value_offsets().Last()); + direction = 0.0; + fill_value_block(direction, layout, density_block, 0.13, 0.19); + return direction; + } + + mfem::Vector make_gravity_gradient_direction(const gravity_layout &layout) { + mfem::Vector direction(layout.value_offsets().Last()); + direction = 0.0; + fill_value_block(direction, layout, gravity_gradient_block, 0.11, 0.29); + return direction; + } + + mfem::Vector + make_gravity_potential_direction(const gravity_layout &layout) { + mfem::Vector direction(layout.value_offsets().Last()); + direction = 0.0; + fill_value_block( + direction, layout, gravity_potential_block, 0.09, 0.41 + ); + return direction; + } + + mfem::Vector + make_combined_fixed_geometry_direction(const gravity_layout &layout) { + mfem::Vector direction = make_density_direction(layout); + const mfem::Vector gravity_gradient_direction = + make_gravity_gradient_direction(layout); + const mfem::Vector gravity_potential_direction = + make_gravity_potential_direction(layout); + direction += gravity_gradient_direction; + direction += gravity_potential_direction; + return direction; + } + + mfem::Vector make_displacement_direction( + const gravity_layout &layout, + const mfem::Vector &displacement_direction + ) { + mfem::Vector direction(layout.value_offsets().Last()); + direction = 0.0; + set_value_block( + direction, layout, displacement_block, displacement_direction + ); + return direction; + } + + mfem::Vector evaluate_centered_difference( + operators::GravityFieldOperator &gravity_operator, + const mfem::Vector &state, + const mfem::Vector &direction, + const double step + ) { + mfem::Vector plus_state(state); + mfem::Vector minus_state(state); + plus_state.Add(step, direction); + minus_state.Add(-step, direction); + + mfem::Vector plus_residual; + mfem::Vector minus_residual; + gravity_operator.Mult(plus_state, plus_residual); + gravity_operator.Mult(minus_state, minus_residual); + + mfem::Vector difference(plus_residual); + difference -= minus_residual; + difference /= 2.0 * step; + return difference; + } + + struct HdivMassVariationTestFields { + mfem::Vector gravity_gradient; + mfem::Vector displacement; + mfem::Vector displacement_direction_1; + mfem::Vector displacement_direction_2; + }; + + double global_relative_error( + const mfem::Vector &computed, + const mfem::Vector &reference, + MPI_Comm communicator + ) { + REQUIRE(computed.Size() == reference.Size()); + + mfem::Vector difference(computed); + difference -= reference; + + return global_norm(difference, communicator) / + std::max(global_norm(reference, communicator), 1.0e-14); + } + + HdivMassVariationTestFields + make_hdiv_mass_variation_test_fields(const fem::FEM &f) { + const int dimension = f.mesh->Dimension(); + + auto gravity_gradient_function = [](const mfem::Vector &position, + mfem::Vector &value) { + value.SetSize(3); + value(0) = + 0.4 + 0.18 * position(0) - 0.07 * position(1) * position(2); + value(1) = + -0.3 + 0.11 * position(1) + 0.05 * position(0) * position(2); + value(2) = + 0.2 - 0.09 * position(2) + 0.04 * position(0) * position(1); + }; + + auto displacement_function = [](const mfem::Vector &position, + mfem::Vector &value) { + value.SetSize(3); + value(0) = 0.025 * position(0) + 0.006 * position(1) * position(2); + value(1) = -0.018 * position(1) + 0.005 * position(0) * position(2); + value(2) = 0.014 * position(2) + 0.004 * position(0) * position(1); + }; + + auto displacement_direction_1_function = + [](const mfem::Vector &position, mfem::Vector &value) { + value.SetSize(3); + value(0) = 0.16 * position(0) + 0.03 * position(1); + value(1) = -0.11 * position(1) + 0.02 * position(2); + value(2) = 0.13 * position(2) - 0.025 * position(0); + }; + + auto displacement_direction_2_function = + [](const mfem::Vector &position, mfem::Vector &value) { + value.SetSize(3); + value(0) = -0.07 * position(1) + 0.025 * position(2); + value(1) = 0.09 * position(0) + 0.04 * position(2); + value(2) = + -0.08 * position(2) + 0.03 * position(0) * position(1); + }; + + mfem::VectorFunctionCoefficient gravity_gradient_coefficient( + dimension, gravity_gradient_function + ); + mfem::VectorFunctionCoefficient displacement_coefficient( + dimension, displacement_function + ); + mfem::VectorFunctionCoefficient displacement_direction_1_coefficient( + dimension, displacement_direction_1_function + ); + mfem::VectorFunctionCoefficient displacement_direction_2_coefficient( + dimension, displacement_direction_2_function + ); + + mfem::ParGridFunction gravity_gradient_grid(f.gravityFluxFes.get()); + mfem::ParGridFunction displacement_grid(f.displacementFes.get()); + mfem::ParGridFunction displacement_direction_1_grid( + f.displacementFes.get() + ); + mfem::ParGridFunction displacement_direction_2_grid( + f.displacementFes.get() + ); + + gravity_gradient_grid.ProjectCoefficient(gravity_gradient_coefficient); + displacement_grid.ProjectCoefficient(displacement_coefficient); + displacement_direction_1_grid.ProjectCoefficient( + displacement_direction_1_coefficient + ); + displacement_direction_2_grid.ProjectCoefficient( + displacement_direction_2_coefficient + ); + + HdivMassVariationTestFields fields; + gravity_gradient_grid.GetTrueDofs(fields.gravity_gradient); + displacement_grid.GetTrueDofs(fields.displacement); + displacement_direction_1_grid.GetTrueDofs( + fields.displacement_direction_1 + ); + displacement_direction_2_grid.GetTrueDofs( + fields.displacement_direction_2 + ); + + return fields; + } + + mfem::Vector centered_hdiv_mass_geometry_difference( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &gravity_gradient, + const mfem::Vector &displacement, + const mfem::Vector &displacement_direction, + const double difference_step + ) { + mfem::Vector plus_displacement(displacement); + mfem::Vector minus_displacement(displacement); + plus_displacement.Add(difference_step, displacement_direction); + minus_displacement.Add(-difference_step, displacement_direction); + + mfem::Vector plus_action; + mfem::Vector minus_action; + + operators::kernels::apply_mapped_hdiv_mass( + f, domain_mapper, gravity_gradient, plus_displacement, plus_action + ); + operators::kernels::apply_mapped_hdiv_mass( + f, domain_mapper, gravity_gradient, minus_displacement, minus_action + ); + + plus_action -= minus_action; + plus_action /= 2.0 * difference_step; + + return plus_action; + } + + mfem::Vector make_source_variation_density(const fem::FEM &f) { + auto density_function = [](const mfem::Vector &position) { + return 1.2 + 0.16 * position(0) - 0.09 * position(1) + + 0.07 * position(2) + 0.04 * position(0) * position(1); + }; + + mfem::FunctionCoefficient density_coefficient(density_function); + mfem::ParGridFunction density_grid(f.densityFes.get()); + mfem::Vector density_true; + + density_grid.ProjectCoefficient(density_coefficient); + density_grid.GetTrueDofs(density_true); + + return density_true; + } + + mfem::Vector centered_source_geometry_difference( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::Vector &density, + const mfem::Vector &displacement, + const mfem::Vector &displacement_direction, + const double difference_step + ) { + mfem::Vector plus_displacement(displacement); + mfem::Vector minus_displacement(displacement); + plus_displacement.Add(difference_step, displacement_direction); + minus_displacement.Add(-difference_step, displacement_direction); + + mfem::Vector plus_action; + mfem::Vector minus_action; + + operators::kernels::apply_mapped_source( + f, domain_mapper, density, plus_displacement, plus_action + ); + operators::kernels::apply_mapped_source( + f, domain_mapper, density, minus_displacement, minus_action + ); + + plus_action -= minus_action; + plus_action /= 2.0 * difference_step; + + return plus_action; + } + double global_dot( + const mfem::Vector &left, + const mfem::Vector &right, + MPI_Comm communicator + ) { + REQUIRE(left.Size() > 0); + REQUIRE(left.Size() == right.Size()); + + const double local_dot = left * right; + double global_dot_value = 0.0; + MPI_Allreduce( + &local_dot, &global_dot_value, 1, MPI_DOUBLE, MPI_SUM, communicator + ); + + return global_dot_value; + } + + mfem::Vector make_secondary_gravity_gradient(const fem::FEM &f) { + auto gravity_gradient_function = [](const mfem::Vector &position, + mfem::Vector &value) { + value.SetSize(3); + value(0) = + -0.17 + 0.09 * position(1) + 0.03 * position(0) * position(2); + value(1) = + 0.31 - 0.14 * position(0) + 0.05 * position(1) * position(2); + value(2) = + -0.22 + 0.12 * position(2) - 0.04 * position(0) * position(1); + }; + + mfem::VectorFunctionCoefficient coefficient( + f.mesh->Dimension(), gravity_gradient_function + ); + mfem::ParGridFunction grid_function(f.gravityFluxFes.get()); + mfem::Vector true_dofs; + + grid_function.ProjectCoefficient(coefficient); + grid_function.GetTrueDofs(true_dofs); + + return true_dofs; + } + + mfem::Vector make_secondary_source_density(const fem::FEM &f) { + auto density_function = [](const mfem::Vector &position) { + return 0.8 - 0.11 * position(0) + 0.13 * position(1) - + 0.06 * position(2) + 0.03 * position(1) * position(2); + }; + + mfem::FunctionCoefficient coefficient(density_function); + mfem::ParGridFunction grid_function(f.densityFes.get()); + mfem::Vector true_dofs; + + grid_function.ProjectCoefficient(coefficient); + grid_function.GetTrueDofs(true_dofs); + + return true_dofs; + } + + mfem::Vector make_vacuum_only_density( + const fem::FEM &f, + const int vacuum_attribute + ) { + mfem::ParGridFunction grid_function(f.densityFes.get()); + grid_function = 0.0; + + mfem::Array element_dofs; + mfem::Vector element_values; + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + REQUIRE(transformation != nullptr); + + if (transformation->Attribute != vacuum_attribute) + continue; + + const mfem::FiniteElement &element = + *f.densityFes->GetFE(element_id); + mfem::DofTransformation *dof_transformation = + f.densityFes->GetElementDofs(element_id, element_dofs); + + element_values.SetSize(element.GetDof()); + for (int i = 0; i < element_values.Size(); ++i) + element_values(i) = 0.9 + 0.01 * static_cast(i); + + if (dof_transformation != nullptr) + dof_transformation->TransformPrimal(element_values); + grid_function.SetSubVector(element_dofs, element_values); + } + + mfem::Vector true_dofs; + grid_function.GetTrueDofs(true_dofs); + + return true_dofs; + } + + template + mfem::Vector make_read_only_value_view( + const mfem::Vector &vector, + const mfem::Array &offsets, + const blocks::value_block + ) { + const int offset = offsets[index]; + const int size = offsets[index + 1] - offset; + return mfem::Vector( + const_cast(vector.GetData()) + offset, size + ); + } + + void check_linearization_context_matches_state( + const operators::context::gravity_field:: + GravityFieldLinearizationContext &context, + const mfem::Vector &state, + const mfem::Array &state_offsets, + MPI_Comm communicator + ) { + using form = blocks::gravity_field_form; + + constexpr auto density_block = utils::blocks::get_value_block( + blocks::density_field.mass_term + ); + constexpr auto displacement_block = + utils::blocks::get_value_block( + blocks::displacement_field.geometry_term + ); + constexpr auto gravity_gradient_block = + utils::blocks::get_value_block( + blocks::gravity_field.gradient_term + ); + + const mfem::Vector density = + make_read_only_value_view(state, state_offsets, density_block); + const mfem::Vector displacement = + make_read_only_value_view(state, state_offsets, displacement_block); + const mfem::Vector gravity_gradient = make_read_only_value_view( + state, state_offsets, gravity_gradient_block + ); + + CHECK_THAT( + global_relative_vector_error( + context.GetDensity(), density, communicator + ), + Catch::Matchers::WithinAbs(0.0, 0.0) + ); + CHECK_THAT( + global_relative_vector_error( + context.GetGeometryContext().GetDisplacement(), displacement, + communicator + ), + Catch::Matchers::WithinAbs(0.0, 0.0) + ); + CHECK_THAT( + global_relative_vector_error( + context.GetGravityGradient(), gravity_gradient, communicator + ), + Catch::Matchers::WithinAbs(0.0, 0.0) + ); + } + + StatelessHDivMassReference assemble_legacy_hdiv_mass_reference( + const fem::FEM &f, + const mfem::Vector &gravity_gradient_true + ) { + MFEM_VERIFY( + f.mesh != nullptr, "The legacy H(div) reference requires a mesh." + ); + MFEM_VERIFY( + f.gravityFluxFes != nullptr, + "The legacy H(div) reference requires the RT finite-element space." + ); + MFEM_VERIFY( + f.mapping != nullptr, + "The legacy H(div) reference requires the legacy domain mapper." + ); + MFEM_VERIFY( + f.domainMapperStateless != nullptr, + "The vacuum attribute is unavailable." + ); + + mfem::Vector gravity_gradient_local; + reference_true_to_local( + *f.gravityFluxFes, gravity_gradient_true, gravity_gradient_local + ); + + mfem::Vector total_local(f.gravityFluxFes->GetVSize()); + mfem::Vector stellar_local(f.gravityFluxFes->GetVSize()); + mfem::Vector vacuum_local(f.gravityFluxFes->GetVSize()); + + total_local = 0.0; + stellar_local = 0.0; + vacuum_local = 0.0; + + StatelessHDivMassReference reference; + const int vacuum_attribute = + f.domainMapperStateless->GetVacuumElementAttribute(); + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + const mfem::FiniteElement &gravity_element = + *f.gravityFluxFes->GetFE(element_id); + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + + MFEM_VERIFY( + transformation != nullptr, + "The legacy H(div) reference received a null element " + "transformation." + ); + + const bool is_vacuum = + transformation->Attribute == vacuum_attribute; + + mfem::Array gravity_dofs; + f.gravityFluxFes->GetElementVDofs(element_id, gravity_dofs); + + mfem::Vector element_gravity_gradient; + gravity_gradient_local.GetSubVector( + gravity_dofs, element_gravity_gradient + ); + + const int gravity_dof_count = gravity_element.GetDof(); + const int dimension = transformation->GetSpaceDim(); + + mfem::DenseMatrix element_matrix(gravity_dof_count); + mfem::DenseMatrix vector_shape(gravity_dof_count, dimension); + mfem::DenseMatrix mapping_jacobian(dimension); + mfem::DenseMatrix mapped_mass_tensor(dimension); + + element_matrix = 0.0; + + const mfem::IntegrationRule &integration_rule = + get_stateless_hdiv_reference_rule( + f, gravity_element, *transformation + ); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + transformation->SetIntPoint(&integration_point); + + /* + * This reproduces the legacy MappedHDivMassCoefficient. + * + * In particular, it does not evaluate or otherwise use + * f.compactificationCoordinate. + */ + f.mapping->ComputeJacobian(*transformation, mapping_jacobian); + + const double mapping_determinant = mapping_jacobian.Det(); + + CAPTURE(element_id, q, transformation->Attribute); + REQUIRE(std::isfinite(mapping_determinant)); + REQUIRE(mapping_determinant > 0.0); + + mfem::MultAtB( + mapping_jacobian, mapping_jacobian, mapped_mass_tensor + ); + mapped_mass_tensor *= 1.0 / std::abs(mapping_determinant); + + gravity_element.CalcVShape(*transformation, vector_shape); + + const double weight = + integration_point.weight * transformation->Weight(); + + for (int i = 0; i < gravity_dof_count; ++i) { + for (int j = 0; j < gravity_dof_count; ++j) { + double entry = 0.0; + + for (int row = 0; row < dimension; ++row) { + for (int column = 0; column < dimension; ++column) { + entry += vector_shape(i, row) * + mapped_mass_tensor(row, column) * + vector_shape(j, column); + } + } + + element_matrix(i, j) += weight * entry; + } + } + + if (is_vacuum) { + ++reference.vacuum_quadrature_points; + } else { + ++reference.stellar_quadrature_points; + } + } + + mfem::Vector element_action(gravity_dof_count); + element_matrix.Mult(element_gravity_gradient, element_action); + + total_local.AddElementVector(gravity_dofs, element_action); + + if (is_vacuum) { + vacuum_local.AddElementVector(gravity_dofs, element_action); + ++reference.vacuum_elements; + } else { + stellar_local.AddElementVector(gravity_dofs, element_action); + ++reference.stellar_elements; + } + } + + reference_local_to_true( + *f.gravityFluxFes, total_local, reference.total_action + ); + reference_local_to_true( + *f.gravityFluxFes, stellar_local, reference.stellar_action + ); + reference_local_to_true( + *f.gravityFluxFes, vacuum_local, reference.vacuum_action + ); + + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + const long long local_counts[4]{ + reference.stellar_elements, reference.vacuum_elements, + reference.stellar_quadrature_points, + reference.vacuum_quadrature_points + }; + + long long global_counts[4]{}; + + MPI_Allreduce( + local_counts, global_counts, 4, MPI_LONG_LONG, MPI_SUM, communicator + ); + + reference.stellar_elements = global_counts[0]; + reference.vacuum_elements = global_counts[1]; + reference.stellar_quadrature_points = global_counts[2]; + reference.vacuum_quadrature_points = global_counts[3]; + + return reference; + } +} // namespace + +TEST_CASE( + "Gravity Field Operator Mult Preserves Zero State And Static Blocks", + tags::unit &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + physics::update_stiffness_matrix(f); + + REQUIRE(f.domainMapperStateless != nullptr); + + const blocks::form_layout layout = make_gravity_layout(f); + + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + mfem::Vector state(layout.value_offsets().Last()); + mfem::Vector residual; + state = 0.0; + constexpr operators::context::gravity_field::GravityFieldRevisions + revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + gravity_operator.Prepare(state, revisions); + gravity_operator.Mult(state, residual); + + REQUIRE(residual.Size() == layout.residual_offsets().Last()); + CHECK_THAT(residual.Norml2(), WithinAbs(0.0, 1.0e-14)); + + const mfem::Vector gravity_potential = + make_test_vector(layout.size(gravity_potential_block), 0.31); + set_block( + state, layout.value_offsets(), gravity_potential_block, + gravity_potential + ); + + gravity_operator.Mult(state, residual); + + const mfem::Vector gradient_residual = get_block( + residual, layout.residual_offsets(), gravity_gradient_residual_block + ); + const mfem::Vector poisson_residual = get_block( + residual, layout.residual_offsets(), gravity_poisson_residual_block + ); + + mfem::Vector expected_gradient_residual( + layout.size(gravity_gradient_residual_block) + ); + f.gravityContext.BT->Mult(gravity_potential, expected_gradient_residual); + + CHECK_THAT( + relative_difference(gradient_residual, expected_gradient_residual), + WithinAbs(0.0, 1.0e-13) + ); + CHECK_THAT(poisson_residual.Norml2(), WithinAbs(0.0, 1.0e-14)); + + state = 0.0; + + const mfem::Vector gravity_gradient = + make_test_vector(layout.size(gravity_gradient_block), 0.73); + set_block( + state, layout.value_offsets(), gravity_gradient_block, gravity_gradient + ); + + gravity_operator.Mult(state, residual); + + const mfem::Vector gradient_only_residual = get_block( + residual, layout.residual_offsets(), gravity_gradient_residual_block + ); + const mfem::Vector poisson_only_residual = get_block( + residual, layout.residual_offsets(), gravity_poisson_residual_block + ); + + mfem::Vector expected_poisson_residual( + layout.size(gravity_poisson_residual_block) + ); + f.gravityContext.b_form->Mult(gravity_gradient, expected_poisson_residual); + + CHECK(gradient_only_residual.Norml2() > 0.0); + CHECK_THAT( + relative_difference(poisson_only_residual, expected_poisson_residual), + WithinAbs(0.0, 1.0e-13) + ); + + const double adjoint_lhs = gravity_gradient * expected_gradient_residual; + const double adjoint_rhs = gravity_potential * expected_poisson_residual; + const double adjoint_scale = + std::max({std::abs(adjoint_lhs), std::abs(adjoint_rhs), 1.0e-14}); + + CHECK_THAT( + std::abs(adjoint_lhs - adjoint_rhs) / adjoint_scale, + WithinAbs(0.0, 1.0e-12) + ); +} + +TEST_CASE( + "Gravity Field Operator Mult Applies Stellar Source With Correct Sign", + tags::unit &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + physics::update_stiffness_matrix(f); + + REQUIRE(f.domainMapperStateless != nullptr); + + const blocks::form_layout layout = make_gravity_layout(f); + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + mfem::Vector state(layout.value_offsets().Last()); + mfem::Vector residual; + state = 0.0; + constexpr operators::context::gravity_field::GravityFieldRevisions + revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + const mfem::Vector density = make_constant_density(f, 1.0); + set_block(state, layout.value_offsets(), density_block, density); + + gravity_operator.Prepare(state, revisions); + gravity_operator.Mult(state, residual); + + const mfem::Vector gradient_residual = get_block( + residual, layout.residual_offsets(), gravity_gradient_residual_block + ); + const mfem::Vector poisson_residual = get_block( + residual, layout.residual_offsets(), gravity_poisson_residual_block + ); + + CHECK_THAT(gradient_residual.Norml2(), WithinAbs(0.0, 1.0e-14)); + CHECK(poisson_residual.Norml2() > 0.0); + + const mfem::Vector constant_test = make_constant_density(f, 1.0); + const double integrated_source_residual = constant_test * poisson_residual; + + INFO("Integrated Poisson source residual = " << integrated_source_residual); + CHECK(integrated_source_residual < 0.0); + + mfem::Vector doubled_state(state); + mfem::Vector doubled_density(density); + doubled_density *= 2.0; + set_block( + doubled_state, layout.value_offsets(), density_block, doubled_density + ); + + mfem::Vector doubled_residual; + gravity_operator.Mult(doubled_state, doubled_residual); + + mfem::Vector expected_doubled_residual(residual); + expected_doubled_residual *= 2.0; + + CHECK_THAT( + relative_difference(doubled_residual, expected_doubled_residual), + WithinAbs(0.0, 1.0e-12) + ); +} + +TEST_CASE( + "Gravity Field Operator Mult Ignores Vacuum Density", + tags::unit &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + physics::update_stiffness_matrix(f); + + REQUIRE(f.domainMapperStateless != nullptr); + + const blocks::form_layout layout = make_gravity_layout(f); + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + mfem::Vector state(layout.value_offsets().Last()); + mfem::Vector residual; + state = 0.0; + + const operators::context::gravity_field::GravityFieldRevisions revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + const mfem::Vector vacuum_density = make_vacuum_density(f, 1.0); + REQUIRE(vacuum_density.Norml2() > 0.0); + + set_block(state, layout.value_offsets(), density_block, vacuum_density); + + gravity_operator.Prepare(state, revisions); + gravity_operator.Mult(state, residual); + + INFO("Vacuum-source residual norm = " << residual.Norml2()); + CHECK_THAT(residual.Norml2(), WithinAbs(0.0, 1.0e-13)); +} + +TEST_CASE( + "Gravity Field Operator Mult Produces A Symmetric Positive Hdiv Mass " + "Action", + tags::unit &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + physics::update_stiffness_matrix(f); + + REQUIRE(f.domainMapperStateless != nullptr); + + const blocks::form_layout layout = make_gravity_layout(f); + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + const mfem::Vector displacement = make_displacement(f); + const mfem::Vector gravity_gradient_a = + make_test_vector(layout.size(gravity_gradient_block), 0.27); + const mfem::Vector gravity_gradient_b = + make_test_vector(layout.size(gravity_gradient_block), 1.13); + + mfem::Vector state_a(layout.value_offsets().Last()); + mfem::Vector state_b(layout.value_offsets().Last()); + mfem::Vector residual_a; + mfem::Vector residual_b; + + state_a = 0.0; + state_b = 0.0; + + set_block( + state_a, layout.value_offsets(), displacement_block, displacement + ); + set_block( + state_a, layout.value_offsets(), gravity_gradient_block, + gravity_gradient_a + ); + set_block( + state_b, layout.value_offsets(), displacement_block, displacement + ); + set_block( + state_b, layout.value_offsets(), gravity_gradient_block, + gravity_gradient_b + ); + + const operators::context::gravity_field::GravityFieldRevisions revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + gravity_operator.Prepare(state_a, revisions); + + gravity_operator.Mult(state_a, residual_a); + gravity_operator.Mult(state_b, residual_b); + + const mfem::Vector mass_action_a = get_block( + residual_a, layout.residual_offsets(), gravity_gradient_residual_block + ); + const mfem::Vector mass_action_b = get_block( + residual_b, layout.residual_offsets(), gravity_gradient_residual_block + ); + + const double energy_a = gravity_gradient_a * mass_action_a; + const double energy_b = gravity_gradient_b * mass_action_b; + const double cross_ab = gravity_gradient_a * mass_action_b; + const double cross_ba = gravity_gradient_b * mass_action_a; + const double symmetry_scale = + std::max({std::abs(cross_ab), std::abs(cross_ba), 1.0e-14}); + + INFO("Mapped H(div) energy A = " << energy_a); + INFO("Mapped H(div) energy B = " << energy_b); + INFO("Mapped H(div) cross action A-M-B = " << cross_ab); + INFO("Mapped H(div) cross action B-M-A = " << cross_ba); + + CHECK(std::isfinite(energy_a)); + CHECK(std::isfinite(energy_b)); + CHECK(energy_a > 0.0); + CHECK(energy_b > 0.0); + CHECK_THAT( + std::abs(cross_ab - cross_ba) / symmetry_scale, WithinAbs(0.0, 1.0e-11) + ); +} + +TEST_CASE( + "Gravity Field Operator Mult Is Additive In Fields At Fixed Displacement", + tags::unit &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + physics::update_stiffness_matrix(f); + + REQUIRE(f.domainMapperStateless != nullptr); + + const blocks::form_layout layout = make_gravity_layout(f); + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + const mfem::Vector displacement = make_displacement(f); + const mfem::Vector density = make_constant_density(f, 0.73); + const mfem::Vector gravity_gradient = + make_test_vector(layout.size(gravity_gradient_block), 0.41); + const mfem::Vector gravity_potential = + make_test_vector(layout.size(gravity_potential_block), 0.89); + + mfem::Vector displacement_state(layout.value_offsets().Last()); + mfem::Vector density_state(layout.value_offsets().Last()); + mfem::Vector gradient_state(layout.value_offsets().Last()); + mfem::Vector potential_state(layout.value_offsets().Last()); + mfem::Vector complete_state(layout.value_offsets().Last()); + + displacement_state = 0.0; + density_state = 0.0; + gradient_state = 0.0; + potential_state = 0.0; + complete_state = 0.0; + + set_block( + displacement_state, layout.value_offsets(), displacement_block, + displacement + ); + + set_block( + density_state, layout.value_offsets(), displacement_block, displacement + ); + set_block(density_state, layout.value_offsets(), density_block, density); + + set_block( + gradient_state, layout.value_offsets(), displacement_block, displacement + ); + set_block( + gradient_state, layout.value_offsets(), gravity_gradient_block, + gravity_gradient + ); + + set_block( + potential_state, layout.value_offsets(), displacement_block, + displacement + ); + set_block( + potential_state, layout.value_offsets(), gravity_potential_block, + gravity_potential + ); + + set_block( + complete_state, layout.value_offsets(), displacement_block, displacement + ); + set_block(complete_state, layout.value_offsets(), density_block, density); + set_block( + complete_state, layout.value_offsets(), gravity_gradient_block, + gravity_gradient + ); + set_block( + complete_state, layout.value_offsets(), gravity_potential_block, + gravity_potential + ); + + mfem::Vector displacement_residual; + mfem::Vector density_residual; + mfem::Vector gradient_residual; + mfem::Vector potential_residual; + mfem::Vector complete_residual; + const operators::context::gravity_field::GravityFieldRevisions revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + gravity_operator.Prepare(complete_state, revisions); + + gravity_operator.Mult(displacement_state, displacement_residual); + gravity_operator.Mult(density_state, density_residual); + gravity_operator.Mult(gradient_state, gradient_residual); + gravity_operator.Mult(potential_state, potential_residual); + gravity_operator.Mult(complete_state, complete_residual); + + CHECK_THAT(displacement_residual.Norml2(), WithinAbs(0.0, 1.0e-14)); + + mfem::Vector additive_residual(density_residual); + additive_residual += gradient_residual; + additive_residual += potential_residual; + + CHECK_THAT( + relative_difference(complete_residual, additive_residual), + WithinAbs(0.0, 1.0e-11) + ); +} + +TEST_CASE( + "Gravity Field Operator Stellar Hdiv Mass Matches Legacy Assembled Mass", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators + &tags::legacy_comparison +) { + constexpr double parity_tolerance = 1.0e-10; + constexpr double vacuum_tolerance = 1.0e-13; + + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.mapping != nullptr); + REQUIRE(f.domainMapperStateless != nullptr); + + const blocks::form_layout layout = make_gravity_layout(f); + const mfem::Vector gravity_gradient = + make_core_supported_gravity_gradient(f); + const mfem::Vector deformed_displacement = make_displacement(f); + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + REQUIRE(global_norm(gravity_gradient, communicator) > 0.0); + + mfem::ParGridFunction local_gravity_gradient(f.gravityFluxFes.get()); + local_gravity_gradient.SetFromTrueDofs(gravity_gradient); + + double local_maximum_vacuum_dof = 0.0; + mfem::Array element_vdofs; + mfem::Vector element_values; + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + if (f.mesh->GetAttribute(element_id) != + f.domainMapperStateless->GetVacuumElementAttribute()) + continue; + + f.gravityFluxFes->GetElementVDofs(element_id, element_vdofs); + local_gravity_gradient.GetSubVector(element_vdofs, element_values); + + if (element_values.Size() > 0) + local_maximum_vacuum_dof = + std::max(local_maximum_vacuum_dof, element_values.Normlinf()); + } + + double global_maximum_vacuum_dof = 0.0; + MPI_Allreduce( + &local_maximum_vacuum_dof, &global_maximum_vacuum_dof, 1, MPI_DOUBLE, + MPI_MAX, communicator + ); + + INFO( + "Maximum gravity-gradient DOF on vacuum elements = " + << global_maximum_vacuum_dof + ); + REQUIRE_THAT(global_maximum_vacuum_dof, WithinAbs(0.0, vacuum_tolerance)); + + for (const bool use_deformation : std::array{false, true}) { + DYNAMIC_SECTION( + "Geometry = " << (use_deformation ? "deformed" : "identity") + ) { + mfem::Vector displacement(layout.size(displacement_block)); + displacement = 0.0; + if (use_deformation) + displacement = deformed_displacement; + + mfem::ParGridFunction legacy_displacement(f.displacementFes.get()); + legacy_displacement.SetFromTrueDofs(displacement); + f.mapping->SetDisplacement(legacy_displacement); + + physics::update_stiffness_matrix(f); + + REQUIRE(f.gravityContext.m_form != nullptr); + REQUIRE(f.gravityContext.b_form != nullptr); + REQUIRE(f.gravityContext.BT != nullptr); + + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + mfem::Vector state(layout.value_offsets().Last()); + mfem::Vector matrix_free_residual; + state = 0.0; + + set_block( + state, layout.value_offsets(), displacement_block, displacement + ); + set_block( + state, layout.value_offsets(), gravity_gradient_block, + gravity_gradient + ); + + constexpr operators::context::gravity_field::GravityFieldRevisions + revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + gravity_operator.Prepare(state, revisions); + gravity_operator.Mult(state, matrix_free_residual); + + const mfem::Vector matrix_free_mass_action = get_block( + matrix_free_residual, layout.residual_offsets(), + gravity_gradient_residual_block + ); + + mfem::Vector legacy_mass_action(f.gravityFluxFes->GetTrueVSize()); + f.gravityContext.m_form->Mult(gravity_gradient, legacy_mass_action); + + const double matrix_free_mass_norm = + global_norm(matrix_free_mass_action, communicator); + const double legacy_mass_norm = + global_norm(legacy_mass_action, communicator); + const double mass_error = global_relative_difference( + matrix_free_mass_action, legacy_mass_action, communicator + ); + + mfem::Vector mass_difference(matrix_free_mass_action); + mass_difference -= legacy_mass_action; + + INFO("Geometry = " << (use_deformation ? "deformed" : "identity")); + INFO("Matrix-free stellar mass norm = " << matrix_free_mass_norm); + INFO("Legacy stellar mass norm = " << legacy_mass_norm); + INFO( + "Absolute stellar mass difference norm = " + << global_norm(mass_difference, communicator) + ); + INFO("Relative stellar mass-action error = " << mass_error); + + REQUIRE(matrix_free_mass_norm > 0.0); + REQUIRE(legacy_mass_norm > 0.0); + CHECK_THAT(mass_error, WithinAbs(0.0, parity_tolerance)); + } + } +} + +TEST_CASE( + "Gravity Field Operator Hdiv Mass Action Matches Stateless Quadrature " + "Reference", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + const utils::Args args = test_utils::setup_args(); + + fem::FEM fem = fem::setup_fem(args.mesh_file, args, 0); + + fem.mapping->ResetDisplacement(); + + physics::update_stiffness_matrix(fem); + + constexpr auto displacement_block = + mean_field::utils::blocks::get_value_block( + blocks::displacement_field.geometry_term + ); + + constexpr auto gravity_gradient_block = + mean_field::utils::blocks::get_value_block( + blocks::gravity_field.gradient_term + ); + + constexpr auto gravity_gradient_residual_block = + mean_field::utils::blocks::get_residual_block< + blocks::gravity_field_form>(blocks::gravity_field.gradient_term); + + const blocks::form_layout layout = + make_gravity_layout(fem); + + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(fem, *fem.domainMapperStateless); + + operators::GravityFieldJacobianOperator gravity_jacobian( + fem, *fem.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + + operators::GravityFieldOperator gravity_operator( + fem, *fem.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + const MPI_Comm communicator = fem.gravityFluxFes->GetComm(); + + const mfem::Vector gravity_gradient_true = + make_full_support_gravity_gradient(fem); + + for (const bool deformed : {false, true}) { + DYNAMIC_SECTION("Geometry = " << (deformed ? "deformed" : "identity")) { + CAPTURE(deformed); + + const mfem::Vector displacement_true = + make_stateless_reference_displacement(fem, deformed); + + mfem::Vector state(layout.value_offsets().Last()); + state = 0.0; + + for (int i = 0; i < gravity_gradient_true.Size(); ++i) { + state(layout.offset(gravity_gradient_block) + i) = + gravity_gradient_true(i); + } + + for (int i = 0; i < displacement_true.Size(); ++i) { + state(layout.offset(displacement_block) + i) = + displacement_true(i); + } + + const operators::context::gravity_field::GravityFieldRevisions + revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + gravity_operator.Prepare(state, revisions); + + mfem::Vector residual; + + gravity_operator.Mult(state, residual); + + mfem::Vector operator_action( + layout.size(gravity_gradient_residual_block) + ); + + for (int i = 0; i < operator_action.Size(); ++i) { + operator_action(i) = residual( + layout.offset(gravity_gradient_residual_block) + i + ); + } + + const StatelessHDivMassReference reference = + evaluate_stateless_hdiv_mass_quadrature_reference( + fem, gravity_gradient_true, displacement_true + ); + + mfem::Vector decomposed_reference(reference.stellar_action); + + decomposed_reference += reference.vacuum_action; + + mfem::Vector action_difference(operator_action); + + action_difference -= reference.total_action; + + const double operator_norm = + global_vector_norm(operator_action, communicator); + + const double reference_norm = + global_vector_norm(reference.total_action, communicator); + + const double stellar_action_norm = + global_vector_norm(reference.stellar_action, communicator); + + const double vacuum_action_norm = + global_vector_norm(reference.vacuum_action, communicator); + + const double absolute_action_error = + global_vector_norm(action_difference, communicator); + + const double relative_action_error = global_relative_vector_error( + operator_action, reference.total_action, communicator + ); + + const double decomposition_error = global_relative_vector_error( + reference.total_action, decomposed_reference, communicator + ); + + const double operator_energy = global_vector_dot( + gravity_gradient_true, operator_action, communicator + ); + + const double reference_energy = global_vector_dot( + gravity_gradient_true, reference.total_action, communicator + ); + + const double stellar_energy = global_vector_dot( + gravity_gradient_true, reference.stellar_action, communicator + ); + + const double vacuum_energy = global_vector_dot( + gravity_gradient_true, reference.vacuum_action, communicator + ); + + const double relative_energy_error = + std::abs(operator_energy - reference_energy) / + std::max( + std::abs(reference_energy), + std::numeric_limits::epsilon() + ); + + const double vacuum_action_fraction = + vacuum_action_norm / + std::max( + reference_norm, std::numeric_limits::epsilon() + ); + + const double vacuum_energy_fraction = + vacuum_energy / reference_energy; + + const double stellar_vacuum_dot = global_vector_dot( + reference.stellar_action, reference.vacuum_action, communicator + ); + + const double stellar_vacuum_alignment = + stellar_vacuum_dot / + std::max( + stellar_action_norm * vacuum_action_norm, + std::numeric_limits::epsilon() + ); + + INFO("Geometry = " << (deformed ? "deformed" : "identity")); + + INFO("Stellar elements = " << reference.stellar_elements); + + INFO("Vacuum elements = " << reference.vacuum_elements); + + INFO( + "Stellar quadrature points = " + << reference.stellar_quadrature_points + ); + + INFO( + "Vacuum quadrature points = " + << reference.vacuum_quadrature_points + ); + + INFO( + "Stellar mapping determinant range = [" + << reference.minimum_stellar_determinant << ", " + << reference.maximum_stellar_determinant << "]" + ); + + INFO( + "Vacuum mapping determinant range = [" + << reference.minimum_vacuum_determinant << ", " + << reference.maximum_vacuum_determinant << "]" + ); + + INFO("Operator mass-action norm = " << operator_norm); + + INFO("Stateless quadrature-reference norm = " << reference_norm); + + INFO("Stellar action norm = " << stellar_action_norm); + + INFO("Vacuum action norm = " << vacuum_action_norm); + + INFO("Vacuum action fraction = " << vacuum_action_fraction); + + INFO( + "Stellar-vacuum action alignment = " << stellar_vacuum_alignment + ); + + INFO("Absolute action error = " << absolute_action_error); + + INFO("Relative action error = " << relative_action_error); + + INFO("Domain-decomposition error = " << decomposition_error); + + INFO("Operator quadratic energy = " << operator_energy); + + INFO("Quadrature-reference energy = " << reference_energy); + + INFO("Stellar energy = " << stellar_energy); + + INFO("Vacuum energy = " << vacuum_energy); + + INFO("Vacuum energy fraction = " << vacuum_energy_fraction); + + INFO("Relative energy error = " << relative_energy_error); + + REQUIRE(reference.stellar_elements > 0); + + REQUIRE(reference.vacuum_elements > 0); + + REQUIRE(reference.stellar_quadrature_points > 0); + + REQUIRE(reference.vacuum_quadrature_points > 0); + + REQUIRE(reference.minimum_stellar_determinant > 0.0); + + REQUIRE(reference.minimum_vacuum_determinant > 0.0); + + REQUIRE(reference_energy > 0.0); + + REQUIRE(stellar_energy > 0.0); + + REQUIRE(vacuum_energy > 0.0); + + constexpr double decomposition_tolerance = 5.0e-14; + + constexpr double action_tolerance = 1.0e-11; + + constexpr double energy_tolerance = 1.0e-11; + + CHECK_THAT( + decomposition_error, + Catch::Matchers::WithinAbs(0.0, decomposition_tolerance) + ); + + CHECK_THAT( + relative_action_error, + Catch::Matchers::WithinAbs(0.0, action_tolerance) + ); + + CHECK_THAT( + relative_energy_error, + Catch::Matchers::WithinAbs(0.0, energy_tolerance) + ); + } + } +} + +TEST_CASE( + "Gravity Field Jacobian Fixed Geometry Blocks Match Centered Differences", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + f.mapping->ResetDisplacement(); + physics::update_stiffness_matrix(f); + + const gravity_layout layout = make_gravity_jacobian_layout(f); + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + mfem::Vector state(layout.value_offsets().Last()); + state = 0.0; + + const mfem::Vector displacement = + make_stateless_reference_displacement(f, true); + set_value_block(state, layout, displacement_block, displacement); + + const operators::context::gravity_field::GravityFieldRevisions revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + gravity_operator.Prepare(state, revisions); + mfem::Operator &gradient = gravity_operator.GetGradient(state); + + MPI_Comm communicator = f.mesh->GetComm(); + + struct DirectionCase { + std::string name; + mfem::Vector direction; + bool expect_gradient_residual; + bool expect_poisson_residual; + }; + + std::vector cases; + cases.push_back({"density", make_density_direction(layout), false, true}); + cases.push_back( + {"gravity gradient", make_gravity_gradient_direction(layout), true, + true} + ); + cases.push_back( + {"gravity potential", make_gravity_potential_direction(layout), true, + false} + ); + + for (const DirectionCase &direction_case : cases) { + DYNAMIC_SECTION("Direction = " << direction_case.name) { + constexpr double difference_step = 1.0e-6; + + mfem::Vector jacobian_action; + gradient.Mult(direction_case.direction, jacobian_action); + + const mfem::Vector finite_difference = evaluate_centered_difference( + gravity_operator, state, direction_case.direction, + difference_step + ); + + const mfem::Vector gradient_action = get_residual_block( + jacobian_action, layout, gravity_gradient_residual_block + ); + const mfem::Vector poisson_action = get_residual_block( + jacobian_action, layout, gravity_poisson_residual_block + ); + + const double relative_error = global_relative_vector_error( + jacobian_action, finite_difference, communicator + ); + const double gradient_norm = + global_vector_norm(gradient_action, communicator); + const double poisson_norm = + global_vector_norm(poisson_action, communicator); + + INFO("Direction = " << direction_case.name); + INFO( + "Jacobian action norm = " + << global_vector_norm(jacobian_action, communicator) + ); + INFO( + "Finite-difference action norm = " + << global_vector_norm(finite_difference, communicator) + ); + INFO("Gradient residual action norm = " << gradient_norm); + INFO("Poisson residual action norm = " << poisson_norm); + INFO("Relative Jacobian error = " << relative_error); + + constexpr double jacobian_tolerance = 2.0e-8; + constexpr double zero_tolerance = 1.0e-13; + + CHECK_THAT( + relative_error, + Catch::Matchers::WithinAbs(0.0, jacobian_tolerance) + ); + + if (direction_case.expect_gradient_residual) { + CHECK(gradient_norm > zero_tolerance); + } else { + CHECK_THAT( + gradient_norm, + Catch::Matchers::WithinAbs(0.0, zero_tolerance) + ); + } + + if (direction_case.expect_poisson_residual) { + CHECK(poisson_norm > zero_tolerance); + } else { + CHECK_THAT( + poisson_norm, + Catch::Matchers::WithinAbs(0.0, zero_tolerance) + ); + } + } + } +} +TEST_CASE( + "Gravity Field Jacobian Combined Fixed Geometry Direction Matches Centered " + "Differences", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + f.mapping->ResetDisplacement(); + physics::update_stiffness_matrix(f); + + const gravity_layout layout = make_gravity_jacobian_layout(f); + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + const mfem::Vector state = make_gravity_jacobian_state(f, layout, true); + const mfem::Vector direction = + make_combined_fixed_geometry_direction(layout); + + operators::context::gravity_field::GravityFieldRevisions revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + gravity_operator.Prepare(state, revisions); + + mfem::Operator &gradient = gravity_operator.GetGradient(state); + mfem::Vector jacobian_action; + gradient.Mult(direction, jacobian_action); + + MPI_Comm communicator = f.mesh->GetComm(); + double best_error = std::numeric_limits::infinity(); + + for (const double step : std::array{1.0e-4, 1.0e-6, 1.0e-7}) { + const mfem::Vector finite_difference = evaluate_centered_difference( + gravity_operator, state, direction, step + ); + const double relative_error = global_relative_vector_error( + jacobian_action, finite_difference, communicator + ); + best_error = std::min(best_error, relative_error); + + INFO("Centered-difference step = " << step); + INFO("Relative Jacobian error = " << relative_error); + + CHECK(relative_error < 2.0e-7); + } + + INFO("Best relative Jacobian error = " << best_error); + CHECK(best_error < 2.0e-8); +} + +TEST_CASE( + "Gravity Field Jacobian Action Is Linear At Fixed Geometry", + tags::unit &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + f.mapping->ResetDisplacement(); + physics::update_stiffness_matrix(f); + + const gravity_layout layout = make_gravity_jacobian_layout(f); + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + const mfem::Vector state = make_gravity_jacobian_state(f, layout, false); + const mfem::Vector direction_a = make_density_direction(layout); + const mfem::Vector direction_b = make_gravity_gradient_direction(layout); + + const operators::context::gravity_field::GravityFieldRevisions revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + gravity_operator.Prepare(state, revisions); + mfem::Operator &gradient = gravity_operator.GetGradient(state); + + constexpr double scale_a = 1.7; + constexpr double scale_b = -0.6; + + mfem::Vector combined_direction(direction_a); + combined_direction *= scale_a; + combined_direction.Add(scale_b, direction_b); + + mfem::Vector action_a; + mfem::Vector action_b; + mfem::Vector combined_action; + + gradient.Mult(direction_a, action_a); + gradient.Mult(direction_b, action_b); + gradient.Mult(combined_direction, combined_action); + + mfem::Vector expected_action(action_a); + expected_action *= scale_a; + expected_action.Add(scale_b, action_b); + + MPI_Comm communicator = f.mesh->GetComm(); + const double relative_error = global_relative_vector_error( + combined_action, expected_action, communicator + ); + + INFO("Relative Jacobian linearity error = " << relative_error); + CHECK_THAT(relative_error, Catch::Matchers::WithinAbs(0.0, 2.0e-13)); +} +TEST_CASE( + "Gravity Field Prepare Updates Shared Linearization Context", + tags::unit &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + f.mapping->ResetDisplacement(); + physics::update_stiffness_matrix(f); + + const gravity_layout layout = make_gravity_jacobian_layout(f); + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + mfem::Vector state_a = make_gravity_jacobian_state(f, layout, false); + const mfem::Vector state_b = make_gravity_jacobian_state(f, layout, true); + + const operators::context::gravity_field::GravityFieldRevisions revisions_a{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + const operators::context::gravity_field::GravityFieldRevisions revisions_b{ + .discretization = {1}, + .displacement = {2}, + .density = {2}, + .gravity_gradient = {2}, + .gravity_potential = {2} + }; + + MPI_Comm communicator = f.mesh->GetComm(); + + gravity_operator.Prepare(state_a, revisions_a); + + mfem::Operator &returned_gradient_a = gravity_operator.GetGradient(state_a); + REQUIRE( + &returned_gradient_a == static_cast(&gravity_jacobian) + ); + + check_linearization_context_matches_state( + linearization_context, state_a, layout.value_offsets(), communicator + ); + + state_a = 0.0; + + CHECK(linearization_context.IsPrepared()); + + const double stored_state_norm = + global_vector_norm(linearization_context.GetDensity(), communicator) + + global_vector_norm( + linearization_context.GetGeometryContext().GetDisplacement(), + communicator + ) + + global_vector_norm( + linearization_context.GetGravityGradient(), communicator + ); + + CHECK(stored_state_norm > 0.0); + + gravity_operator.Prepare(state_b, revisions_b); + + mfem::Operator &returned_gradient_b = gravity_operator.GetGradient(state_b); + REQUIRE( + &returned_gradient_b == static_cast(&gravity_jacobian) + ); + + check_linearization_context_matches_state( + linearization_context, state_b, layout.value_offsets(), communicator + ); +} +TEST_CASE( + "Mapped Hdiv Mass Variation Is Linear In Displacement Direction", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mapping::DomainMapperStateless &domain_mapper = + *f.domainMapperStateless; + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + mfem::Vector zero_direction(f.displacementFes->GetTrueVSize()); + mfem::Vector zero_gravity_gradient(f.gravityFluxFes->GetTrueVSize()); + zero_direction = 0.0; + zero_gravity_gradient = 0.0; + + mfem::Vector zero_direction_action; + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, fields.gravity_gradient, fields.displacement, + zero_direction, zero_direction_action + ); + + INFO( + "Zero-direction action norm = " + << global_norm(zero_direction_action, communicator) + ); + CHECK(global_norm(zero_direction_action, communicator) < 1.0e-13); + + mfem::Vector zero_gravity_action; + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, zero_gravity_gradient, fields.displacement, + fields.displacement_direction_1, zero_gravity_action + ); + + INFO( + "Zero-gravity action norm = " + << global_norm(zero_gravity_action, communicator) + ); + CHECK(global_norm(zero_gravity_action, communicator) < 1.0e-13); + + constexpr double scale_1 = 1.7; + constexpr double scale_2 = -0.6; + + mfem::Vector combined_direction(fields.displacement_direction_1); + combined_direction *= scale_1; + combined_direction.Add(scale_2, fields.displacement_direction_2); + + mfem::Vector action_1; + mfem::Vector action_2; + mfem::Vector combined_action; + + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, fields.gravity_gradient, fields.displacement, + fields.displacement_direction_1, action_1 + ); + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, fields.gravity_gradient, fields.displacement, + fields.displacement_direction_2, action_2 + ); + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, fields.gravity_gradient, fields.displacement, + combined_direction, combined_action + ); + + mfem::Vector expected_action(action_1); + expected_action *= scale_1; + expected_action.Add(scale_2, action_2); + + const double linearity_error = + global_relative_error(combined_action, expected_action, communicator); + + INFO( + "Combined action norm = " << global_norm(combined_action, communicator) + ); + INFO( + "Expected action norm = " << global_norm(expected_action, communicator) + ); + INFO("Displacement-direction linearity error = " << linearity_error); + + CHECK_THAT(linearity_error, Catch::Matchers::WithinAbs(0.0, 2.0e-12)); +} + +TEST_CASE( + "Mapped Hdiv Mass Variation Matches Centered Geometry Differences", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mapping::DomainMapperStateless &domain_mapper = + *f.domainMapperStateless; + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + constexpr double difference_step = 1.0e-5; + constexpr double comparison_tolerance = 2.0e-7; + + mfem::Vector identity_displacement(f.displacementFes->GetTrueVSize()); + identity_displacement = 0.0; + + for (const bool deformed : std::array{false, true}) { + const mfem::Vector &base_displacement = + deformed ? fields.displacement : identity_displacement; + + mfem::Vector analytic_action; + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, fields.gravity_gradient, base_displacement, + fields.displacement_direction_1, analytic_action + ); + + const mfem::Vector finite_difference_action = + centered_hdiv_mass_geometry_difference( + f, domain_mapper, fields.gravity_gradient, base_displacement, + fields.displacement_direction_1, difference_step + ); + + const double relative_error = global_relative_error( + analytic_action, finite_difference_action, communicator + ); + + INFO("Geometry = " << (deformed ? "deformed" : "identity")); + INFO( + "Analytic variation norm = " + << global_norm(analytic_action, communicator) + ); + INFO( + "Finite-difference variation norm = " + << global_norm(finite_difference_action, communicator) + ); + INFO("Relative H(div) mass-variation error = " << relative_error); + + CHECK_THAT( + relative_error, + Catch::Matchers::WithinAbs(0.0, comparison_tolerance) + ); + } +} + +TEST_CASE( + "Mapped Hdiv Mass Geometry Difference Converges To Analytic Variation", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators + &tags::convergence +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mapping::DomainMapperStateless &domain_mapper = + *f.domainMapperStateless; + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + mfem::Vector analytic_action; + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, fields.gravity_gradient, fields.displacement, + fields.displacement_direction_1, analytic_action + ); + + constexpr std::array difference_steps{8.0e-2, 4.0e-2, 2.0e-2}; + std::array errors{}; + + for (std::size_t i = 0; i < difference_steps.size(); ++i) { + const mfem::Vector finite_difference_action = + centered_hdiv_mass_geometry_difference( + f, domain_mapper, fields.gravity_gradient, fields.displacement, + fields.displacement_direction_1, difference_steps[i] + ); + + errors[i] = global_relative_error( + finite_difference_action, analytic_action, communicator + ); + + INFO("Difference step = " << difference_steps[i]); + INFO("Relative error = " << errors[i]); + } + + const double first_observed_order = + std::log(errors[0] / errors[1]) / std::log(2.0); + const double second_observed_order = + std::log(errors[1] / errors[2]) / std::log(2.0); + + INFO( + "Errors = [" << errors[0] << ", " << errors[1] << ", " << errors[2] + << "]" + ); + INFO("First observed convergence order = " << first_observed_order); + INFO("Second observed convergence order = " << second_observed_order); + + CHECK(errors[1] < errors[0]); + CHECK(errors[2] < errors[1]); + CHECK(first_observed_order > 1.8); + CHECK(second_observed_order > 1.8); +} + +TEST_CASE( + "Mapped Source Variation Is Linear In Displacement Direction", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mapping::DomainMapperStateless &domain_mapper = + *f.domainMapperStateless; + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + const mfem::Vector density = make_source_variation_density(f); + MPI_Comm communicator = f.mesh->GetComm(); + + mfem::Vector zero_density(f.densityFes->GetTrueVSize()); + mfem::Vector zero_direction(f.displacementFes->GetTrueVSize()); + zero_density = 0.0; + zero_direction = 0.0; + + mfem::Vector zero_direction_action; + operators::kernels::apply_mapped_source_variation( + f, domain_mapper, density, fields.displacement, zero_direction, + zero_direction_action + ); + + REQUIRE( + zero_direction_action.Size() == f.gravityPotentialFes->GetTrueVSize() + ); + CHECK(global_norm(zero_direction_action, communicator) < 1.0e-13); + + mfem::Vector zero_density_action; + operators::kernels::apply_mapped_source_variation( + f, domain_mapper, zero_density, fields.displacement, + fields.displacement_direction_1, zero_density_action + ); + + REQUIRE( + zero_density_action.Size() == f.gravityPotentialFes->GetTrueVSize() + ); + CHECK(global_norm(zero_density_action, communicator) < 1.0e-13); + + constexpr double scale_1 = 1.4; + constexpr double scale_2 = -0.7; + + mfem::Vector combined_direction(fields.displacement_direction_1); + combined_direction *= scale_1; + combined_direction.Add(scale_2, fields.displacement_direction_2); + + mfem::Vector action_1; + mfem::Vector action_2; + mfem::Vector combined_action; + + operators::kernels::apply_mapped_source_variation( + f, domain_mapper, density, fields.displacement, + fields.displacement_direction_1, action_1 + ); + operators::kernels::apply_mapped_source_variation( + f, domain_mapper, density, fields.displacement, + fields.displacement_direction_2, action_2 + ); + operators::kernels::apply_mapped_source_variation( + f, domain_mapper, density, fields.displacement, combined_direction, + combined_action + ); + + REQUIRE(action_1.Size() == f.gravityPotentialFes->GetTrueVSize()); + REQUIRE(action_2.Size() == f.gravityPotentialFes->GetTrueVSize()); + REQUIRE(combined_action.Size() == f.gravityPotentialFes->GetTrueVSize()); + + mfem::Vector expected_action(action_1); + expected_action *= scale_1; + expected_action.Add(scale_2, action_2); + + const double linearity_error = + global_relative_error(combined_action, expected_action, communicator); + + INFO( + "Combined source-variation norm = " + << global_norm(combined_action, communicator) + ); + INFO( + "Expected source-variation norm = " + << global_norm(expected_action, communicator) + ); + INFO("Source-variation linearity error = " << linearity_error); + + CHECK_THAT(linearity_error, Catch::Matchers::WithinAbs(0.0, 2.0e-12)); +} + +TEST_CASE( + "Mapped Source Variation Matches Centered Geometry Differences", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mapping::DomainMapperStateless &domain_mapper = + *f.domainMapperStateless; + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + const mfem::Vector density = make_source_variation_density(f); + MPI_Comm communicator = f.mesh->GetComm(); + + constexpr double difference_step = 1.0e-5; + constexpr double comparison_tolerance = 2.0e-7; + + mfem::Vector identity_displacement(f.displacementFes->GetTrueVSize()); + identity_displacement = 0.0; + + for (const bool deformed : std::array{false, true}) { + const mfem::Vector &base_displacement = + deformed ? fields.displacement : identity_displacement; + + mfem::Vector analytic_action; + operators::kernels::apply_mapped_source_variation( + f, domain_mapper, density, base_displacement, + fields.displacement_direction_1, analytic_action + ); + + const mfem::Vector finite_difference_action = + centered_source_geometry_difference( + f, domain_mapper, density, base_displacement, + fields.displacement_direction_1, difference_step + ); + + REQUIRE( + analytic_action.Size() == f.gravityPotentialFes->GetTrueVSize() + ); + REQUIRE( + finite_difference_action.Size() == + f.gravityPotentialFes->GetTrueVSize() + ); + + const double relative_error = global_relative_error( + analytic_action, finite_difference_action, communicator + ); + + INFO("Geometry = " << (deformed ? "deformed" : "identity")); + INFO( + "Analytic source-variation norm = " + << global_norm(analytic_action, communicator) + ); + INFO( + "Finite-difference source-variation norm = " + << global_norm(finite_difference_action, communicator) + ); + INFO("Relative source-variation error = " << relative_error); + + CHECK_THAT( + relative_error, + Catch::Matchers::WithinAbs(0.0, comparison_tolerance) + ); + } +} + +TEST_CASE( + "Mapped Source Geometry Difference Converges To Analytic Variation", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators + &tags::convergence +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mapping::DomainMapperStateless &domain_mapper = + *f.domainMapperStateless; + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + const mfem::Vector density = make_source_variation_density(f); + MPI_Comm communicator = f.mesh->GetComm(); + + mfem::Vector analytic_action; + operators::kernels::apply_mapped_source_variation( + f, domain_mapper, density, fields.displacement, + fields.displacement_direction_1, analytic_action + ); + + REQUIRE(analytic_action.Size() == f.gravityPotentialFes->GetTrueVSize()); + + constexpr std::array difference_steps{8.0e-2, 4.0e-2, 2.0e-2}; + std::array errors{}; + + for (std::size_t i = 0; i < difference_steps.size(); ++i) { + const mfem::Vector finite_difference_action = + centered_source_geometry_difference( + f, domain_mapper, density, fields.displacement, + fields.displacement_direction_1, difference_steps[i] + ); + + REQUIRE( + finite_difference_action.Size() == + f.gravityPotentialFes->GetTrueVSize() + ); + errors[i] = global_relative_error( + finite_difference_action, analytic_action, communicator + ); + } + + const double first_observed_order = + std::log(errors[0] / errors[1]) / std::log(2.0); + const double second_observed_order = + std::log(errors[1] / errors[2]) / std::log(2.0); + + INFO( + "Errors = [" << errors[0] << ", " << errors[1] << ", " << errors[2] + << "]" + ); + INFO("First observed convergence order = " << first_observed_order); + INFO("Second observed convergence order = " << second_observed_order); + + CHECK(errors[1] < errors[0]); + CHECK(errors[2] < errors[1]); + CHECK(first_observed_order > 1.8); + CHECK(second_observed_order > 1.8); +} + +TEST_CASE( + "Mapped Hdiv Mass Variation Is Symmetric", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mapping::DomainMapperStateless &domain_mapper = + *f.domainMapperStateless; + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + const mfem::Vector second_gravity_gradient = + make_secondary_gravity_gradient(f); + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + mfem::Vector identity_displacement(f.displacementFes->GetTrueVSize()); + identity_displacement = 0.0; + + for (const bool deformed : std::array{false, true}) { + const mfem::Vector &base_displacement = + deformed ? fields.displacement : identity_displacement; + + mfem::Vector first_action; + mfem::Vector second_action; + + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, fields.gravity_gradient, base_displacement, + fields.displacement_direction_1, first_action + ); + + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, second_gravity_gradient, base_displacement, + fields.displacement_direction_1, second_action + ); + + REQUIRE(first_action.Size() == f.gravityFluxFes->GetTrueVSize()); + REQUIRE(second_action.Size() == f.gravityFluxFes->GetTrueVSize()); + + const double left_pairing = + global_dot(fields.gravity_gradient, second_action, communicator); + const double right_pairing = + global_dot(second_gravity_gradient, first_action, communicator); + const double symmetry_error = + std::abs(left_pairing - right_pairing) / + std::max( + {std::abs(left_pairing), std::abs(right_pairing), 1.0e-14} + ); + + INFO("Geometry = " << (deformed ? "deformed" : "identity")); + INFO("g1^T delta_M g2 = " << left_pairing); + INFO("g2^T delta_M g1 = " << right_pairing); + INFO("Relative symmetry error = " << symmetry_error); + + CHECK_THAT(symmetry_error, Catch::Matchers::WithinAbs(0.0, 1.0e-11)); + } +} + +TEST_CASE( + "Mapped Geometry Variations Are Linear In Base Fields", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mapping::DomainMapperStateless &domain_mapper = + *f.domainMapperStateless; + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + const mfem::Vector second_gravity_gradient = + make_secondary_gravity_gradient(f); + const mfem::Vector first_density = make_source_variation_density(f); + const mfem::Vector second_density = make_secondary_source_density(f); + + constexpr double scale_1 = 1.3; + constexpr double scale_2 = -0.4; + + { + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + mfem::Vector combined_gravity_gradient(fields.gravity_gradient); + combined_gravity_gradient *= scale_1; + combined_gravity_gradient.Add(scale_2, second_gravity_gradient); + + mfem::Vector first_action; + mfem::Vector second_action; + mfem::Vector combined_action; + + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, fields.gravity_gradient, fields.displacement, + fields.displacement_direction_1, first_action + ); + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, second_gravity_gradient, fields.displacement, + fields.displacement_direction_1, second_action + ); + operators::kernels::apply_mapped_hdiv_mass_variation( + f, domain_mapper, combined_gravity_gradient, fields.displacement, + fields.displacement_direction_1, combined_action + ); + + REQUIRE(first_action.Size() == f.gravityFluxFes->GetTrueVSize()); + REQUIRE(second_action.Size() == f.gravityFluxFes->GetTrueVSize()); + REQUIRE(combined_action.Size() == f.gravityFluxFes->GetTrueVSize()); + + mfem::Vector expected_action(first_action); + expected_action *= scale_1; + expected_action.Add(scale_2, second_action); + + const double linearity_error = global_relative_error( + combined_action, expected_action, communicator + ); + + INFO("H(div) base-field linearity error = " << linearity_error); + CHECK_THAT(linearity_error, Catch::Matchers::WithinAbs(0.0, 3.0e-12)); + } + + { + MPI_Comm communicator = f.mesh->GetComm(); + + mfem::Vector combined_density(first_density); + combined_density *= scale_1; + combined_density.Add(scale_2, second_density); + + mfem::Vector first_action; + mfem::Vector second_action; + mfem::Vector combined_action; + + operators::kernels::apply_mapped_source_variation( + f, domain_mapper, first_density, fields.displacement, + fields.displacement_direction_1, first_action + ); + operators::kernels::apply_mapped_source_variation( + f, domain_mapper, second_density, fields.displacement, + fields.displacement_direction_1, second_action + ); + operators::kernels::apply_mapped_source_variation( + f, domain_mapper, combined_density, fields.displacement, + fields.displacement_direction_1, combined_action + ); + + REQUIRE(first_action.Size() == f.gravityPotentialFes->GetTrueVSize()); + REQUIRE(second_action.Size() == f.gravityPotentialFes->GetTrueVSize()); + REQUIRE( + combined_action.Size() == f.gravityPotentialFes->GetTrueVSize() + ); + + mfem::Vector expected_action(first_action); + expected_action *= scale_1; + expected_action.Add(scale_2, second_action); + + const double linearity_error = global_relative_error( + combined_action, expected_action, communicator + ); + + INFO("Source base-field linearity error = " << linearity_error); + CHECK_THAT(linearity_error, Catch::Matchers::WithinAbs(0.0, 3.0e-12)); + } +} + +TEST_CASE( + "Mapped Source Variation Ignores Vacuum Density", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mapping::DomainMapperStateless &domain_mapper = + *f.domainMapperStateless; + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + const int vacuum_attribute = domain_mapper.GetVacuumElementAttribute(); + const mfem::Vector vacuum_density = + make_vacuum_only_density(f, vacuum_attribute); + MPI_Comm communicator = f.mesh->GetComm(); + + const double vacuum_density_norm = + global_norm(vacuum_density, communicator); + REQUIRE(vacuum_density_norm > 0.0); + + mfem::Vector action; + operators::kernels::apply_mapped_source_variation( + f, domain_mapper, vacuum_density, fields.displacement, + fields.displacement_direction_1, action + ); + + REQUIRE(action.Size() == f.gravityPotentialFes->GetTrueVSize()); + + const double action_norm = global_norm(action, communicator); + + INFO("Vacuum density norm = " << vacuum_density_norm); + INFO("Source-variation action norm = " << action_norm); + + CHECK_THAT(action_norm, Catch::Matchers::WithinAbs(0.0, 1.0e-14)); +} + +TEST_CASE( + "Gravity Field Jacobian Displacement Blocks Match Geometry Kernels", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + f.mapping->ResetDisplacement(); + physics::update_stiffness_matrix(f); + + REQUIRE(f.domainMapperStateless != nullptr); + + const gravity_layout layout = make_gravity_jacobian_layout(f); + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + const mfem::Vector state = make_gravity_jacobian_state(f, layout, true); + const mfem::Vector direction = + make_displacement_direction(layout, fields.displacement_direction_1); + const mfem::Vector density = get_value_block(state, layout, density_block); + const mfem::Vector displacement = + get_value_block(state, layout, displacement_block); + const mfem::Vector gravity_gradient = + get_value_block(state, layout, gravity_gradient_block); + + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + const operators::context::gravity_field::GravityFieldRevisions revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + gravity_operator.Prepare(state, revisions); + + mfem::Vector jacobian_action; + gravity_jacobian.Mult(direction, jacobian_action); + + REQUIRE(jacobian_action.Size() == layout.residual_offsets().Last()); + + const mfem::Vector gradient_action = get_residual_block( + jacobian_action, layout, gravity_gradient_residual_block + ); + const mfem::Vector poisson_action = get_residual_block( + jacobian_action, layout, gravity_poisson_residual_block + ); + + mfem::Vector expected_gradient_action; + mfem::Vector expected_poisson_action; + operators::kernels::apply_mapped_hdiv_mass_variation( + f, *f.domainMapperStateless, gravity_gradient, displacement, + fields.displacement_direction_1, expected_gradient_action + ); + operators::kernels::apply_mapped_source_variation( + f, *f.domainMapperStateless, density, displacement, + fields.displacement_direction_1, expected_poisson_action + ); + expected_poisson_action *= -1.0; + + MPI_Comm communicator = f.mesh->GetComm(); + const double gradient_error = global_relative_error( + gradient_action, expected_gradient_action, communicator + ); + const double poisson_error = global_relative_error( + poisson_action, expected_poisson_action, communicator + ); + + INFO( + "Gradient displacement action norm = " + << global_norm(gradient_action, communicator) + ); + INFO( + "Poisson displacement action norm = " + << global_norm(poisson_action, communicator) + ); + INFO("Gradient displacement-block error = " << gradient_error); + INFO("Poisson displacement-block error = " << poisson_error); + + REQUIRE(global_norm(gradient_action, communicator) > 1.0e-12); + REQUIRE(global_norm(poisson_action, communicator) > 1.0e-12); + CHECK_THAT(gradient_error, WithinAbs(0.0, 2.0e-12)); + CHECK_THAT(poisson_error, WithinAbs(0.0, 2.0e-12)); +} + +TEST_CASE( + "Gravity Field Jacobian Displacement Direction Matches Centered " + "Differences", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + f.mapping->ResetDisplacement(); + physics::update_stiffness_matrix(f); + + REQUIRE(f.domainMapperStateless != nullptr); + + const gravity_layout layout = make_gravity_jacobian_layout(f); + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + const mfem::Vector direction = + make_displacement_direction(layout, fields.displacement_direction_1); + + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + constexpr double difference_step = 1.0e-5; + constexpr double comparison_tolerance = 3.0e-7; + constexpr double nonzero_tolerance = 1.0e-12; + + MPI_Comm communicator = f.mesh->GetComm(); + + REQUIRE(direction.Size() == layout.value_offsets().Last()); + REQUIRE(global_vector_norm(direction, communicator) > nonzero_tolerance); + + for (const bool deformed : std::array{false, true}) { + DYNAMIC_SECTION("Geometry = " << (deformed ? "deformed" : "identity")) { + const mfem::Vector state = + make_gravity_jacobian_state(f, layout, deformed); + + REQUIRE(state.Size() == layout.value_offsets().Last()); + + const operators::context::gravity_field::GravityFieldRevisions + base_revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + gravity_operator.Prepare(state, base_revisions); + + REQUIRE(linearization_context.IsPrepared()); + + check_linearization_context_matches_state( + linearization_context, state, layout.value_offsets(), + communicator + ); + + const double base_density_norm = global_vector_norm( + linearization_context.GetDensity(), communicator + ); + const double base_gravity_gradient_norm = global_vector_norm( + linearization_context.GetGravityGradient(), communicator + ); + + INFO("Base density norm = " << base_density_norm); + INFO("Base gravity-gradient norm = " << base_gravity_gradient_norm); + + REQUIRE(base_density_norm > nonzero_tolerance); + REQUIRE(base_gravity_gradient_norm > nonzero_tolerance); + + mfem::Operator &gradient = gravity_operator.GetGradient(state); + REQUIRE( + &gradient == static_cast(&gravity_jacobian) + ); + + mfem::Vector jacobian_action; + gradient.Mult(direction, jacobian_action); + + REQUIRE(jacobian_action.Size() == layout.residual_offsets().Last()); + + mfem::Vector plus_state(state); + mfem::Vector minus_state(state); + plus_state.Add(difference_step, direction); + minus_state.Add(-difference_step, direction); + + auto plus_revisions = base_revisions; + plus_revisions.displacement.value++; + + mfem::Vector plus_residual; + gravity_operator.Prepare(plus_state, plus_revisions); + gravity_operator.Mult(plus_state, plus_residual); + + REQUIRE(plus_residual.Size() == layout.residual_offsets().Last()); + + auto minus_revisions = plus_revisions; + minus_revisions.displacement.value++; + + mfem::Vector minus_residual; + gravity_operator.Prepare(minus_state, minus_revisions); + gravity_operator.Mult(minus_state, minus_residual); + + REQUIRE(minus_residual.Size() == layout.residual_offsets().Last()); + + mfem::Vector finite_difference(plus_residual); + finite_difference -= minus_residual; + finite_difference /= 2.0 * difference_step; + + const mfem::Vector gradient_action = get_residual_block( + jacobian_action, layout, gravity_gradient_residual_block + ); + const mfem::Vector poisson_action = get_residual_block( + jacobian_action, layout, gravity_poisson_residual_block + ); + const mfem::Vector finite_difference_gradient = get_residual_block( + finite_difference, layout, gravity_gradient_residual_block + ); + const mfem::Vector finite_difference_poisson = get_residual_block( + finite_difference, layout, gravity_poisson_residual_block + ); + + const double jacobian_gradient_norm = + global_vector_norm(gradient_action, communicator); + const double jacobian_poisson_norm = + global_vector_norm(poisson_action, communicator); + const double finite_difference_gradient_norm = + global_vector_norm(finite_difference_gradient, communicator); + const double finite_difference_poisson_norm = + global_vector_norm(finite_difference_poisson, communicator); + + REQUIRE(jacobian_gradient_norm > nonzero_tolerance); + REQUIRE(jacobian_poisson_norm > nonzero_tolerance); + REQUIRE(finite_difference_gradient_norm > nonzero_tolerance); + REQUIRE(finite_difference_poisson_norm > nonzero_tolerance); + + mfem::Vector gradient_difference(gradient_action); + gradient_difference -= finite_difference_gradient; + + mfem::Vector poisson_difference(poisson_action); + poisson_difference -= finite_difference_poisson; + + mfem::Vector combined_difference(jacobian_action); + combined_difference -= finite_difference; + + const double absolute_gradient_error = + global_vector_norm(gradient_difference, communicator); + const double absolute_poisson_error = + global_vector_norm(poisson_difference, communicator); + const double absolute_combined_error = + global_vector_norm(combined_difference, communicator); + + const double gradient_error = global_relative_error( + gradient_action, finite_difference_gradient, communicator + ); + const double poisson_error = global_relative_error( + poisson_action, finite_difference_poisson, communicator + ); + const double combined_error = global_relative_error( + jacobian_action, finite_difference, communicator + ); + + INFO("Geometry = " << (deformed ? "deformed" : "identity")); + INFO("Jacobian gradient action norm = " << jacobian_gradient_norm); + INFO( + "Finite-difference gradient norm = " + << finite_difference_gradient_norm + ); + INFO("Jacobian Poisson action norm = " << jacobian_poisson_norm); + INFO( + "Finite-difference Poisson norm = " + << finite_difference_poisson_norm + ); + INFO( + "Absolute gradient residual error = " << absolute_gradient_error + ); + INFO( + "Absolute Poisson residual error = " << absolute_poisson_error + ); + INFO( + "Absolute combined residual error = " << absolute_combined_error + ); + INFO("Gradient residual relative error = " << gradient_error); + INFO("Poisson residual relative error = " << poisson_error); + INFO("Combined residual relative error = " << combined_error); + + REQUIRE(std::isfinite(gradient_error)); + REQUIRE(std::isfinite(poisson_error)); + REQUIRE(std::isfinite(combined_error)); + + CHECK_THAT(gradient_error, WithinAbs(0.0, comparison_tolerance)); + CHECK_THAT(poisson_error, WithinAbs(0.0, comparison_tolerance)); + CHECK_THAT(combined_error, WithinAbs(0.0, comparison_tolerance)); + } + } +} +TEST_CASE( + "Gravity Field Jacobian Displacement Difference Converges At Second Order", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators + &tags::convergence +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + f.mapping->ResetDisplacement(); + physics::update_stiffness_matrix(f); + + REQUIRE(f.domainMapperStateless != nullptr); + + const gravity_layout layout = make_gravity_jacobian_layout(f); + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + const mfem::Vector state = make_gravity_jacobian_state(f, layout, true); + const mfem::Vector direction = + make_displacement_direction(layout, fields.displacement_direction_1); + + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + operators::context::gravity_field::GravityFieldRevisions revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + MPI_Comm communicator = f.mesh->GetComm(); + + gravity_operator.Prepare(state, revisions); + + REQUIRE(linearization_context.IsPrepared()); + + check_linearization_context_matches_state( + linearization_context, state, layout.value_offsets(), communicator + ); + + mfem::Operator &gradient = gravity_operator.GetGradient(state); + REQUIRE(&gradient == static_cast(&gravity_jacobian)); + + mfem::Vector jacobian_action; + gradient.Mult(direction, jacobian_action); + + REQUIRE(jacobian_action.Size() == layout.residual_offsets().Last()); + + const double jacobian_action_norm = + global_vector_norm(jacobian_action, communicator); + + INFO("Jacobian action norm = " << jacobian_action_norm); + REQUIRE(jacobian_action_norm > 1.0e-12); + + auto evaluate_geometry_centered_difference = + [&](const double difference_step) { + mfem::Vector plus_state(state); + mfem::Vector minus_state(state); + plus_state.Add(difference_step, direction); + minus_state.Add(-difference_step, direction); + + revisions.displacement.value++; + + mfem::Vector plus_residual; + gravity_operator.Prepare(plus_state, revisions); + gravity_operator.Mult(plus_state, plus_residual); + + revisions.displacement.value++; + + mfem::Vector minus_residual; + gravity_operator.Prepare(minus_state, revisions); + gravity_operator.Mult(minus_state, minus_residual); + + REQUIRE(plus_residual.Size() == layout.residual_offsets().Last()); + REQUIRE(minus_residual.Size() == layout.residual_offsets().Last()); + + mfem::Vector finite_difference(plus_residual); + finite_difference -= minus_residual; + finite_difference /= 2.0 * difference_step; + + return finite_difference; + }; + + constexpr std::array difference_steps{8.0e-2, 4.0e-2, 2.0e-2}; + + std::array errors{}; + std::array finite_difference_norms{}; + + for (std::size_t i = 0; i < difference_steps.size(); ++i) { + const mfem::Vector finite_difference = + evaluate_geometry_centered_difference(difference_steps[i]); + + finite_difference_norms[i] = + global_vector_norm(finite_difference, communicator); + errors[i] = global_relative_error( + finite_difference, jacobian_action, communicator + ); + + INFO( + "Step = " << difference_steps[i] << ", finite-difference norm = " + << finite_difference_norms[i] + << ", relative error = " << errors[i] + ); + + REQUIRE(finite_difference_norms[i] > 1.0e-12); + REQUIRE(std::isfinite(errors[i])); + REQUIRE(errors[i] > 0.0); + } + + const double first_observed_order = + std::log(errors[0] / errors[1]) / std::log(2.0); + const double second_observed_order = + std::log(errors[1] / errors[2]) / std::log(2.0); + + INFO( + "Difference steps = [" << difference_steps[0] << ", " + << difference_steps[1] << ", " + << difference_steps[2] << "]" + ); + INFO( + "Finite-difference norms = [" << finite_difference_norms[0] << ", " + << finite_difference_norms[1] << ", " + << finite_difference_norms[2] << "]" + ); + INFO( + "Relative errors = [" << errors[0] << ", " << errors[1] << ", " + << errors[2] << "]" + ); + INFO("First observed convergence order = " << first_observed_order); + INFO("Second observed convergence order = " << second_observed_order); + + REQUIRE(std::isfinite(first_observed_order)); + REQUIRE(std::isfinite(second_observed_order)); + + CHECK(errors[1] < errors[0]); + CHECK(errors[2] < errors[1]); + CHECK(first_observed_order > 1.8); + CHECK(second_observed_order > 1.8); +} + +TEST_CASE( + "Gravity Field Jacobian Complete Coupled Direction Matches Centered " + "Differences", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + f.mapping->ResetDisplacement(); + physics::update_stiffness_matrix(f); + + REQUIRE(f.domainMapperStateless != nullptr); + + const gravity_layout layout = make_gravity_jacobian_layout(f); + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + const mfem::Vector state = make_gravity_jacobian_state(f, layout, true); + + mfem::Vector direction = make_combined_fixed_geometry_direction(layout); + set_value_block( + direction, layout, displacement_block, fields.displacement_direction_2 + ); + + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + operators::context::gravity_field::GravityFieldRevisions base_revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + MPI_Comm communicator = f.mesh->GetComm(); + + REQUIRE(state.Size() == layout.value_offsets().Last()); + REQUIRE(direction.Size() == layout.value_offsets().Last()); + REQUIRE(global_vector_norm(direction, communicator) > 1.0e-12); + + gravity_operator.Prepare(state, base_revisions); + + REQUIRE(linearization_context.IsPrepared()); + + check_linearization_context_matches_state( + linearization_context, state, layout.value_offsets(), communicator + ); + + mfem::Operator &gradient = gravity_operator.GetGradient(state); + REQUIRE(&gradient == static_cast(&gravity_jacobian)); + + mfem::Vector jacobian_action; + gradient.Mult(direction, jacobian_action); + + REQUIRE(jacobian_action.Size() == layout.residual_offsets().Last()); + + constexpr double difference_step = 1.0e-5; + + mfem::Vector plus_state(state); + mfem::Vector minus_state(state); + plus_state.Add(difference_step, direction); + minus_state.Add(-difference_step, direction); + + auto plus_revisions = base_revisions; + plus_revisions.displacement.value++; + plus_revisions.density.value++; + plus_revisions.gravity_gradient.value++; + plus_revisions.gravity_potential.value++; + + mfem::Vector plus_residual; + gravity_operator.Prepare(plus_state, plus_revisions); + gravity_operator.Mult(plus_state, plus_residual); + + REQUIRE(plus_residual.Size() == layout.residual_offsets().Last()); + + auto minus_revisions = plus_revisions; + minus_revisions.displacement.value++; + minus_revisions.density.value++; + minus_revisions.gravity_gradient.value++; + minus_revisions.gravity_potential.value++; + + mfem::Vector minus_residual; + gravity_operator.Prepare(minus_state, minus_revisions); + gravity_operator.Mult(minus_state, minus_residual); + + REQUIRE(minus_residual.Size() == layout.residual_offsets().Last()); + + mfem::Vector finite_difference(plus_residual); + finite_difference -= minus_residual; + finite_difference /= 2.0 * difference_step; + + const mfem::Vector gradient_action = get_residual_block( + jacobian_action, layout, gravity_gradient_residual_block + ); + const mfem::Vector poisson_action = get_residual_block( + jacobian_action, layout, gravity_poisson_residual_block + ); + const mfem::Vector finite_difference_gradient = get_residual_block( + finite_difference, layout, gravity_gradient_residual_block + ); + const mfem::Vector finite_difference_poisson = get_residual_block( + finite_difference, layout, gravity_poisson_residual_block + ); + + const double jacobian_gradient_norm = + global_vector_norm(gradient_action, communicator); + const double jacobian_poisson_norm = + global_vector_norm(poisson_action, communicator); + const double finite_difference_gradient_norm = + global_vector_norm(finite_difference_gradient, communicator); + const double finite_difference_poisson_norm = + global_vector_norm(finite_difference_poisson, communicator); + + constexpr double nonzero_tolerance = 1.0e-12; + + REQUIRE(jacobian_gradient_norm > nonzero_tolerance); + REQUIRE(jacobian_poisson_norm > nonzero_tolerance); + REQUIRE(finite_difference_gradient_norm > nonzero_tolerance); + REQUIRE(finite_difference_poisson_norm > nonzero_tolerance); + + mfem::Vector gradient_difference(gradient_action); + gradient_difference -= finite_difference_gradient; + + mfem::Vector poisson_difference(poisson_action); + poisson_difference -= finite_difference_poisson; + + mfem::Vector combined_difference(jacobian_action); + combined_difference -= finite_difference; + + const double absolute_gradient_error = + global_vector_norm(gradient_difference, communicator); + const double absolute_poisson_error = + global_vector_norm(poisson_difference, communicator); + const double absolute_combined_error = + global_vector_norm(combined_difference, communicator); + + const double gradient_error = global_relative_error( + gradient_action, finite_difference_gradient, communicator + ); + const double poisson_error = global_relative_error( + poisson_action, finite_difference_poisson, communicator + ); + const double combined_error = + global_relative_error(jacobian_action, finite_difference, communicator); + + INFO("Jacobian gradient action norm = " << jacobian_gradient_norm); + INFO( + "Finite-difference gradient norm = " << finite_difference_gradient_norm + ); + INFO("Jacobian Poisson action norm = " << jacobian_poisson_norm); + INFO("Finite-difference Poisson norm = " << finite_difference_poisson_norm); + INFO("Absolute gradient residual error = " << absolute_gradient_error); + INFO("Absolute Poisson residual error = " << absolute_poisson_error); + INFO("Absolute combined residual error = " << absolute_combined_error); + INFO("Gradient residual relative error = " << gradient_error); + INFO("Poisson residual relative error = " << poisson_error); + INFO("Combined residual relative error = " << combined_error); + + REQUIRE(std::isfinite(gradient_error)); + REQUIRE(std::isfinite(poisson_error)); + REQUIRE(std::isfinite(combined_error)); + + CHECK_THAT(gradient_error, WithinAbs(0.0, 5.0e-7)); + CHECK_THAT(poisson_error, WithinAbs(0.0, 5.0e-7)); + CHECK_THAT(combined_error, WithinAbs(0.0, 5.0e-7)); +} + +TEST_CASE( + "Reduced Gravity Field Operator Solves Deformed Gravity System With MINRES", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.mapping != nullptr); + REQUIRE(f.domainMapperStateless != nullptr); + + const gravity_layout layout = make_gravity_jacobian_layout(f); + const HdivMassVariationTestFields fields = + make_hdiv_mass_variation_test_fields(f); + const mfem::Vector density = make_source_variation_density(f); + const mfem::Vector displacement = fields.displacement; + + mfem::ParGridFunction legacy_displacement(f.displacementFes.get()); + legacy_displacement.SetFromTrueDofs(displacement); + f.mapping->SetDisplacement(legacy_displacement); + physics::update_stiffness_matrix(f); + + REQUIRE(f.gravityContext.b_form != nullptr); + REQUIRE(f.gravityContext.BT != nullptr); + REQUIRE(f.gravityContext.block_prec != nullptr); + + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + operators::context::gravity_field::GravityFieldGeometryContext + reduced_geometry_context(f, *f.domainMapperStateless); + operators::ReducedGravityFieldOperator reduced_operator( + gravity_operator, reduced_geometry_context, displacement + ); + + REQUIRE(reduced_geometry_context.IsPrepared()); + REQUIRE(reduced_operator.Width() == layout.residual_offsets().Last()); + REQUIRE(reduced_operator.Height() == layout.residual_offsets().Last()); + REQUIRE(reduced_operator.Width() == reduced_operator.Height()); + + const std::uint64_t mass_preparations_before_solve = + reduced_geometry_context.GetMassOperator().GetPreparationCount(); + const std::uint64_t source_preparations_before_solve = + reduced_geometry_context.GetSourceOperator().GetPreparationCount(); + + REQUIRE(mass_preparations_before_solve > 0); + REQUIRE(source_preparations_before_solve > 0); + + mfem::Vector right_hand_side; + reduced_operator.BuildRightHandSide(density, right_hand_side); + + REQUIRE(right_hand_side.Size() == reduced_operator.Height()); + + MPI_Comm communicator = f.mesh->GetComm(); + const double right_hand_side_norm = + global_norm(right_hand_side, communicator); + + INFO("Reduced gravity-system size = " << reduced_operator.Height()); + INFO("Gravity right-hand-side norm = " << right_hand_side_norm); + INFO("Mass preparations before solve = " << mass_preparations_before_solve); + INFO( + "Source preparations before solve = " + << source_preparations_before_solve + ); + + REQUIRE(right_hand_side_norm > 0.0); + + mfem::Vector gravity_state(reduced_operator.Width()); + gravity_state = 0.0; + + constexpr double relative_solver_tolerance = 1.0e-14; + constexpr double absolute_solver_tolerance = 1.0e-14; + const int maximum_iterations = 2000; + + mfem::MINRESSolver minres(communicator); + minres.SetOperator(reduced_operator); + minres.SetPreconditioner(*f.gravityContext.block_prec); + minres.SetRelTol(relative_solver_tolerance); + minres.SetAbsTol(absolute_solver_tolerance); + minres.SetMaxIter(maximum_iterations); + minres.SetPrintLevel(1); + + MEAN_FIELD_PROFILE_RESET(); + MEAN_FIELD_PROFILE_CALL_WARMUP( + "MINRES total", 0, minres.Mult(right_hand_side, gravity_state) + ); + MEAN_FIELD_PROFILE_PRINT(communicator); + + REQUIRE(gravity_state.Size() == reduced_operator.Width()); + + const std::uint64_t mass_preparations_after_solve = + reduced_geometry_context.GetMassOperator().GetPreparationCount(); + const std::uint64_t source_preparations_after_solve = + reduced_geometry_context.GetSourceOperator().GetPreparationCount(); + + INFO("Mass preparations after solve = " << mass_preparations_after_solve); + INFO( + "Source preparations after solve = " << source_preparations_after_solve + ); + + CHECK(mass_preparations_after_solve == mass_preparations_before_solve); + CHECK(source_preparations_after_solve == source_preparations_before_solve); + + mfem::Vector operator_action; + reduced_operator.Mult(gravity_state, operator_action); + + mfem::Vector reduced_residual(operator_action); + reduced_residual -= right_hand_side; + + const mfem::Vector gradient_residual = get_residual_block( + reduced_residual, layout, gravity_gradient_residual_block + ); + const mfem::Vector poisson_residual = get_residual_block( + reduced_residual, layout, gravity_poisson_residual_block + ); + const mfem::Vector solved_gravity_gradient = get_residual_block( + gravity_state, layout, gravity_gradient_residual_block + ); + const mfem::Vector solved_gravity_potential = get_residual_block( + gravity_state, layout, gravity_poisson_residual_block + ); + + const double gravity_state_norm = global_norm(gravity_state, communicator); + const double gravity_gradient_norm = + global_norm(solved_gravity_gradient, communicator); + const double gravity_potential_norm = + global_norm(solved_gravity_potential, communicator); + const double residual_norm = global_norm(reduced_residual, communicator); + const double gradient_residual_norm = + global_norm(gradient_residual, communicator); + const double poisson_residual_norm = + global_norm(poisson_residual, communicator); + const double relative_residual = residual_norm / right_hand_side_norm; + const double relative_gradient_residual = + gradient_residual_norm / right_hand_side_norm; + const double relative_poisson_residual = + poisson_residual_norm / right_hand_side_norm; + + INFO("MINRES converged = " << minres.GetConverged()); + INFO("MINRES iterations = " << minres.GetNumIterations()); + INFO("MINRES reported final norm = " << minres.GetFinalNorm()); + INFO("Gravity-state norm = " << gravity_state_norm); + INFO("Solved gravity-gradient norm = " << gravity_gradient_norm); + INFO("Solved gravity-potential norm = " << gravity_potential_norm); + INFO("Direct residual norm = " << residual_norm); + INFO("Direct relative residual = " << relative_residual); + INFO( + "Relative gradient-equation residual = " << relative_gradient_residual + ); + INFO("Relative Poisson-equation residual = " << relative_poisson_residual); + + CHECK(minres.GetConverged()); + CHECK(minres.GetNumIterations() <= maximum_iterations); + REQUIRE(gravity_state_norm > 0.0); + REQUIRE(gravity_gradient_norm > 0.0); + REQUIRE(gravity_potential_norm > 0.0); + + constexpr double direct_residual_tolerance = 1.0e-11; + + CHECK_THAT(relative_residual, WithinAbs(0.0, direct_residual_tolerance)); + CHECK_THAT( + relative_gradient_residual, WithinAbs(0.0, direct_residual_tolerance) + ); + CHECK_THAT( + relative_poisson_residual, WithinAbs(0.0, direct_residual_tolerance) + ); + + mfem::Vector full_state(layout.value_offsets().Last()); + full_state = 0.0; + + set_value_block(full_state, layout, density_block, density); + set_value_block(full_state, layout, displacement_block, displacement); + set_value_block( + full_state, layout, gravity_gradient_block, solved_gravity_gradient + ); + set_value_block( + full_state, layout, gravity_potential_block, solved_gravity_potential + ); + + const operators::context::gravity_field::GravityFieldRevisions + full_state_revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + gravity_operator.Prepare(full_state, full_state_revisions); + + REQUIRE(linearization_context.IsPrepared()); + + check_linearization_context_matches_state( + linearization_context, full_state, layout.value_offsets(), communicator + ); + + mfem::Vector full_residual; + gravity_operator.Mult(full_state, full_residual); + + REQUIRE(full_residual.Size() == layout.residual_offsets().Last()); + + mfem::Vector residual_representation_difference(full_residual); + residual_representation_difference -= reduced_residual; + + const double residual_representation_error = + global_norm(residual_representation_difference, communicator) / + right_hand_side_norm; + const double full_relative_residual = + global_norm(full_residual, communicator) / right_hand_side_norm; + + INFO("Full gravity residual relative norm = " << full_relative_residual); + INFO( + "Reduced/full residual representation error = " + << residual_representation_error + ); + + CHECK_THAT( + full_relative_residual, WithinAbs(0.0, direct_residual_tolerance) + ); + CHECK_THAT(residual_representation_error, WithinAbs(0.0, 1.0e-12)); +} + +TEST_CASE( + "Gravity Hdiv Operator Difference Is Localized To Vacuum Compactification", + tags::integration &tags::solver &tags::gravity &tags::mfem_operators + &tags::legacy_comparison +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.mapping != nullptr); + REQUIRE(f.domainMapperStateless != nullptr); + REQUIRE(f.compactificationCoordinate != nullptr); + + using form = blocks::gravity_field_form; + + constexpr auto displacement_block = + mean_field::utils::blocks::get_value_block( + blocks::displacement_field.geometry_term + ); + + constexpr auto gravity_gradient_block = + mean_field::utils::blocks::get_value_block( + blocks::gravity_field.gradient_term + ); + + constexpr auto gravity_gradient_residual_block = + mean_field::utils::blocks::get_residual_block( + blocks::gravity_field.gradient_term + ); + + const std::array value_sizes{ + f.densityFes->GetTrueVSize(), f.displacementFes->GetTrueVSize(), + f.gravityFluxFes->GetTrueVSize(), f.gravityPotentialFes->GetTrueVSize() + }; + + const std::array residual_sizes{ + f.gravityFluxFes->GetTrueVSize(), f.gravityPotentialFes->GetTrueVSize() + }; + + const blocks::form_layout layout(value_sizes, residual_sizes); + + const mfem::Vector gravity_gradient_true = + make_full_support_gravity_gradient(f); + + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + REQUIRE(global_vector_norm(gravity_gradient_true, communicator) > 0.0); + + for (const bool deformed : std::array{false, true}) { + DYNAMIC_SECTION("Geometry = " << (deformed ? "deformed" : "identity")) { + const mfem::Vector displacement_true = + make_stateless_reference_displacement(f, deformed); + + /* + * Prepare the legacy geometry and assemble its PA operator. + * The legacy mapper performs its vacuum map without consulting + * the exterior-coordinate GridFunction. + */ + mfem::ParGridFunction legacy_displacement(f.displacementFes.get()); + legacy_displacement.SetFromTrueDofs(displacement_true); + f.mapping->SetDisplacement(legacy_displacement); + + physics::update_stiffness_matrix(f); + + REQUIRE(f.gravityContext.m_form != nullptr); + + operators::context::gravity_field::GravityFieldLinearizationContext + linearization_context(f, *f.domainMapperStateless); + + operators::GravityFieldJacobianOperator gravity_jacobian( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), layout.residual_offsets() + ); + + operators::GravityFieldOperator gravity_operator( + f, *f.domainMapperStateless, linearization_context, + layout.value_offsets(), gravity_jacobian + ); + + mfem::Vector state(layout.value_offsets().Last()); + state = 0.0; + + for (int i = 0; i < displacement_true.Size(); ++i) { + state(layout.offset(displacement_block) + i) = + displacement_true(i); + } + + for (int i = 0; i < gravity_gradient_true.Size(); ++i) { + state(layout.offset(gravity_gradient_block) + i) = + gravity_gradient_true(i); + } + + const operators::context::gravity_field::GravityFieldRevisions + revisions{ + .discretization = {1}, + .displacement = {1}, + .density = {1}, + .gravity_gradient = {1}, + .gravity_potential = {1} + }; + + gravity_operator.Prepare(state, revisions); + + mfem::Vector new_residual; + gravity_operator.Mult(state, new_residual); + + mfem::Vector new_operator_mass_action( + layout.size(gravity_gradient_residual_block) + ); + + for (int i = 0; i < new_operator_mass_action.Size(); ++i) { + new_operator_mass_action(i) = new_residual( + layout.offset(gravity_gradient_residual_block) + i + ); + } + + mfem::Vector legacy_operator_mass_action( + f.gravityFluxFes->GetTrueVSize() + ); + + legacy_operator_mass_action = 0.0; + f.gravityContext.m_form->Mult( + gravity_gradient_true, legacy_operator_mass_action + ); + + const StatelessHDivMassReference new_reference = + evaluate_stateless_hdiv_mass_quadrature_reference( + f, gravity_gradient_true, displacement_true + ); + const StatelessHDivMassReference legacy_reference = + assemble_legacy_hdiv_mass_reference(f, gravity_gradient_true); + + mfem::Vector new_decomposed_action(new_reference.stellar_action); + new_decomposed_action += new_reference.vacuum_action; + + mfem::Vector legacy_decomposed_action( + legacy_reference.stellar_action + ); + legacy_decomposed_action += legacy_reference.vacuum_action; + + mfem::Vector total_gap(new_reference.total_action); + total_gap -= legacy_reference.total_action; + + mfem::Vector stellar_gap(new_reference.stellar_action); + stellar_gap -= legacy_reference.stellar_action; + + mfem::Vector vacuum_gap(new_reference.vacuum_action); + vacuum_gap -= legacy_reference.vacuum_action; + + mfem::Vector decomposed_gap(stellar_gap); + decomposed_gap += vacuum_gap; + + mfem::Vector unexplained_by_vacuum(total_gap); + unexplained_by_vacuum -= vacuum_gap; + + const double new_operator_reference_error = + global_relative_difference( + new_operator_mass_action, new_reference.total_action, + communicator + ); + + const double legacy_operator_reference_error = + global_relative_difference( + legacy_operator_mass_action, legacy_reference.total_action, + communicator + ); + + const double new_decomposition_error = global_relative_difference( + new_reference.total_action, new_decomposed_action, communicator + ); + + const double legacy_decomposition_error = + global_relative_difference( + legacy_reference.total_action, legacy_decomposed_action, + communicator + ); + + const double gap_decomposition_error = global_relative_difference( + total_gap, decomposed_gap, communicator + ); + + const double stellar_relative_difference = + global_relative_difference( + new_reference.stellar_action, + legacy_reference.stellar_action, communicator + ); + + const double vacuum_relative_difference = + global_relative_difference( + new_reference.vacuum_action, legacy_reference.vacuum_action, + communicator + ); + + const double total_relative_difference = global_relative_difference( + new_reference.total_action, legacy_reference.total_action, + communicator + ); + + const double total_gap_norm = + global_vector_norm(total_gap, communicator); + + const double stellar_gap_norm = + global_vector_norm(stellar_gap, communicator); + + const double vacuum_gap_norm = + global_vector_norm(vacuum_gap, communicator); + + const double unexplained_gap_norm = + global_vector_norm(unexplained_by_vacuum, communicator); + + const double stellar_fraction_of_gap = + stellar_gap_norm / + std::max( + total_gap_norm, std::numeric_limits::epsilon() + ); + + const double unexplained_fraction_of_gap = + unexplained_gap_norm / + std::max( + total_gap_norm, std::numeric_limits::epsilon() + ); + + const double new_total_energy = global_vector_dot( + gravity_gradient_true, new_reference.total_action, communicator + ); + + const double legacy_total_energy = global_vector_dot( + gravity_gradient_true, legacy_reference.total_action, + communicator + ); + + const double new_stellar_energy = global_vector_dot( + gravity_gradient_true, new_reference.stellar_action, + communicator + ); + + const double legacy_stellar_energy = global_vector_dot( + gravity_gradient_true, legacy_reference.stellar_action, + communicator + ); + + const double new_vacuum_energy = global_vector_dot( + gravity_gradient_true, new_reference.vacuum_action, communicator + ); + + const double legacy_vacuum_energy = global_vector_dot( + gravity_gradient_true, legacy_reference.vacuum_action, + communicator + ); + + const double total_energy_gap = + new_total_energy - legacy_total_energy; + + const double stellar_energy_gap = + new_stellar_energy - legacy_stellar_energy; + + const double vacuum_energy_gap = + new_vacuum_energy - legacy_vacuum_energy; + + const double energy_gap_decomposition_error = + std::abs( + total_energy_gap - stellar_energy_gap - vacuum_energy_gap + ) / + std::max( + std::abs(total_energy_gap), + std::numeric_limits::epsilon() + ); + + INFO("Geometry = " << (deformed ? "deformed" : "identity")); + INFO( + "New operator/reference error = " + << new_operator_reference_error + ); + INFO( + "Legacy operator/reference error = " + << legacy_operator_reference_error + ); + INFO( + "New regional decomposition error = " << new_decomposition_error + ); + INFO( + "Legacy regional decomposition error = " + << legacy_decomposition_error + ); + INFO("Gap decomposition error = " << gap_decomposition_error); + INFO( + "New/legacy total mass-action difference = " + << total_relative_difference + ); + INFO( + "New/legacy stellar mass-action difference = " + << stellar_relative_difference + ); + INFO( + "New/legacy vacuum mass-action difference = " + << vacuum_relative_difference + ); + INFO("Total operator-gap norm = " << total_gap_norm); + INFO("Stellar operator-gap norm = " << stellar_gap_norm); + INFO("Vacuum operator-gap norm = " << vacuum_gap_norm); + INFO( + "Stellar fraction of operator gap = " << stellar_fraction_of_gap + ); + INFO( + "Operator gap unexplained by vacuum = " + << unexplained_fraction_of_gap + ); + INFO("New total H(div) energy = " << new_total_energy); + INFO("Legacy total H(div) energy = " << legacy_total_energy); + INFO("New stellar H(div) energy = " << new_stellar_energy); + INFO("Legacy stellar H(div) energy = " << legacy_stellar_energy); + INFO("New vacuum H(div) energy = " << new_vacuum_energy); + INFO("Legacy vacuum H(div) energy = " << legacy_vacuum_energy); + INFO("Total H(div) energy gap = " << total_energy_gap); + INFO("Stellar H(div) energy gap = " << stellar_energy_gap); + INFO("Vacuum H(div) energy gap = " << vacuum_energy_gap); + INFO( + "Energy-gap decomposition error = " + << energy_gap_decomposition_error + ); + + REQUIRE(new_reference.stellar_elements > 0); + REQUIRE(new_reference.vacuum_elements > 0); + REQUIRE(legacy_reference.stellar_elements > 0); + REQUIRE(legacy_reference.vacuum_elements > 0); + + REQUIRE(new_total_energy > 0.0); + REQUIRE(legacy_total_energy > 0.0); + REQUIRE(new_stellar_energy > 0.0); + REQUIRE(legacy_stellar_energy > 0.0); + REQUIRE(new_vacuum_energy > 0.0); + REQUIRE(legacy_vacuum_energy > 0.0); + + constexpr double operator_reference_tolerance = 1.0e-11; + constexpr double decomposition_tolerance = 5.0e-13; + constexpr double stellar_parity_tolerance = 1.0e-10; + constexpr double gap_localization_tolerance = 1.0e-9; + + CHECK_THAT( + new_operator_reference_error, + Catch::Matchers::WithinAbs(0.0, operator_reference_tolerance) + ); + + CHECK_THAT( + legacy_operator_reference_error, + Catch::Matchers::WithinAbs(0.0, operator_reference_tolerance) + ); + + CHECK_THAT( + new_decomposition_error, + Catch::Matchers::WithinAbs(0.0, decomposition_tolerance) + ); + + CHECK_THAT( + legacy_decomposition_error, + Catch::Matchers::WithinAbs(0.0, decomposition_tolerance) + ); + + CHECK_THAT( + gap_decomposition_error, + Catch::Matchers::WithinAbs(0.0, decomposition_tolerance) + ); + + CHECK_THAT( + stellar_relative_difference, + Catch::Matchers::WithinAbs(0.0, stellar_parity_tolerance) + ); + + /* + * The previous global comparison already showed a material + * difference. Confirm that this test continues to exercise it. + */ + REQUIRE(total_gap_norm > 1.0e-12); + REQUIRE(vacuum_gap_norm > 1.0e-12); + REQUIRE(vacuum_relative_difference > 1.0e-8); + + /* + * If these pass, the old/new difference has been directly + * localized to the vacuum compactification prescription. + */ + CHECK_THAT( + stellar_fraction_of_gap, + Catch::Matchers::WithinAbs(0.0, gap_localization_tolerance) + ); + + CHECK_THAT( + unexplained_fraction_of_gap, + Catch::Matchers::WithinAbs(0.0, gap_localization_tolerance) + ); + + CHECK_THAT( + energy_gap_decomposition_error, + Catch::Matchers::WithinAbs(0.0, decomposition_tolerance) + ); + } + } +} diff --git a/tests/operators/kernels/barotropic_closure_kernels.cpp b/tests/operators/kernels/barotropic_closure_kernels.cpp new file mode 100644 index 0000000..53dd05a --- /dev/null +++ b/tests/operators/kernels/barotropic_closure_kernels.cpp @@ -0,0 +1,628 @@ +#include + +#include +#include +#include + +import mean_field; +import test_helpers; + +namespace { + mfem::Vector make_zero_displacement(const mean_field::fem::FEM &f) { + mfem::Vector displacement(f.displacementFes->GetTrueVSize()); + displacement = 0.0; + return displacement; + } + + mfem::Vector project_constant( + mfem::ParFiniteElementSpace &finiteElementSpace, + const double value + ) { + mfem::ConstantCoefficient coefficient(value); + mfem::ParGridFunction field(&finiteElementSpace); + + field.ProjectCoefficient(coefficient); + + mfem::Vector trueVector; + field.GetTrueDofs(trueVector); + return trueVector; + } + + namespace barotropic_closure_geometry_test_utils { + mfem::Vector project_scalar_field( + mfem::ParFiniteElementSpace &finiteElementSpace, + mfem::Coefficient &coefficient + ) { + mfem::ParGridFunction field(&finiteElementSpace); + + field.ProjectCoefficient(coefficient); + + mfem::Vector trueVector; + field.GetTrueDofs(trueVector); + + return trueVector; + } + + mfem::Vector make_base_density(const mean_field::fem::FEM &f) { + mfem::FunctionCoefficient coefficient( + [](const mfem::Vector &position) { + return 0.55 + 0.025 * position(0) - 0.010 * position(1) + + 0.006 * position(2); + } + ); + + return project_scalar_field(*f.densityFes, coefficient); + } + + mfem::Vector make_base_enthalpy(const mean_field::fem::FEM &f) { + mfem::FunctionCoefficient coefficient( + [](const mfem::Vector &position) { + return 0.90 + 0.020 * position(0) - 0.010 * position(1) + + 0.005 * position(2); + } + ); + + return project_scalar_field(*f.enthalpyFes, coefficient); + } + } // namespace barotropic_closure_geometry_test_utils +} // namespace + +TEST_CASE( + "Barotropic Closure Vanishes For A Representable Constant State", + tags::hydro &tags::residuals &tags::unit &tags::closure &tags::kernels + &tags::barotrope +) { + auto args = test_utils::setup_args(); + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + constexpr double enthalpyValue = 0.8; + + const double densityValue = barotrope.density_from_enthalpy(enthalpyValue); + + const mfem::Vector enthalpy = + project_constant(*f.enthalpyFes, enthalpyValue); + + const mfem::Vector density = project_constant(*f.densityFes, densityValue); + + const mfem::Vector displacement = make_zero_displacement(f); + + mfem::Vector residual; + mfem::Vector scale; + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, density, enthalpy, displacement, + residual + ); + + mean_field::operators::kernels::apply_barotropic_closure_density_action( + f, *f.domainMapperStateless, barotrope, density, displacement, scale + ); + + const MPI_Comm communicator = f.mesh->GetComm(); + + const double relativeResidual = + gravity_prepared_test_utils::global_norm(residual, communicator) / + gravity_prepared_test_utils::global_norm(scale, communicator); + + INFO("Relative constant-state closure residual = " << relativeResidual); + + CHECK(relativeResidual < 5.0e-12); +} + +TEST_CASE( + "Barotropic Closure Density Action Matches The Stellar Mass Matrix", + tags::hydro &tags::jacobian &tags::unit &tags::closure &tags::kernels + &tags::barotrope +) { + auto args = test_utils::setup_args(); + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + const mfem::Vector displacement = make_zero_displacement(f); + + const mfem::Vector densityVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.37 + ); + + mfem::Vector kernelAction; + + mean_field::operators::kernels::apply_barotropic_closure_density_action( + f, *f.domainMapperStateless, barotrope, densityVariation, displacement, + kernelAction + ); + + mfem::Array stellarMarker(f.mesh->attributes.Max()); + stellarMarker = 0; + + const int vacuumAttribute = + f.domainMapperStateless->GetVacuumElementAttribute(); + + for (int attributeIndex = 0; attributeIndex < f.mesh->attributes.Size(); + ++attributeIndex) { + const int attribute = f.mesh->attributes[attributeIndex]; + + if (attribute != vacuumAttribute) { + stellarMarker[attribute - 1] = 1; + } + } + + mfem::ParBilinearForm massForm(f.densityFes.get()); + + massForm.AddDomainIntegrator(new mfem::MassIntegrator(), stellarMarker); + + massForm.Assemble(); + massForm.Finalize(); + + std::unique_ptr massMatrix( + massForm.ParallelAssemble() + ); + + REQUIRE(massMatrix != nullptr); + REQUIRE(massMatrix->Width() == densityVariation.Size()); + + mfem::Vector referenceAction(massMatrix->Height()); + referenceAction = 0.0; + + massMatrix->Mult(densityVariation, referenceAction); + const double relativeError = gravity_prepared_test_utils::relative_error( + kernelAction, referenceAction, f.mesh->GetComm() + ); + + INFO("Density-action mass-matrix error = " << relativeError); + + CHECK(relativeError < 5.0e-12); +} + +TEST_CASE( + "Barotropic Closure Jacobian Matches A Combined Centered Difference", + tags::hydro &tags::jacobian &tags::unit &tags::closure &tags::kernels + &tags::barotrope +) { + auto args = test_utils::setup_args(); + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + mfem::FunctionCoefficient densityCoefficient( + [](const mfem::Vector &position) { + return 0.4 + 0.03 * position(0) - 0.01 * position(1); + } + ); + + mfem::FunctionCoefficient enthalpyCoefficient( + [](const mfem::Vector &position) { + return 0.9 + 0.02 * position(0) - 0.01 * position(1); + } + ); + + mfem::FunctionCoefficient enthalpyVariationCoefficient( + [](const mfem::Vector &position) { + return 0.07 + 0.015 * position(0) + 0.008 * position(2); + } + ); + + mfem::ParGridFunction densityField(f.densityFes.get()); + mfem::ParGridFunction enthalpyField(f.enthalpyFes.get()); + mfem::ParGridFunction enthalpyVariationField(f.enthalpyFes.get()); + + densityField.ProjectCoefficient(densityCoefficient); + enthalpyField.ProjectCoefficient(enthalpyCoefficient); + enthalpyVariationField.ProjectCoefficient(enthalpyVariationCoefficient); + + mfem::Vector density; + mfem::Vector enthalpy; + mfem::Vector enthalpyVariation; + + densityField.GetTrueDofs(density); + enthalpyField.GetTrueDofs(enthalpy); + enthalpyVariationField.GetTrueDofs(enthalpyVariation); + + const mfem::Vector densityVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.63 + ); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 1.0); + + constexpr double differenceStep = 1.0e-6; + + const mfem::Vector plusDensity = + gravity_prepared_test_utils::linear_combination( + density, 1.0, densityVariation, differenceStep + ); + + const mfem::Vector minusDensity = + gravity_prepared_test_utils::linear_combination( + density, 1.0, densityVariation, -differenceStep + ); + + const mfem::Vector plusEnthalpy = + gravity_prepared_test_utils::linear_combination( + enthalpy, 1.0, enthalpyVariation, differenceStep + ); + + const mfem::Vector minusEnthalpy = + gravity_prepared_test_utils::linear_combination( + enthalpy, 1.0, enthalpyVariation, -differenceStep + ); + + mfem::Vector plusResidual; + mfem::Vector minusResidual; + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, plusDensity, plusEnthalpy, + displacement, plusResidual + ); + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, minusDensity, minusEnthalpy, + displacement, minusResidual + ); + + mfem::Vector finiteDifference(plusResidual); + finiteDifference -= minusResidual; + finiteDifference *= 1.0 / (2.0 * differenceStep); + + mfem::Vector densityAction; + mfem::Vector enthalpyAction; + + mean_field::operators::kernels::apply_barotropic_closure_density_action( + f, *f.domainMapperStateless, barotrope, densityVariation, displacement, + densityAction + ); + + mean_field::operators::kernels::apply_barotropic_closure_enthalpy_action( + f, *f.domainMapperStateless, barotrope, enthalpy, enthalpyVariation, + displacement, enthalpyAction + ); + + mfem::Vector analyticAction(densityAction); + analyticAction += enthalpyAction; + + const double relativeError = gravity_prepared_test_utils::relative_error( + analyticAction, finiteDifference, f.mesh->GetComm() + ); + + INFO("Combined EOS Jacobian error = " << relativeError); + + CHECK(relativeError < 2.0e-8); +} + +TEST_CASE( + "Barotropic Closure Density Action Excludes Vacuum And Uses Mapped Volume", + tags::hydro &tags::mapping &tags::unit &tags::closure &tags::barotrope + &tags::kernels +) { + auto args = test_utils::setup_args(); + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + const mfem::Vector stellarDensity = + gravity_prepared_test_utils::make_domain_supported_density(f, true); + + const mfem::Vector vacuumDensity = + gravity_prepared_test_utils::make_domain_supported_density(f, false); + + const mfem::Vector identityDisplacement = + gravity_prepared_test_utils::make_displacement(f, 0.0); + + const mfem::Vector deformedDisplacement = + gravity_prepared_test_utils::make_displacement(f, 1.0); + + mfem::Vector stellarAction; + mfem::Vector vacuumAction; + mfem::Vector deformedAction; + + mean_field::operators::kernels::apply_barotropic_closure_density_action( + f, *f.domainMapperStateless, barotrope, stellarDensity, + identityDisplacement, stellarAction + ); + + mean_field::operators::kernels::apply_barotropic_closure_density_action( + f, *f.domainMapperStateless, barotrope, vacuumDensity, + identityDisplacement, vacuumAction + ); + + mean_field::operators::kernels::apply_barotropic_closure_density_action( + f, *f.domainMapperStateless, barotrope, stellarDensity, + deformedDisplacement, deformedAction + ); + + const MPI_Comm communicator = f.mesh->GetComm(); + + const double stellarNorm = + gravity_prepared_test_utils::global_norm(stellarAction, communicator); + + const double vacuumNorm = + gravity_prepared_test_utils::global_norm(vacuumAction, communicator); + + const double geometryChange = gravity_prepared_test_utils::relative_error( + deformedAction, stellarAction, communicator + ); + + INFO("Stellar action norm = " << stellarNorm); + INFO("Vacuum action norm = " << vacuumNorm); + INFO("Relative mapped-volume change = " << geometryChange); + + CHECK(stellarNorm > 0.0); + CHECK(vacuumNorm <= 1.0e-13 * stellarNorm); + CHECK(geometryChange > 1.0e-5); +} + +TEST_CASE( + "Barotropic Closure Displacement Action Matches Centered Differences", + tags::barotrope &tags::closure &tags::hydro &tags::integration + &tags::jacobian &tags::mapping &tags::physics +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + const mfem::Vector baseDensity = + barotropic_closure_geometry_test_utils::make_base_density(f); + + const mfem::Vector baseEnthalpy = + barotropic_closure_geometry_test_utils::make_base_enthalpy(f); + + const mfem::Vector displacementVariation = + gravity_prepared_test_utils::make_displacement(f, 0.65); + + constexpr double differenceStep = 1.0e-5; + + const MPI_Comm communicator = f.mesh->GetComm(); + + for (const double deformationScale : {0.0, 1.0}) { + DYNAMIC_SECTION("Base deformation scale = " << deformationScale) { + const mfem::Vector baseDisplacement = + gravity_prepared_test_utils::make_displacement( + f, deformationScale + ); + + mfem::Vector plusDisplacement(baseDisplacement); + + mfem::Vector minusDisplacement(baseDisplacement); + + plusDisplacement.Add(differenceStep, displacementVariation); + + minusDisplacement.Add(-differenceStep, displacementVariation); + + mfem::Vector plusResidual; + mfem::Vector minusResidual; + mfem::Vector analyticAction; + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, baseDensity, + baseEnthalpy, plusDisplacement, plusResidual + ); + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, baseDensity, + baseEnthalpy, minusDisplacement, minusResidual + ); + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, baseDensity, + baseEnthalpy, baseDisplacement, displacementVariation, + analyticAction + ); + + mfem::Vector finiteDifference(plusResidual); + + finiteDifference -= minusResidual; + finiteDifference *= 1.0 / (2.0 * differenceStep); + + const double analyticNorm = + gravity_prepared_test_utils::global_norm( + analyticAction, communicator + ); + + const double finiteDifferenceNorm = + gravity_prepared_test_utils::global_norm( + finiteDifference, communicator + ); + + const double relativeError = + gravity_prepared_test_utils::relative_error( + analyticAction, finiteDifference, communicator + ); + + INFO("Base deformation scale = " << deformationScale); + + INFO("Analytic geometry-action norm = " << analyticNorm); + + INFO( + "Finite-difference geometry-action norm = " + << finiteDifferenceNorm + ); + + INFO("Geometry-action relative error = " << relativeError); + + REQUIRE(analyticNorm > 1.0e-12); + REQUIRE(finiteDifferenceNorm > 1.0e-12); + + CHECK(relativeError < 5.0e-8); + } + } +} + +TEST_CASE( + "Barotropic Closure Displacement Action Is Linear In Its Direction", + tags::barotrope &tags::closure &tags::hydro &tags::jacobian &tags::mapping + &tags::physics &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + const mfem::Vector baseDensity = + barotropic_closure_geometry_test_utils::make_base_density(f); + + const mfem::Vector baseEnthalpy = + barotropic_closure_geometry_test_utils::make_base_enthalpy(f); + + const mfem::Vector baseDisplacement = + gravity_prepared_test_utils::make_displacement(f, 0.8); + + const mfem::Vector firstDirection = + gravity_prepared_test_utils::make_displacement(f, 0.4); + + mfem::Vector secondDirection = + gravity_prepared_test_utils::make_deterministic_vector( + f.displacementFes->GetTrueVSize(), 0.91 + ); + + secondDirection *= 0.01; + + constexpr double firstScale = 1.7; + constexpr double secondScale = -0.43; + + mfem::Vector combinedDirection(firstDirection); + + combinedDirection *= firstScale; + + combinedDirection.Add(secondScale, secondDirection); + + mfem::Vector zeroDirection(f.displacementFes->GetTrueVSize()); + zeroDirection = 0.0; + + mfem::Vector firstAction; + mfem::Vector secondAction; + mfem::Vector combinedAction; + mfem::Vector zeroAction; + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, baseDensity, baseEnthalpy, + baseDisplacement, firstDirection, firstAction + ); + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, baseDensity, baseEnthalpy, + baseDisplacement, secondDirection, secondAction + ); + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, baseDensity, baseEnthalpy, + baseDisplacement, combinedDirection, combinedAction + ); + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, baseDensity, baseEnthalpy, + baseDisplacement, zeroDirection, zeroAction + ); + + mfem::Vector expectedAction(firstAction); + + expectedAction *= firstScale; + + expectedAction.Add(secondScale, secondAction); + + const MPI_Comm communicator = f.mesh->GetComm(); + + const double expectedNorm = + gravity_prepared_test_utils::global_norm(expectedAction, communicator); + + const double linearityError = gravity_prepared_test_utils::relative_error( + combinedAction, expectedAction, communicator + ); + + const double zeroActionNorm = + gravity_prepared_test_utils::global_norm(zeroAction, communicator); + + INFO("Expected combined-action norm = " << expectedNorm); + + INFO("Directional-linearity error = " << linearityError); + + INFO("Zero-direction action norm = " << zeroActionNorm); + + REQUIRE(expectedNorm > 1.0e-12); + + CHECK(linearityError < 5.0e-12); + + CHECK(zeroActionNorm <= 5.0e-14 * expectedNorm); +} + +TEST_CASE( + "Barotropic Closure Displacement Action Excludes Vacuum", + tags::barotrope &tags::closure &tags::hydro &tags::mapping &tags::physics + &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + const mfem::Vector stellarDensity = + gravity_prepared_test_utils::make_domain_supported_density(f, true); + + const mfem::Vector vacuumDensity = + gravity_prepared_test_utils::make_domain_supported_density(f, false); + + mfem::Vector zeroEnthalpy(f.enthalpyFes->GetTrueVSize()); + zeroEnthalpy = 0.0; + + const mfem::Vector baseDisplacement = + gravity_prepared_test_utils::make_displacement(f, 0.7); + + const mfem::Vector displacementVariation = + gravity_prepared_test_utils::make_displacement(f, 0.5); + + mfem::Vector stellarAction; + mfem::Vector vacuumAction; + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, stellarDensity, + zeroEnthalpy, baseDisplacement, displacementVariation, stellarAction + ); + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, vacuumDensity, zeroEnthalpy, + baseDisplacement, displacementVariation, vacuumAction + ); + + const MPI_Comm communicator = f.mesh->GetComm(); + + const double stellarNorm = + gravity_prepared_test_utils::global_norm(stellarAction, communicator); + + const double vacuumNorm = + gravity_prepared_test_utils::global_norm(vacuumAction, communicator); + + INFO("Stellar geometry-action norm = " << stellarNorm); + + INFO("Vacuum geometry-action norm = " << vacuumNorm); + + REQUIRE(stellarNorm > 1.0e-12); + + CHECK(vacuumNorm <= 1.0e-13 * stellarNorm); +} diff --git a/tests/operators/kernels/gravity_kernels.cpp b/tests/operators/kernels/gravity_kernels.cpp new file mode 100644 index 0000000..e69de29 diff --git a/tests/operators/kernels/hydrostatic_equilibrium_kernels.cpp b/tests/operators/kernels/hydrostatic_equilibrium_kernels.cpp new file mode 100644 index 0000000..a7844a7 --- /dev/null +++ b/tests/operators/kernels/hydrostatic_equilibrium_kernels.cpp @@ -0,0 +1,1054 @@ +#include +#include +#include + +#include +#include + +import mean_field; +import test_helpers; + +namespace hydrostatic_kernel_test_utils { + mfem::Vector project_scalar( + mfem::ParFiniteElementSpace &finiteElementSpace, + mfem::Coefficient &coefficient + ) { + mfem::ParGridFunction field(&finiteElementSpace); + + field.ProjectCoefficient(coefficient); + + mfem::Vector trueVector; + field.GetTrueDofs(trueVector); + + return trueVector; + } + + mfem::Vector make_constant_field( + mfem::ParFiniteElementSpace &finiteElementSpace, + const double value + ) { + mfem::ConstantCoefficient coefficient(value); + + return project_scalar(finiteElementSpace, coefficient); + } + + mfem::Vector make_enthalpy(const mean_field::fem::FEM &f) { + mfem::FunctionCoefficient coefficient([](const mfem::Vector &position) { + return 1.10 + 0.035 * position(0) - 0.021 * position(1) + + 0.014 * position(2); + }); + + return project_scalar(*f.enthalpyFes, coefficient); + } + + mfem::Vector make_potential(const mean_field::fem::FEM &f) { + mfem::FunctionCoefficient coefficient([](const mfem::Vector &position) { + return -0.72 + 0.018 * position(0) + 0.011 * position(1) - + 0.025 * position(2); + }); + + return project_scalar(*f.gravityPotentialFes, coefficient); + } + + mean_field::physics::RigidRotation make_rotation() { + mfem::Vector angularVelocity(3); + + angularVelocity(0) = 0.21; + angularVelocity(1) = -0.13; + angularVelocity(2) = 0.48; + + mfem::Vector center(3); + + center(0) = 0.04; + center(1) = -0.03; + center(2) = 0.02; + + return mean_field::physics::RigidRotation(angularVelocity, center); + } + + mean_field::physics::RigidRotation make_zero_rotation() { + mfem::Vector angularVelocity(3); + mfem::Vector center(3); + + angularVelocity = 0.0; + center = 0.0; + + return mean_field::physics::RigidRotation(angularVelocity, center); + } + + mfem::Vector centered_difference( + const mfem::Vector &plusResidual, + const mfem::Vector &minusResidual, + const double epsilon + ) { + mfem::Vector difference(plusResidual); + + difference -= minusResidual; + difference *= 1.0 / (2.0 * epsilon); + + return difference; + } + + double sum_normalized_error( + const mfem::Vector &computed, + const mfem::Vector &reference, + const double normalization, + const MPI_Comm communicator + ) { + mfem::Vector difference(computed); + difference -= reference; + + return gravity_prepared_test_utils::global_norm( + difference, communicator + ) / + std::max(normalization, std::numeric_limits::epsilon()); + } + + mfem::Vector + make_vacuum_supported_potential(const mean_field::fem::FEM &f) { + mfem::Vector attributeValues(f.mesh->attributes.Max()); + + attributeValues = 0.0; + + const int vacuumAttribute = + f.domainMapperStateless->GetVacuumElementAttribute(); + + for (int attributeIndex = 0; attributeIndex < f.mesh->attributes.Size(); + ++attributeIndex) { + const int attribute = f.mesh->attributes[attributeIndex]; + + if (attribute == vacuumAttribute) { + attributeValues(attribute - 1) = 1.0; + } + } + + mfem::PWConstCoefficient coefficient(attributeValues); + + return project_scalar(*f.gravityPotentialFes, coefficient); + } + + class HydrostaticEnthalpyMassOperator final : public mfem::Operator { + public: + HydrostaticEnthalpyMassOperator( + const mean_field::fem::FEM &f, + const mean_field::mapping::DomainMapperStateless &domainMapper, + const mfem::Vector &displacementTrue + ) + : mfem::Operator(f.enthalpyFes->GetTrueVSize()), + f_(f), + domainMapper_(domainMapper), + displacementTrue_(displacementTrue) { + } + + void Mult( + const mfem::Vector &input, + mfem::Vector &output + ) const override { + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_enthalpy_action( + f_, domainMapper_, input, displacementTrue_, output + ); + } + + private: + const mean_field::fem::FEM &f_; + + const mean_field::mapping::DomainMapperStateless &domainMapper_; + + const mfem::Vector &displacementTrue_; + }; +} // namespace hydrostatic_kernel_test_utils + +TEST_CASE( + "Rigid Rotation Potential Derivative Matches Centered Differences", + tags::barotrope &tags::hydro &tags::jacobian &tags::physics &tags::unit +) { + const mean_field::physics::RigidRotation rotation = + hydrostatic_kernel_test_utils::make_rotation(); + + mfem::Vector position(3); + mfem::Vector direction(3); + + position(0) = 0.71; + position(1) = -0.42; + position(2) = 0.36; + + direction(0) = -0.17; + direction(1) = 0.29; + direction(2) = 0.11; + + constexpr double epsilon = 1.0e-7; + + mfem::Vector plusPosition(position); + mfem::Vector minusPosition(position); + + plusPosition.Add(epsilon, direction); + minusPosition.Add(-epsilon, direction); + + const double centeredDerivative = + (rotation.potential(plusPosition) - rotation.potential(minusPosition)) / + (2.0 * epsilon); + + const double analyticDerivative = + rotation.potential_directional_derivative(position, direction); + + const double relativeError = + std::abs(centeredDerivative - analyticDerivative) / + std::max( + std::abs(analyticDerivative), std::numeric_limits::epsilon() + ); + + INFO("Rigid-rotation derivative error = " << relativeError); + + CHECK(relativeError < 2.0e-9); +} + +TEST_CASE( + "Hydrostatic Residual Vanishes For A Manufactured Rotating State", + tags::barotrope &tags::hydro &tags::integration &tags::kernels + &tags::physics &tags::residuals +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::RigidRotation rotation = + hydrostatic_kernel_test_utils::make_rotation(); + + constexpr double bernoulliConstant = 0.73; + constexpr double potentialValue = -0.21; + constexpr double constantOffset = 0.40; + + mfem::FunctionCoefficient enthalpyCoefficient( + [&rotation](const mfem::Vector &position) { + return bernoulliConstant - potentialValue + + rotation.potential(position); + } + ); + + const mfem::Vector interpolatedEnthalpy = + hydrostatic_kernel_test_utils::project_scalar( + *f.enthalpyFes, enthalpyCoefficient + ); + + const mfem::Vector potential = + hydrostatic_kernel_test_utils::make_constant_field( + *f.gravityPotentialFes, potentialValue + ); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.0); + + const MPI_Comm communicator = f.mesh->GetComm(); + + /* + * First measure the residual of the nodally interpolated + * analytic equilibrium. Because the order-3 enthalpy space + * cannot exactly represent the quadratic rotation potential + * on an order-4 curved mesh, this measures the representation + * floor rather than an algebraic residual. + */ + mfem::Vector interpolatedResidual; + mfem::Vector interpolatedReferenceResidual; + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, interpolatedEnthalpy, potential, + displacement, bernoulliConstant, interpolatedResidual + ); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, interpolatedEnthalpy, potential, + displacement, bernoulliConstant + constantOffset, + interpolatedReferenceResidual + ); + + const double interpolatedResidualNorm = + gravity_prepared_test_utils::global_norm( + interpolatedResidual, communicator + ); + + const double interpolatedReferenceNorm = + gravity_prepared_test_utils::global_norm( + interpolatedReferenceResidual, communicator + ); + + REQUIRE(interpolatedReferenceNorm > 1.0e-12); + + const double representationFloor = + interpolatedResidualNorm / interpolatedReferenceNorm; + + INFO( + "Interpolated rotating-state residual norm = " + << interpolatedResidualNorm + ); + + INFO( + "Interpolated rotating-state relative " + "representation floor = " + << representationFloor + ); + + /* + * This remains an independent physical/sign check. A wrong + * rotation sign or coordinate convention would produce an + * order-unity error rather than the observed projection floor. + */ + CHECK(representationFloor < 2.0e-5); + + /* + * Construct the weakly manufactured discrete equilibrium. + * + * If r_I is the residual of the nodal interpolant, solve + * + * M_h delta_h = -r_I, + * + * where M_h is exactly the stellar-domain enthalpy action. + * Then h_I + delta_h satisfies the discrete weak equilibrium. + * + * Vacuum-only enthalpy DOFs form a nullspace, but the right-hand + * side is in the range of M_h. Starting CG from zero keeps the + * iteration in the active stellar subspace. + */ + hydrostatic_kernel_test_utils::HydrostaticEnthalpyMassOperator + enthalpyMassOperator(f, *f.domainMapperStateless, displacement); + + mfem::Vector correctionRightHandSide(interpolatedResidual); + + correctionRightHandSide *= -1.0; + + mfem::Vector enthalpyCorrection(f.enthalpyFes->GetTrueVSize()); + + enthalpyCorrection = 0.0; + + mfem::CGSolver projectionSolver(communicator); + + projectionSolver.SetOperator(enthalpyMassOperator); + + projectionSolver.SetRelTol(1.0e-12); + projectionSolver.SetAbsTol(1.0e-15); + projectionSolver.SetMaxIter(1000); + projectionSolver.SetPrintLevel(0); + + projectionSolver.Mult(correctionRightHandSide, enthalpyCorrection); + + INFO( + "Discrete-equilibrium projection converged = " + << projectionSolver.GetConverged() + ); + + INFO( + "Discrete-equilibrium projection iterations = " + << projectionSolver.GetNumIterations() + ); + + INFO( + "Discrete-equilibrium projection final norm = " + << projectionSolver.GetFinalNorm() + ); + + REQUIRE(projectionSolver.GetConverged()); + + mfem::Vector correctionEquationResidual; + + enthalpyMassOperator.Mult(enthalpyCorrection, correctionEquationResidual); + + correctionEquationResidual -= correctionRightHandSide; + + const double correctionEquationNorm = + gravity_prepared_test_utils::global_norm( + correctionEquationResidual, communicator + ); + + INFO( + "Discrete-equilibrium correction-equation " + "residual norm = " + << correctionEquationNorm + ); + + CHECK( + correctionEquationNorm <= + std::max(5.0e-12 * interpolatedResidualNorm, 5.0e-15) + ); + + mfem::Vector discreteEnthalpy(interpolatedEnthalpy); + + discreteEnthalpy += enthalpyCorrection; + + mfem::Vector exactResidual; + mfem::Vector referenceResidual; + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, discreteEnthalpy, potential, + displacement, bernoulliConstant, exactResidual + ); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, discreteEnthalpy, potential, + displacement, bernoulliConstant + constantOffset, referenceResidual + ); + + const double exactNorm = + gravity_prepared_test_utils::global_norm(exactResidual, communicator); + + const double referenceNorm = gravity_prepared_test_utils::global_norm( + referenceResidual, communicator + ); + + const double correctionNorm = gravity_prepared_test_utils::global_norm( + enthalpyCorrection, communicator + ); + + INFO("Enthalpy representation correction norm = " << correctionNorm); + + INFO("Discrete manufactured residual norm = " << exactNorm); + + INFO("Discrete reference residual norm = " << referenceNorm); + + REQUIRE(referenceNorm > 1.0e-12); + + CHECK(exactNorm <= 5.0e-12 * referenceNorm); +} + +TEST_CASE( + "Exact Constant Hydrostatic Equilibrium Remains Zero Under Deformation", + tags::barotrope &tags::hydro &tags::integration &tags::jacobian + &tags::kernels &tags::mapping &tags::physics +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::RigidRotation rotation = + hydrostatic_kernel_test_utils::make_zero_rotation(); + + constexpr double enthalpyValue = 1.20; + constexpr double potentialValue = -0.35; + + constexpr double bernoulliConstant = enthalpyValue + potentialValue; + + const mfem::Vector enthalpy = + hydrostatic_kernel_test_utils::make_constant_field( + *f.enthalpyFes, enthalpyValue + ); + + const mfem::Vector potential = + hydrostatic_kernel_test_utils::make_constant_field( + *f.gravityPotentialFes, potentialValue + ); + + const mfem::Vector displacementVariation = + gravity_prepared_test_utils::make_displacement(f, 0.67); + + const MPI_Comm communicator = f.mesh->GetComm(); + + for (const double deformationScale : {0.0, 0.5, 1.0}) { + DYNAMIC_SECTION("Deformation scale = " << deformationScale) { + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement( + f, deformationScale + ); + + mfem::Vector exactResidual; + mfem::Vector referenceResidual; + mfem::Vector exactGeometryAction; + mfem::Vector referenceGeometryAction; + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, enthalpy, potential, + displacement, bernoulliConstant, exactResidual + ); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, enthalpy, potential, + displacement, bernoulliConstant + 0.50, referenceResidual + ); + + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_displacement_action( + f, *f.domainMapperStateless, rotation, enthalpy, potential, + displacement, bernoulliConstant, displacementVariation, + exactGeometryAction + ); + + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_displacement_action( + f, *f.domainMapperStateless, rotation, enthalpy, potential, + displacement, bernoulliConstant + 0.50, + displacementVariation, referenceGeometryAction + ); + + const double exactResidualNorm = + gravity_prepared_test_utils::global_norm( + exactResidual, communicator + ); + + const double referenceResidualNorm = + gravity_prepared_test_utils::global_norm( + referenceResidual, communicator + ); + + const double exactGeometryNorm = + gravity_prepared_test_utils::global_norm( + exactGeometryAction, communicator + ); + + const double referenceGeometryNorm = + gravity_prepared_test_utils::global_norm( + referenceGeometryAction, communicator + ); + + REQUIRE(referenceResidualNorm > 1.0e-12); + + REQUIRE(referenceGeometryNorm > 1.0e-14); + + CHECK(exactResidualNorm <= 5.0e-12 * referenceResidualNorm); + + CHECK(exactGeometryNorm <= 5.0e-12 * referenceGeometryNorm); + } + } +} + +TEST_CASE( + "Hydrostatic Equilibrium Excludes Vacuum Elements", + tags::barotrope &tags::hydro &tags::kernels &tags::mapping &tags::physics + &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::RigidRotation rotation = + hydrostatic_kernel_test_utils::make_zero_rotation(); + + const mfem::Vector zeroEnthalpy(f.enthalpyFes->GetTrueVSize()); + + mfem::Vector enthalpy(zeroEnthalpy); + enthalpy = 0.0; + + const mfem::Vector vacuumPotential = + hydrostatic_kernel_test_utils::make_vacuum_supported_potential(f); + + const mfem::Vector stellarPotential = + hydrostatic_kernel_test_utils::make_constant_field( + *f.gravityPotentialFes, 1.0 + ); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 1.0); + + mfem::Vector residual; + mfem::Vector vacuumAction; + mfem::Vector stellarAction; + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, enthalpy, vacuumPotential, + displacement, 0.0, residual + ); + + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_potential_action( + f, *f.domainMapperStateless, vacuumPotential, displacement, + vacuumAction + ); + + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_potential_action( + f, *f.domainMapperStateless, stellarPotential, displacement, + stellarAction + ); + + const MPI_Comm communicator = f.mesh->GetComm(); + + const double residualNorm = + gravity_prepared_test_utils::global_norm(residual, communicator); + + const double vacuumActionNorm = + gravity_prepared_test_utils::global_norm(vacuumAction, communicator); + + const double stellarActionNorm = + gravity_prepared_test_utils::global_norm(stellarAction, communicator); + + REQUIRE(stellarActionNorm > 1.0e-12); + + CHECK(residualNorm <= 5.0e-13 * stellarActionNorm); + + CHECK(vacuumActionNorm <= 5.0e-13 * stellarActionNorm); +} + +TEST_CASE( + "Hydrostatic Jacobian Matches Blocks And Centered Differences", + tags::barotrope &tags::hydro &tags::integration &tags::jacobian + &tags::kernels &tags::mapping &tags::physics +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::RigidRotation rotation = + hydrostatic_kernel_test_utils::make_rotation(); + + const mfem::Vector enthalpy = + hydrostatic_kernel_test_utils::make_enthalpy(f); + + const mfem::Vector potential = + hydrostatic_kernel_test_utils::make_potential(f); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 1.0); + + const mfem::Vector enthalpyVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), 0.23 + ); + + const mfem::Vector potentialVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), 0.47 + ); + + const mfem::Vector displacementVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.displacementFes->GetTrueVSize(), 0.71 + ); + + constexpr double bernoulliConstant = 0.41; + constexpr double constantVariation = -0.37; + constexpr double epsilon = 1.0e-7; + + mfem::Vector enthalpyAction; + mfem::Vector potentialAction; + mfem::Vector constantAction; + mfem::Vector displacementAction; + mfem::Vector completeAction; + + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_enthalpy_action( + f, *f.domainMapperStateless, enthalpyVariation, displacement, + enthalpyAction + ); + + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_potential_action( + f, *f.domainMapperStateless, potentialVariation, displacement, + potentialAction + ); + + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_constant_action( + f, *f.domainMapperStateless, constantVariation, displacement, + constantAction + ); + + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_displacement_action( + f, *f.domainMapperStateless, rotation, enthalpy, potential, + displacement, bernoulliConstant, displacementVariation, + displacementAction + ); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium_action( + f, *f.domainMapperStateless, rotation, enthalpy, potential, + displacement, bernoulliConstant, enthalpyVariation, potentialVariation, + constantVariation, displacementVariation, completeAction + ); + + mfem::Vector blockAction(enthalpyAction); + blockAction += potentialAction; + blockAction += constantAction; + blockAction += displacementAction; + + const MPI_Comm communicator = f.mesh->GetComm(); + + const double blockError = gravity_prepared_test_utils::relative_error( + completeAction, blockAction, communicator + ); + + INFO("Hydrostatic block reconstruction error = " << blockError); + + CHECK(blockError < 5.0e-13); + + auto evaluate_residual = [&f, &rotation]( + const mfem::Vector &trialEnthalpy, + const mfem::Vector &trialPotential, + const mfem::Vector &trialDisplacement, + const double trialConstant + ) { + mfem::Vector residual; + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, trialEnthalpy, + trialPotential, trialDisplacement, trialConstant, residual + ); + + return residual; + }; + + mfem::Vector plusEnthalpy(enthalpy); + mfem::Vector minusEnthalpy(enthalpy); + + plusEnthalpy.Add(epsilon, enthalpyVariation); + + minusEnthalpy.Add(-epsilon, enthalpyVariation); + + const mfem::Vector enthalpyDifference = + hydrostatic_kernel_test_utils::centered_difference( + evaluate_residual( + plusEnthalpy, potential, displacement, bernoulliConstant + ), + evaluate_residual( + minusEnthalpy, potential, displacement, bernoulliConstant + ), + epsilon + ); + + mfem::Vector plusPotential(potential); + mfem::Vector minusPotential(potential); + + plusPotential.Add(epsilon, potentialVariation); + + minusPotential.Add(-epsilon, potentialVariation); + + const mfem::Vector potentialDifference = + hydrostatic_kernel_test_utils::centered_difference( + evaluate_residual( + enthalpy, plusPotential, displacement, bernoulliConstant + ), + evaluate_residual( + enthalpy, minusPotential, displacement, bernoulliConstant + ), + epsilon + ); + + const mfem::Vector constantDifference = + hydrostatic_kernel_test_utils::centered_difference( + evaluate_residual( + enthalpy, potential, displacement, + bernoulliConstant + epsilon * constantVariation + ), + evaluate_residual( + enthalpy, potential, displacement, + bernoulliConstant - epsilon * constantVariation + ), + epsilon + ); + + mfem::Vector plusDisplacement(displacement); + mfem::Vector minusDisplacement(displacement); + + plusDisplacement.Add(epsilon, displacementVariation); + + minusDisplacement.Add(-epsilon, displacementVariation); + + const mfem::Vector displacementDifference = + hydrostatic_kernel_test_utils::centered_difference( + evaluate_residual( + enthalpy, potential, plusDisplacement, bernoulliConstant + ), + evaluate_residual( + enthalpy, potential, minusDisplacement, bernoulliConstant + ), + epsilon + ); + + const double enthalpyError = gravity_prepared_test_utils::relative_error( + enthalpyAction, enthalpyDifference, communicator + ); + + const double potentialError = gravity_prepared_test_utils::relative_error( + potentialAction, potentialDifference, communicator + ); + + const double constantError = gravity_prepared_test_utils::relative_error( + constantAction, constantDifference, communicator + ); + + const double displacementError = + gravity_prepared_test_utils::relative_error( + displacementAction, displacementDifference, communicator + ); + + INFO("Hydrostatic enthalpy-block error = " << enthalpyError); + + INFO("Hydrostatic potential-block error = " << potentialError); + + INFO("Hydrostatic constant-block error = " << constantError); + + INFO("Hydrostatic displacement-block error = " << displacementError); + + CHECK(enthalpyError < 2.0e-8); + CHECK(potentialError < 2.0e-8); + CHECK(constantError < 2.0e-8); + CHECK(displacementError < 2.0e-7); + + mfem::Vector combinedPlusEnthalpy(enthalpy); + mfem::Vector combinedMinusEnthalpy(enthalpy); + mfem::Vector combinedPlusPotential(potential); + mfem::Vector combinedMinusPotential(potential); + mfem::Vector combinedPlusDisplacement(displacement); + mfem::Vector combinedMinusDisplacement(displacement); + + combinedPlusEnthalpy.Add(epsilon, enthalpyVariation); + + combinedMinusEnthalpy.Add(-epsilon, enthalpyVariation); + + combinedPlusPotential.Add(epsilon, potentialVariation); + + combinedMinusPotential.Add(-epsilon, potentialVariation); + + combinedPlusDisplacement.Add(epsilon, displacementVariation); + + combinedMinusDisplacement.Add(-epsilon, displacementVariation); + + const mfem::Vector combinedDifference = + hydrostatic_kernel_test_utils::centered_difference( + evaluate_residual( + combinedPlusEnthalpy, combinedPlusPotential, + combinedPlusDisplacement, + bernoulliConstant + epsilon * constantVariation + ), + evaluate_residual( + combinedMinusEnthalpy, combinedMinusPotential, + combinedMinusDisplacement, + bernoulliConstant - epsilon * constantVariation + ), + epsilon + ); + + const double blockNormSum = + gravity_prepared_test_utils::global_norm(enthalpyAction, communicator) + + gravity_prepared_test_utils::global_norm( + potentialAction, communicator + ) + + gravity_prepared_test_utils::global_norm(constantAction, communicator) + + gravity_prepared_test_utils::global_norm( + displacementAction, communicator + ); + + const double simultaneousError = + hydrostatic_kernel_test_utils::sum_normalized_error( + completeAction, combinedDifference, blockNormSum, communicator + ); + + INFO("Hydrostatic simultaneous Jacobian error = " << simultaneousError); + + CHECK(simultaneousError < 2.0e-7); +} + +TEST_CASE( + "Hydrostatic Displacement Action Is Linear In Its Direction", + tags::barotrope &tags::hydro &tags::integration &tags::jacobian + &tags::mapping &tags::physics &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::RigidRotation rotation = + hydrostatic_kernel_test_utils::make_rotation(); + + const mfem::Vector enthalpy = + hydrostatic_kernel_test_utils::make_enthalpy(f); + + const mfem::Vector potential = + hydrostatic_kernel_test_utils::make_potential(f); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 1.0); + + const mfem::Vector firstDirection = + gravity_prepared_test_utils::make_deterministic_vector( + f.displacementFes->GetTrueVSize(), 0.31 + ); + + const mfem::Vector secondDirection = + gravity_prepared_test_utils::make_deterministic_vector( + f.displacementFes->GetTrueVSize(), 0.83 + ); + + constexpr double firstScale = 0.43; + constexpr double secondScale = -0.29; + constexpr double bernoulliConstant = 0.41; + + const mfem::Vector combinedDirection = + gravity_prepared_test_utils::linear_combination( + firstDirection, firstScale, secondDirection, secondScale + ); + + mfem::Vector firstAction; + mfem::Vector secondAction; + mfem::Vector combinedAction; + + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_displacement_action( + f, *f.domainMapperStateless, rotation, enthalpy, potential, + displacement, bernoulliConstant, firstDirection, firstAction + ); + + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_displacement_action( + f, *f.domainMapperStateless, rotation, enthalpy, potential, + displacement, bernoulliConstant, secondDirection, secondAction + ); + + mean_field::operators::kernels:: + apply_hydrostatic_equilibrium_displacement_action( + f, *f.domainMapperStateless, rotation, enthalpy, potential, + displacement, bernoulliConstant, combinedDirection, combinedAction + ); + + const mfem::Vector expectedAction = + gravity_prepared_test_utils::linear_combination( + firstAction, firstScale, secondAction, secondScale + ); + + const double linearityError = gravity_prepared_test_utils::relative_error( + combinedAction, expectedAction, f.mesh->GetComm() + ); + + INFO("Hydrostatic displacement-linearity error = " << linearityError); + + CHECK(linearityError < 5.0e-12); +} + +TEST_CASE( + "Hydrostatic Residual Is Translationally Invariant On Deformed Geometry", + tags::barotrope &tags::hydro &tags::integration &tags::kernels + &tags::mapping &tags::physics &tags::residuals +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + mfem::Vector angularVelocity(3); + + angularVelocity(0) = 0.21; + angularVelocity(1) = -0.13; + angularVelocity(2) = 0.48; + + mfem::Vector center(3); + + center(0) = 0.04; + center(1) = -0.03; + center(2) = 0.02; + + mfem::Vector translation(3); + + translation(0) = 0.071; + translation(1) = -0.053; + translation(2) = 0.037; + + mfem::Vector translatedCenter(center); + translatedCenter += translation; + + const mean_field::physics::RigidRotation baseRotation( + angularVelocity, center + ); + + const mean_field::physics::RigidRotation translatedRotation( + angularVelocity, translatedCenter + ); + + const mfem::Vector enthalpy = + hydrostatic_kernel_test_utils::make_enthalpy(f); + + const mfem::Vector potential = + hydrostatic_kernel_test_utils::make_potential(f); + + /* + * Use a nontrivially deformed base state so this checks rotation + * and mapped geometry simultaneously. The comparison state adds + * an exactly representable rigid translation to that deformation. + */ + const mfem::Vector baseDisplacement = + gravity_prepared_test_utils::make_displacement(f, 0.73); + + mfem::ParGridFunction translationField(f.displacementFes.get()); + + mfem::VectorFunctionCoefficient translationCoefficient( + f.mesh->Dimension(), + [&translation](const mfem::Vector &, mfem::Vector &value) { + value.SetSize(translation.Size()); + value = translation; + } + ); + + translationField.ProjectCoefficient(translationCoefficient); + + mfem::Vector translationTrue; + translationField.GetTrueDofs(translationTrue); + + mfem::Vector translatedDisplacement(baseDisplacement); + + translatedDisplacement += translationTrue; + + constexpr double bernoulliConstant = 0.41; + + mfem::Vector baseResidual; + mfem::Vector translatedResidual; + mfem::Vector untranslatedCenterResidual; + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, baseRotation, enthalpy, potential, + baseDisplacement, bernoulliConstant, baseResidual + ); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, translatedRotation, enthalpy, potential, + translatedDisplacement, bernoulliConstant, translatedResidual + ); + + /* + * Negative control: translate the geometry but leave the rotation + * center fixed. This must not agree with the covariant result. + */ + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, baseRotation, enthalpy, potential, + translatedDisplacement, bernoulliConstant, untranslatedCenterResidual + ); + + const MPI_Comm communicator = f.mesh->GetComm(); + + const double baseResidualNorm = + gravity_prepared_test_utils::global_norm(baseResidual, communicator); + + const double translatedResidualNorm = + gravity_prepared_test_utils::global_norm( + translatedResidual, communicator + ); + + const double translationInvarianceError = + gravity_prepared_test_utils::relative_error( + translatedResidual, baseResidual, communicator + ); + + const double fixedCenterDifference = + gravity_prepared_test_utils::relative_error( + untranslatedCenterResidual, translatedResidual, communicator + ); + + INFO("Base deformed hydrostatic residual norm = " << baseResidualNorm); + + INFO("Translated hydrostatic residual norm = " << translatedResidualNorm); + + INFO( + "Mapped-rotation translation invariance error = " + << translationInvarianceError + ); + + INFO( + "Relative change with untranslated rotation center = " + << fixedCenterDifference + ); + + REQUIRE(baseResidualNorm > 1.0e-12); + REQUIRE(translatedResidualNorm > 1.0e-12); + REQUIRE(fixedCenterDifference > 1.0e-5); + + CHECK(translationInvarianceError < 5.0e-12); +} \ No newline at end of file diff --git a/tests/operators/kernels/pressure_force_kernels.cpp b/tests/operators/kernels/pressure_force_kernels.cpp new file mode 100644 index 0000000..7c6bb97 --- /dev/null +++ b/tests/operators/kernels/pressure_force_kernels.cpp @@ -0,0 +1,424 @@ +#include +#include +#include + +#include + +#include + +import mean_field; +import test_helpers; + +namespace pressure_force_kernel_test_utils { + [[nodiscard]] mfem::Vector make_deterministic_vector( + const int size, + const double phase + ) { + mfem::Vector vector(size); + + for (int index = 0; index < size; ++index) { + const double position = static_cast(index + 1); + + vector(index) = 0.71 + 0.19 * std::sin(0.31 * position + phase) + + 0.08 * std::cos(0.17 * position - 0.5 * phase); + } + + return vector; + } + + [[nodiscard]] mfem::Vector + make_zero_displacement(const mean_field::fem::FEM &f) { + mfem::Vector displacementTrue(f.displacementFes->GetTrueVSize()); + displacementTrue = 0.0; + return displacementTrue; + } + + [[nodiscard]] mfem::Vector + make_vacuum_only_enthalpy(const mean_field::fem::FEM &f) { + mfem::Vector enthalpyTrue = + make_deterministic_vector(f.enthalpyFes->GetTrueVSize(), 0.43); + + mfem::Array stellarElementMask; + mean_field::utils::populate_element_mask( + f.mesh.get(), mean_field::utils::DOMAINS::STELLAR, + stellarElementMask + ); + + mfem::Array stellarEnthalpyTrueDofs; + mean_field::utils::populate_domain_tdofs( + f.enthalpyFes.get(), stellarElementMask, stellarEnthalpyTrueDofs + ); + + for (int listIndex = 0; listIndex < stellarEnthalpyTrueDofs.Size(); + ++listIndex) { + const int trueDof = stellarEnthalpyTrueDofs[listIndex]; + + MFEM_VERIFY( + trueDof >= 0 && trueDof < enthalpyTrue.Size(), + "The stellar enthalpy true-DOF mask contains an " + "invalid index." + ); + + enthalpyTrue(trueDof) = 0.0; + } + + return enthalpyTrue; + } + + [[nodiscard]] mfem::Vector + make_positive_asymmetric_enthalpy(const mean_field::fem::FEM &f) { + mfem::FunctionCoefficient coefficient([](const mfem::Vector &position) { + return 1.10 + 0.07 * position(0) - 0.04 * position(1) + + 0.03 * position(2); + }); + + mfem::ParGridFunction enthalpyField(f.enthalpyFes.get()); + + enthalpyField.ProjectCoefficient(coefficient); + + mfem::Vector enthalpyTrue; + enthalpyField.GetTrueDofs(enthalpyTrue); + + return enthalpyTrue; + } + + [[nodiscard]] mfem::Vector make_component_test_field( + const mean_field::fem::FEM &f, + const int component, + const int coordinate + ) { + const int dimension = f.mesh->Dimension(); + + MFEM_VERIFY( + component >= 0 && component < dimension, + "The requested vector component is invalid." + ); + + MFEM_VERIFY( + coordinate >= -1 && coordinate < dimension, + "The requested coordinate is invalid." + ); + + /* + * coordinate == -1 gives the rigid translation e_component. + * + * Otherwise this gives + * + * w = x_coordinate e_component. + */ + mfem::VectorFunctionCoefficient coefficient( + dimension, + [component, coordinate, + dimension](const mfem::Vector &position, mfem::Vector &value) { + value.SetSize(dimension); + value = 0.0; + + value(component) = coordinate < 0 ? 1.0 : position(coordinate); + } + ); + + mfem::ParGridFunction field(f.displacementFes.get()); + + field.ProjectCoefficient(coefficient); + + mfem::Vector fieldTrue; + field.GetTrueDofs(fieldTrue); + + return fieldTrue; + } + + [[nodiscard]] double global_dot( + const mfem::Vector &left, + const mfem::Vector &right, + MPI_Comm communicator + ) { + MFEM_VERIFY( + left.Size() == right.Size(), + "The global dot-product vectors have different sizes." + ); + + const double localDot = left * right; + double globalDot = 0.0; + + MPI_Allreduce( + &localDot, &globalDot, 1, MPI_DOUBLE, MPI_SUM, communicator + ); + + return globalDot; + } +} // namespace pressure_force_kernel_test_utils + +TEST_CASE( + "Pressure Force Residual Vanishes For Zero Enthalpy", + tags::barotrope &tags::pressure &tags::kernels &tags::integration +) { + mean_field::utils::Args args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.okay()); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 0.25); + + mfem::Vector enthalpyTrue(f.enthalpyFes->GetTrueVSize()); + enthalpyTrue = 0.0; + + const mfem::Vector displacementTrue = + pressure_force_kernel_test_utils::make_zero_displacement(f); + + mfem::Vector residualTrue; + + mean_field::operators::kernels::apply_pressure_force_residual( + f, *f.domainMapperStateless, barotrope, enthalpyTrue, displacementTrue, + residualTrue + ); + + REQUIRE(residualTrue.Size() == f.displacementFes->GetTrueVSize()); + + const double residualNorm = gravity_prepared_test_utils::global_norm( + residualTrue, f.mesh->GetComm() + ); + + CHECK(residualNorm == 0.0); +} + +TEST_CASE( + "Pressure Force Residual Excludes Vacuum Enthalpy Exactly", + tags::barotrope &tags::pressure &tags::kernels &tags::integration +) { + mean_field::utils::Args args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.okay()); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 0.25); + + const mfem::Vector enthalpyTrue = + pressure_force_kernel_test_utils::make_vacuum_only_enthalpy(f); + + const double enthalpyNorm = gravity_prepared_test_utils::global_norm( + enthalpyTrue, f.mesh->GetComm() + ); + + /* + * Ensure this is a real exclusion test rather than another + * all-zero-input test. + */ + REQUIRE(enthalpyNorm > 0.0); + + const mfem::Vector displacementTrue = + pressure_force_kernel_test_utils::make_zero_displacement(f); + + mfem::Vector residualTrue; + + mean_field::operators::kernels::apply_pressure_force_residual( + f, *f.domainMapperStateless, barotrope, enthalpyTrue, displacementTrue, + residualTrue + ); + + REQUIRE(residualTrue.Size() == f.displacementFes->GetTrueVSize()); + + const double residualNorm = gravity_prepared_test_utils::global_norm( + residualTrue, f.mesh->GetComm() + ); + + CHECK(residualNorm == 0.0); +} + +TEST_CASE( + "Pressure Force Residual Is Nonzero For Positive Stellar Pressure", + tags::barotrope &tags::pressure &tags::kernels &tags::integration +) { + mean_field::utils::Args args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.okay()); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 0.25); + + /* + * With n = 3 and K = 1/4: + * + * P(1) = 1/4. + */ + mfem::Vector enthalpyTrue(f.enthalpyFes->GetTrueVSize()); + enthalpyTrue = 1.0; + + const mfem::Vector displacementTrue = + pressure_force_kernel_test_utils::make_zero_displacement(f); + + mfem::Vector residualTrue; + + mean_field::operators::kernels::apply_pressure_force_residual( + f, *f.domainMapperStateless, barotrope, enthalpyTrue, displacementTrue, + residualTrue + ); + + const double residualNorm = gravity_prepared_test_utils::global_norm( + residualTrue, f.mesh->GetComm() + ); + + INFO("Positive-pressure residual norm = " << residualNorm); + + CHECK(std::isfinite(residualNorm)); + + CHECK(residualNorm > 100.0 * std::numeric_limits::epsilon()); +} + +TEST_CASE( + "Pressure Force Residual Does No Work Against Rigid Translations", + tags::barotrope &tags::pressure &tags::kernels &tags::integration + &tags::accuracy +) { + mean_field::utils::Args args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.okay()); + + REQUIRE(f.displacementFes->GetOrdering() == mfem::Ordering::byNODES); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 0.25); + + const mfem::Vector enthalpyTrue = + pressure_force_kernel_test_utils::make_positive_asymmetric_enthalpy(f); + + const mfem::Vector displacementTrue = + pressure_force_kernel_test_utils::make_zero_displacement(f); + + mfem::Vector residualTrue; + + mean_field::operators::kernels::apply_pressure_force_residual( + f, *f.domainMapperStateless, barotrope, enthalpyTrue, displacementTrue, + residualTrue + ); + + const double residualNorm = gravity_prepared_test_utils::global_norm( + residualTrue, f.mesh->GetComm() + ); + + REQUIRE(residualNorm > 0.0); + + const int dimension = f.mesh->Dimension(); + + for (int component = 0; component < dimension; ++component) { + const mfem::Vector translationTrue = + pressure_force_kernel_test_utils::make_component_test_field( + f, component, -1 + ); + + const double translationNorm = gravity_prepared_test_utils::global_norm( + translationTrue, f.mesh->GetComm() + ); + + const double translationWork = + pressure_force_kernel_test_utils::global_dot( + translationTrue, residualTrue, f.mesh->GetComm() + ); + + const double dotProductScale = + std::fmax(residualNorm * translationNorm, 1.0); + + CAPTURE(component, translationWork, dotProductScale); + + CHECK(std::abs(translationWork) <= 5.0e-12 * dotProductScale); + } +} + +TEST_CASE( + "Pressure Force Residual Respects byNODES Component Layout", + tags::barotrope &tags::pressure &tags::kernels &tags::integration + &tags::accuracy +) { + mean_field::utils::Args args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.okay()); + + REQUIRE(f.displacementFes->GetOrdering() == mfem::Ordering::byNODES); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 0.25); + + const mfem::Vector enthalpyTrue = + pressure_force_kernel_test_utils::make_positive_asymmetric_enthalpy(f); + + const mfem::Vector displacementTrue = + pressure_force_kernel_test_utils::make_zero_displacement(f); + + mfem::Vector residualTrue; + + mean_field::operators::kernels::apply_pressure_force_residual( + f, *f.domainMapperStateless, barotrope, enthalpyTrue, displacementTrue, + residualTrue + ); + + const int dimension = f.mesh->Dimension(); + + REQUIRE(dimension == 3); + + mfem::DenseMatrix virtualWork(dimension, dimension); + + for (int component = 0; component < dimension; ++component) { + for (int coordinate = 0; coordinate < dimension; ++coordinate) { + const mfem::Vector affineTestTrue = + pressure_force_kernel_test_utils::make_component_test_field( + f, component, coordinate + ); + + virtualWork(component, coordinate) = + pressure_force_kernel_test_utils::global_dot( + affineTestTrue, residualTrue, f.mesh->GetComm() + ); + } + } + + double meanDiagonalWork = 0.0; + + for (int component = 0; component < dimension; ++component) { + meanDiagonalWork += virtualWork(component, component); + } + + meanDiagonalWork /= static_cast(dimension); + + // INFO( + // "Affine pressure virtual-work tensor:\n" + // << virtualWork + // ); + + INFO("Mean diagonal virtual work = " << meanDiagonalWork); + + REQUIRE( + std::abs(meanDiagonalWork) > + 100.0 * std::numeric_limits::epsilon() + ); + + const double comparisonTolerance = 1.0e-8 * std::abs(meanDiagonalWork); + + for (int component = 0; component < dimension; ++component) { + for (int coordinate = 0; coordinate < dimension; ++coordinate) { + const double computedWork = virtualWork(component, coordinate); + + CAPTURE( + component, coordinate, computedWork, meanDiagonalWork, + comparisonTolerance + ); + + if (component == coordinate) { + CHECK( + std::abs(computedWork - meanDiagonalWork) <= + comparisonTolerance + ); + } else { + CHECK(std::abs(computedWork) <= comparisonTolerance); + } + } + } +} \ No newline at end of file diff --git a/tests/operators/prepared_barotropic_closure.cpp b/tests/operators/prepared_barotropic_closure.cpp new file mode 100644 index 0000000..c1ec5b5 --- /dev/null +++ b/tests/operators/prepared_barotropic_closure.cpp @@ -0,0 +1,995 @@ +#include +#include +#include +#include +#include +#include + +import mean_field; +import test_helpers; + +namespace { + mfem::Vector project_scalar( + mfem::ParFiniteElementSpace &finiteElementSpace, + mfem::Coefficient &coefficient + ) { + mfem::ParGridFunction field(&finiteElementSpace); + + field.ProjectCoefficient(coefficient); + + mfem::Vector trueVector; + field.GetTrueDofs(trueVector); + return trueVector; + } + + mfem::Vector make_base_density(const mean_field::fem::FEM &f) { + mfem::FunctionCoefficient coefficient([](const mfem::Vector &position) { + return 0.42 + 0.025 * position(0) - 0.012 * position(1) + + 0.007 * position(2); + }); + + return project_scalar(*f.densityFes, coefficient); + } + + mfem::Vector make_base_enthalpy(const mean_field::fem::FEM &f) { + mfem::FunctionCoefficient coefficient([](const mfem::Vector &position) { + return 0.92 + 0.018 * position(0) - 0.011 * position(1) + + 0.006 * position(2); + }); + + return project_scalar(*f.enthalpyFes, coefficient); + } + + mfem::Vector make_enthalpy_variation(const mean_field::fem::FEM &f) { + mfem::FunctionCoefficient coefficient([](const mfem::Vector &position) { + return 0.065 + 0.014 * position(0) + 0.009 * position(2); + }); + + return project_scalar(*f.enthalpyFes, coefficient); + } + + mfem::Vector make_combined_variation( + const mfem::Vector &densityVariation, + const mfem::Vector &enthalpyVariation + ) { + mfem::Vector combinedVariation( + densityVariation.Size() + enthalpyVariation.Size() + ); + + for (int densityDof = 0; densityDof < densityVariation.Size(); + ++densityDof) { + combinedVariation(densityDof) = densityVariation(densityDof); + } + + for (int enthalpyDof = 0; enthalpyDof < enthalpyVariation.Size(); + ++enthalpyDof) { + combinedVariation(densityVariation.Size() + enthalpyDof) = + enthalpyVariation(enthalpyDof); + } + + return combinedVariation; + } + struct ClosureCondition { + const char *name; + + double polytropicIndex; + double polytropicConstant; + + double enthalpyOffset; + double enthalpyGradient; + + double densityFactor; + double densityOffset; + double densityGradient; + + double deformationScale; + double directionPhase; + }; + + inline constexpr std::array conditions{ + {{.name = "Linear barotrope on identity geometry", + .polytropicIndex = 1.0, + .polytropicConstant = 0.8, + .enthalpyOffset = 0.65, + .enthalpyGradient = 0.06, + .densityFactor = 0.80, + .densityOffset = 0.015, + .densityGradient = 0.004, + .deformationScale = 0.0, + .directionPhase = 0.31}, + {.name = "Fractional barotrope on moderate deformation", + .polytropicIndex = 1.5, + .polytropicConstant = 1.2, + .enthalpyOffset = 0.90, + .enthalpyGradient = 0.09, + .densityFactor = 1.15, + .densityOffset = -0.003, + .densityGradient = 0.003, + .deformationScale = 0.45, + .directionPhase = 0.53}, + {.name = "Target n=3 barotrope on strong deformation", + .polytropicIndex = 3.0, + .polytropicConstant = 1.5, + .enthalpyOffset = 1.20, + .enthalpyGradient = 0.12, + .densityFactor = 1.40, + .densityOffset = 0.006, + .densityGradient = 0.002, + .deformationScale = 1.0, + .directionPhase = 0.79}} + }; + + double evaluate_enthalpy( + const mfem::Vector &position, + const ClosureCondition &condition + ) { + return condition.enthalpyOffset + + condition.enthalpyGradient * + (0.50 * position(0) - 0.30 * position(1) + + 0.20 * position(2)); + } + + mfem::Vector project_scalar_field( + mfem::ParFiniteElementSpace &finiteElementSpace, + mfem::Coefficient &coefficient + ) { + mfem::ParGridFunction field(&finiteElementSpace); + + field.ProjectCoefficient(coefficient); + + mfem::Vector trueVector; + field.GetTrueDofs(trueVector); + + return trueVector; + } + + mfem::Vector make_enthalpy( + const mean_field::fem::FEM &f, + const ClosureCondition &condition + ) { + mfem::FunctionCoefficient coefficient( + [condition](const mfem::Vector &position) { + return evaluate_enthalpy(position, condition); + } + ); + + return project_scalar_field(*f.enthalpyFes, coefficient); + } + + mfem::Vector make_density( + const mean_field::fem::FEM &f, + const mean_field::physics::PolytropicBarotrope &barotrope, + const ClosureCondition &condition + ) { + mfem::FunctionCoefficient coefficient( + [&barotrope, condition](const mfem::Vector &position) { + const double enthalpy = evaluate_enthalpy(position, condition); + + return condition.densityFactor * + barotrope.density_from_enthalpy(enthalpy) + + condition.densityOffset + + condition.densityGradient * + (0.40 * position(0) + 0.25 * position(1) - + 0.15 * position(2)); + } + ); + + return project_scalar_field(*f.densityFes, coefficient); + } + + mfem::Vector make_constant_field( + mfem::ParFiniteElementSpace &finiteElementSpace, + const double value + ) { + mfem::ConstantCoefficient coefficient(value); + + return project_scalar_field(finiteElementSpace, coefficient); + } + +} // namespace + +TEST_CASE( + "Prepared Barotropic Closure Matches Stateless Kernels", + tags::hydro &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + mean_field::operators::PreparedBarotropicClosureOperator preparedOperator( + f, *f.domainMapperStateless, barotrope + ); + + REQUIRE_FALSE(preparedOperator.IsPrepared()); + REQUIRE(preparedOperator.Height() == f.densityFes->GetTrueVSize()); + REQUIRE( + preparedOperator.Width() == + f.densityFes->GetTrueVSize() + f.enthalpyFes->GetTrueVSize() + ); + REQUIRE(preparedOperator.GetDensitySize() == f.densityFes->GetTrueVSize()); + REQUIRE( + preparedOperator.GetEnthalpySize() == f.enthalpyFes->GetTrueVSize() + ); + + const mfem::Vector baseDensity = make_base_density(f); + + const mfem::Vector baseEnthalpy = make_base_enthalpy(f); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 1.0); + + const mfem::Vector densityVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.43 + ); + + const mfem::Vector displacementVariation = + gravity_prepared_test_utils::make_displacement(f, 0.63); + + const mfem::Vector enthalpyVariation = make_enthalpy_variation(f); + + mfem::Vector zeroDensity(f.densityFes->GetTrueVSize()); + zeroDensity = 0.0; + + mfem::Vector zeroEnthalpy(f.enthalpyFes->GetTrueVSize()); + zeroEnthalpy = 0.0; + + preparedOperator.Prepare(baseDensity, baseEnthalpy, displacement); + + mfem::Vector preparedResidual; + mfem::Vector preparedDensityAction; + mfem::Vector preparedEnthalpyAction; + mfem::Vector preparedSplitAction; + mfem::Vector preparedCombinedAction; + + preparedOperator.BuildResidual(preparedResidual); + + preparedOperator.Mult( + densityVariation, zeroEnthalpy, displacementVariation, + preparedDensityAction + ); + + preparedOperator.Mult( + zeroDensity, enthalpyVariation, displacementVariation, + preparedEnthalpyAction + ); + + preparedOperator.Mult( + densityVariation, enthalpyVariation, displacementVariation, + preparedSplitAction + ); + + const mfem::Vector combinedVariation = + make_combined_variation(densityVariation, enthalpyVariation); + + preparedOperator.Mult(combinedVariation, preparedCombinedAction); + + mfem::Vector referenceResidual; + mfem::Vector referenceDensityAction; + mfem::Vector referenceEnthalpyAction; + mfem::Vector referenceDisplacementAction; + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, baseDensity, baseEnthalpy, + displacement, referenceResidual + ); + + mean_field::operators::kernels::apply_barotropic_closure_density_action( + f, *f.domainMapperStateless, barotrope, densityVariation, displacement, + referenceDensityAction + ); + + mean_field::operators::kernels::apply_barotropic_closure_enthalpy_action( + f, *f.domainMapperStateless, barotrope, baseEnthalpy, enthalpyVariation, + displacement, referenceEnthalpyAction + ); + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, baseDensity, baseEnthalpy, + displacement, displacementVariation, referenceDisplacementAction + ); + + mfem::Vector referenceCombinedAction(referenceDensityAction); + referenceCombinedAction += referenceEnthalpyAction; + referenceCombinedAction += referenceDisplacementAction; + + const MPI_Comm communicator = f.mesh->GetComm(); + + const double residualError = gravity_prepared_test_utils::relative_error( + preparedResidual, referenceResidual, communicator + ); + + const double densityError = gravity_prepared_test_utils::relative_error( + preparedDensityAction, referenceDensityAction, communicator + ); + + const double enthalpyError = gravity_prepared_test_utils::relative_error( + preparedEnthalpyAction, referenceEnthalpyAction, communicator + ); + + const double splitError = gravity_prepared_test_utils::relative_error( + preparedSplitAction, referenceCombinedAction, communicator + ); + + const double combinedError = gravity_prepared_test_utils::relative_error( + preparedCombinedAction, referenceCombinedAction, communicator + ); + + INFO("Prepared residual error = " << residualError); + INFO("Prepared density-action error = " << densityError); + INFO("Prepared enthalpy-action error = " << enthalpyError); + INFO("Prepared split-action error = " << splitError); + INFO("Prepared combined-action error = " << combinedError); + + CHECK(preparedOperator.IsPrepared()); + CHECK(preparedOperator.GetPreparationCount() == 1); + CHECK(residualError < 2.0e-12); + CHECK(densityError < 2.0e-12); + CHECK(enthalpyError < 2.0e-12); + CHECK(splitError < 2.0e-12); + CHECK(combinedError < 2.0e-12); +} + +TEST_CASE( + "Prepared Barotropic Closure Jacobian Matches Centered Difference", + tags::hydro &tags::jacobian &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + mfem::Vector baseDensity = make_base_density(f); + + mfem::Vector baseEnthalpy = make_base_enthalpy(f); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 1.0); + + const mfem::Vector densityVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.71 + ); + + const mfem::Vector displacementVariation = + gravity_prepared_test_utils::make_displacement(f, 0.63); + + const mfem::Vector enthalpyVariation = make_enthalpy_variation(f); + + mean_field::operators::PreparedBarotropicClosureOperator preparedOperator( + f, *f.domainMapperStateless, barotrope + ); + + preparedOperator.Prepare(baseDensity, baseEnthalpy, displacement); + + mfem::Vector analyticAction; + + preparedOperator.Mult( + densityVariation, enthalpyVariation, displacementVariation, + analyticAction + ); + + constexpr double differenceStep = 1.0e-6; + + const mfem::Vector plusDensity = + gravity_prepared_test_utils::linear_combination( + baseDensity, 1.0, densityVariation, differenceStep + ); + + const mfem::Vector minusDensity = + gravity_prepared_test_utils::linear_combination( + baseDensity, 1.0, densityVariation, -differenceStep + ); + + const mfem::Vector plusEnthalpy = + gravity_prepared_test_utils::linear_combination( + baseEnthalpy, 1.0, enthalpyVariation, differenceStep + ); + + const mfem::Vector minusEnthalpy = + gravity_prepared_test_utils::linear_combination( + baseEnthalpy, 1.0, enthalpyVariation, -differenceStep + ); + + mfem::Vector plusResidual; + mfem::Vector minusResidual; + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, plusDensity, plusEnthalpy, + displacement, plusResidual + ); + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, minusDensity, minusEnthalpy, + displacement, minusResidual + ); + + mfem::Vector finiteDifference(plusResidual); + finiteDifference -= minusResidual; + finiteDifference *= 1.0 / (2.0 * differenceStep); + + const double relativeError = gravity_prepared_test_utils::relative_error( + analyticAction, finiteDifference, f.mesh->GetComm() + ); + + INFO("Prepared EOS centered-difference error = " << relativeError); + + CHECK(relativeError < 2.0e-8); +} + +TEST_CASE( + "Prepared Barotropic Closure Reuses Frozen Data", + tags::hydro &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + mean_field::operators::PreparedBarotropicClosureOperator preparedOperator( + f, *f.domainMapperStateless, barotrope + ); + + CHECK_FALSE(preparedOperator.IsPrepared()); + CHECK(preparedOperator.GetPreparationCount() == 0); + + mfem::Vector baseDensity = make_base_density(f); + + mfem::Vector baseEnthalpy = make_base_enthalpy(f); + + mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 1.0); + + const mfem::Vector displacementVariation = + gravity_prepared_test_utils::make_displacement(f, 0.63); + + const mfem::Vector densityVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.31 + ); + + const mfem::Vector enthalpyVariation = make_enthalpy_variation(f); + + preparedOperator.Prepare(baseDensity, baseEnthalpy, displacement); + + REQUIRE(preparedOperator.IsPrepared()); + REQUIRE(preparedOperator.GetPreparationCount() == 1); + + mfem::Vector firstResidual; + mfem::Vector firstAction; + + preparedOperator.BuildResidual(firstResidual); + + preparedOperator.Mult( + densityVariation, enthalpyVariation, displacementVariation, firstAction + ); + + baseDensity = 7.0; + baseEnthalpy = 3.0; + displacement *= -4.0; + + const std::uint64_t preparationCount = + preparedOperator.GetPreparationCount(); + + mfem::Vector repeatedResidual; + mfem::Vector repeatedAction; + + preparedOperator.BuildResidual(repeatedResidual); + + preparedOperator.Mult( + densityVariation, enthalpyVariation, displacementVariation, + repeatedAction + ); + + const MPI_Comm communicator = f.mesh->GetComm(); + + const double residualReuseError = + gravity_prepared_test_utils::relative_error( + repeatedResidual, firstResidual, communicator + ); + + const double actionReuseError = gravity_prepared_test_utils::relative_error( + repeatedAction, firstAction, communicator + ); + + INFO("Frozen residual reuse error = " << residualReuseError); + INFO("Frozen action reuse error = " << actionReuseError); + + CHECK(residualReuseError < 2.0e-14); + CHECK(actionReuseError < 2.0e-14); + CHECK(preparedOperator.GetPreparationCount() == preparationCount); +} + +TEST_CASE( + "Prepared Barotropic Closure Reprepares For New Geometry", + tags::hydro &tags::mapping &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + const mfem::Vector baseDensity = make_base_density(f); + + const mfem::Vector baseEnthalpy = make_base_enthalpy(f); + + const mfem::Vector densityVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.59 + ); + + mfem::Vector zeroEnthalpy(f.enthalpyFes->GetTrueVSize()); + zeroEnthalpy = 0.0; + + mean_field::operators::PreparedBarotropicClosureOperator preparedOperator( + f, *f.domainMapperStateless, barotrope + ); + + mfem::Vector identityAction; + mfem::Vector deformedAction; + + for (const double deformationScale : {0.0, 1.0}) { + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, deformationScale); + + const mfem::Vector displacementVariation = + gravity_prepared_test_utils::make_displacement(f, 0.63); + + preparedOperator.Prepare(baseDensity, baseEnthalpy, displacement); + + mfem::Vector preparedResidual; + mfem::Vector preparedAction; + mfem::Vector referenceResidual; + mfem::Vector referenceAction; + + preparedOperator.BuildResidual(preparedResidual); + + preparedOperator.Mult( + densityVariation, zeroEnthalpy, displacementVariation, + preparedAction + ); + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, baseDensity, baseEnthalpy, + displacement, referenceResidual + ); + + mean_field::operators::kernels::apply_barotropic_closure_density_action( + f, *f.domainMapperStateless, barotrope, densityVariation, + displacement, referenceAction + ); + + const MPI_Comm communicator = f.mesh->GetComm(); + + const double residualError = + gravity_prepared_test_utils::relative_error( + preparedResidual, referenceResidual, communicator + ); + + const double actionError = gravity_prepared_test_utils::relative_error( + preparedAction, referenceAction, communicator + ); + + INFO("Deformation scale = " << deformationScale); + INFO("Reprepared residual error = " << residualError); + INFO("Reprepared action error = " << actionError); + + CHECK(residualError < 2.0e-12); + CHECK(actionError < 2.0e-12); + + if (deformationScale == 0.0) { + identityAction = preparedAction; + } else { + deformedAction = preparedAction; + } + } + + const double geometryChange = gravity_prepared_test_utils::relative_error( + deformedAction, identityAction, f.mesh->GetComm() + ); + + INFO("Prepared closure geometry change = " << geometryChange); + + CHECK(preparedOperator.GetPreparationCount() == 2); + CHECK(geometryChange > 1.0e-5); +} + +TEST_CASE( + "Complete Barotropic Closure Matches Blocks And Centered Differences " + "Across Conditions", + tags::barotrope &tags::closure &tags::hydro &tags::integration + &tags::jacobian &tags::mapping &tags::physics &tags::prepared +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const MPI_Comm communicator = f.mesh->GetComm(); + + constexpr double differenceStep = 1.0e-5; + + for (std::size_t conditionIndex = 0; conditionIndex < + + conditions.size(); + ++conditionIndex) { + const auto &condition = + + conditions[conditionIndex]; + + DYNAMIC_SECTION(condition.name) { + const mean_field::physics::PolytropicBarotrope barotrope( + condition.polytropicIndex, condition.polytropicConstant + ); + + const mfem::Vector baseDensity = + + make_density(f, barotrope, condition); + + const mfem::Vector baseEnthalpy = + + make_enthalpy(f, condition); + + const mfem::Vector baseDisplacement = + gravity_prepared_test_utils::make_displacement( + f, condition.deformationScale + ); + + mfem::Vector densityVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.densityFes->GetTrueVSize(), condition.directionPhase + ); + + mfem::Vector enthalpyVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), + condition.directionPhase + 0.27 + ); + + mfem::Vector displacementVariation = + gravity_prepared_test_utils::make_displacement( + f, condition.directionPhase + ); + + mfem::Vector densityAction; + mfem::Vector enthalpyAction; + mfem::Vector displacementAction; + + mean_field::operators::kernels:: + apply_barotropic_closure_density_action( + f, *f.domainMapperStateless, barotrope, densityVariation, + baseDisplacement, densityAction + ); + + mean_field::operators::kernels:: + apply_barotropic_closure_enthalpy_action( + f, *f.domainMapperStateless, barotrope, baseEnthalpy, + enthalpyVariation, baseDisplacement, enthalpyAction + ); + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, baseDensity, + baseEnthalpy, baseDisplacement, displacementVariation, + displacementAction + ); + + double densityActionNorm = gravity_prepared_test_utils::global_norm( + densityAction, communicator + ); + + double enthalpyActionNorm = + gravity_prepared_test_utils::global_norm( + enthalpyAction, communicator + ); + + double displacementActionNorm = + gravity_prepared_test_utils::global_norm( + displacementAction, communicator + ); + + REQUIRE(densityActionNorm > 1.0e-12); + REQUIRE(enthalpyActionNorm > 1.0e-12); + REQUIRE(displacementActionNorm > 1.0e-12); + + const double targetActionNorm = std::min( + {densityActionNorm, enthalpyActionNorm, displacementActionNorm} + ); + + const double densityScale = targetActionNorm / densityActionNorm; + + const double enthalpyScale = targetActionNorm / enthalpyActionNorm; + + const double displacementScale = + targetActionNorm / displacementActionNorm; + + densityVariation *= densityScale; + densityAction *= densityScale; + + enthalpyVariation *= enthalpyScale; + enthalpyAction *= enthalpyScale; + + displacementVariation *= displacementScale; + displacementAction *= displacementScale; + + densityActionNorm = gravity_prepared_test_utils::global_norm( + densityAction, communicator + ); + + enthalpyActionNorm = gravity_prepared_test_utils::global_norm( + enthalpyAction, communicator + ); + + displacementActionNorm = gravity_prepared_test_utils::global_norm( + displacementAction, communicator + ); + + mean_field::operators::context::barotropic:: + BarotropicClosureLinearizationContext context( + f, *f.domainMapperStateless, barotrope + ); + + const std::uint64_t revisionBase = + 100 + static_cast(10 * conditionIndex); + + const mean_field::operators::context::barotropic:: + BarotropicClosureRevisions revisions{ + .density = revisionBase + 1, + .enthalpy = revisionBase + 2, + .displacement = revisionBase + 3 + }; + + context.Prepare( + baseDensity, baseEnthalpy, baseDisplacement, revisions + ); + + mfem::Vector preparedResidual; + mfem::Vector referenceResidual; + + context.BuildResidual(preparedResidual); + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, baseDensity, + baseEnthalpy, baseDisplacement, referenceResidual + ); + + const double residualEvaluationError = + gravity_prepared_test_utils::relative_error( + preparedResidual, referenceResidual, communicator + ); + + mfem::Vector preparedAction; + + context.GetOperator().Mult( + densityVariation, enthalpyVariation, displacementVariation, + preparedAction + ); + + mfem::Vector blockSum(densityAction); + + blockSum += enthalpyAction; + blockSum += displacementAction; + + const double blockAssemblyError = + gravity_prepared_test_utils::relative_error( + preparedAction, blockSum, communicator + ); + + mfem::Vector plusDensity(baseDensity); + + mfem::Vector minusDensity(baseDensity); + + mfem::Vector plusEnthalpy(baseEnthalpy); + + mfem::Vector minusEnthalpy(baseEnthalpy); + + mfem::Vector plusDisplacement(baseDisplacement); + + mfem::Vector minusDisplacement(baseDisplacement); + + plusDensity.Add(differenceStep, densityVariation); + + minusDensity.Add(-differenceStep, densityVariation); + + plusEnthalpy.Add(differenceStep, enthalpyVariation); + + minusEnthalpy.Add(-differenceStep, enthalpyVariation); + + plusDisplacement.Add(differenceStep, displacementVariation); + + minusDisplacement.Add(-differenceStep, displacementVariation); + + mfem::Vector plusResidual; + mfem::Vector minusResidual; + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, plusDensity, + plusEnthalpy, plusDisplacement, plusResidual + ); + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, minusDensity, + minusEnthalpy, minusDisplacement, minusResidual + ); + + mfem::Vector finiteDifference(plusResidual); + + finiteDifference -= minusResidual; + + finiteDifference *= 1.0 / (2.0 * differenceStep); + + mfem::Vector finiteDifferenceError(preparedAction); + + finiteDifferenceError -= finiteDifference; + + const double finiteDifferenceErrorNorm = + gravity_prepared_test_utils::global_norm( + finiteDifferenceError, communicator + ); + + const double blockNormSum = + densityActionNorm + enthalpyActionNorm + displacementActionNorm; + + const double blockScaledDifferenceError = + finiteDifferenceErrorNorm / blockNormSum; + + const double completeRelativeError = + gravity_prepared_test_utils::relative_error( + preparedAction, finiteDifference, communicator + ); + + INFO("Condition = " << condition.name); + + INFO("Polytropic index = " << condition.polytropicIndex); + + INFO("Deformation scale = " << condition.deformationScale); + + INFO("Prepared residual error = " << residualEvaluationError); + + INFO("Complete block-assembly error = " << blockAssemblyError); + + INFO("Density-action norm = " << densityActionNorm); + + INFO("Enthalpy-action norm = " << enthalpyActionNorm); + + INFO("Displacement-action norm = " << displacementActionNorm); + + INFO( + "Complete centered-difference relative error = " + << completeRelativeError + ); + + INFO( + "Block-scaled centered-difference error = " + << blockScaledDifferenceError + ); + + CHECK(context.GetPreparationCount() == 1); + CHECK(residualEvaluationError < 5.0e-12); + CHECK(blockAssemblyError < 5.0e-12); + CHECK(blockScaledDifferenceError < 2.0e-7); + } + } +} + +TEST_CASE( + "Exact Constant Barotropic Closure Remains Zero Under Deformation", + tags::barotrope &tags::closure &tags::hydro &tags::integration + &tags::jacobian &tags::mapping &tags::physics +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.domainMapperStateless != nullptr); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + constexpr double enthalpyValue = 1.20; + + const double equilibriumDensityValue = + barotrope.density_from_enthalpy(enthalpyValue); + + const mfem::Vector enthalpy = + make_constant_field(*f.enthalpyFes, enthalpyValue); + + const mfem::Vector equilibriumDensity = + make_constant_field(*f.densityFes, equilibriumDensityValue); + + const mfem::Vector referenceDensity = + make_constant_field(*f.densityFes, equilibriumDensityValue + 1.0); + + const mfem::Vector displacementVariation = + gravity_prepared_test_utils::make_displacement(f, 0.67); + + const MPI_Comm communicator = f.mesh->GetComm(); + + for (const double deformationScale : {0.0, 0.5, 1.0}) { + DYNAMIC_SECTION("Deformation scale = " << deformationScale) { + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement( + f, deformationScale + ); + + mfem::Vector exactResidual; + mfem::Vector referenceResidual; + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, equilibriumDensity, + enthalpy, displacement, exactResidual + ); + + mean_field::operators::kernels::apply_barotropic_closure( + f, *f.domainMapperStateless, barotrope, referenceDensity, + enthalpy, displacement, referenceResidual + ); + + mfem::Vector exactGeometryAction; + mfem::Vector referenceGeometryAction; + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, equilibriumDensity, + enthalpy, displacement, displacementVariation, + exactGeometryAction + ); + + mean_field::operators::kernels:: + apply_barotropic_closure_displacement_action( + f, *f.domainMapperStateless, barotrope, referenceDensity, + enthalpy, displacement, displacementVariation, + referenceGeometryAction + ); + + const double exactResidualNorm = + gravity_prepared_test_utils::global_norm( + exactResidual, communicator + ); + + const double referenceResidualNorm = + gravity_prepared_test_utils::global_norm( + referenceResidual, communicator + ); + + const double exactGeometryNorm = + gravity_prepared_test_utils::global_norm( + exactGeometryAction, communicator + ); + + const double referenceGeometryNorm = + gravity_prepared_test_utils::global_norm( + referenceGeometryAction, communicator + ); + + INFO("Deformation scale = " << deformationScale); + + INFO("Exact-closure residual norm = " << exactResidualNorm); + + INFO("Reference residual norm = " << referenceResidualNorm); + + INFO("Exact-closure geometry-action norm = " << exactGeometryNorm); + + INFO("Reference geometry-action norm = " << referenceGeometryNorm); + + REQUIRE(referenceResidualNorm > 1.0e-12); + REQUIRE(referenceGeometryNorm > 1.0e-14); + + CHECK(exactResidualNorm <= 5.0e-12 * referenceResidualNorm); + + CHECK(exactGeometryNorm <= 5.0e-12 * referenceGeometryNorm); + } + } +} \ No newline at end of file diff --git a/tests/operators/prepared_gravity_source.cpp b/tests/operators/prepared_gravity_source.cpp new file mode 100644 index 0000000..fe31e90 --- /dev/null +++ b/tests/operators/prepared_gravity_source.cpp @@ -0,0 +1,157 @@ +#include +#include +#include + +import mean_field; +import test_helpers; + +using namespace mean_field; +using Catch::Matchers::WithinAbs; +namespace prepared_test = gravity_prepared_test_utils; + +TEST_CASE( + "Prepared Mapped Gravity Source Matches Stateless Kernel", + tags::integration &tags::mfem_operators &tags::prepared +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + operators::PreparedMappedGravitySourceOperator prepared_operator( + f, *f.domainMapperStateless + ); + REQUIRE(prepared_operator.Width() == f.densityFes->GetTrueVSize()); + REQUIRE( + prepared_operator.Height() == f.gravityPotentialFes->GetTrueVSize() + ); + + const mfem::Vector density = prepared_test::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.41 + ); + const MPI_Comm communicator = f.mesh->GetComm(); + + mfem::Vector identity_action; + mfem::Vector deformed_action; + + for (const double deformation_scale : {0.0, 1.0}) { + const mfem::Vector displacement = + prepared_test::make_displacement(f, deformation_scale); + + prepared_operator.Prepare(displacement); + + mfem::Vector prepared_action; + mfem::Vector reference_action; + + prepared_operator.Mult(density, prepared_action); + operators::kernels::apply_mapped_source( + f, *f.domainMapperStateless, density, displacement, reference_action + ); + + const double relative_error = prepared_test::relative_error( + prepared_action, reference_action, communicator + ); + + INFO("Deformation scale = " << deformation_scale); + INFO( + "Prepared source norm = " + << prepared_test::global_norm(prepared_action, communicator) + ); + INFO( + "Reference source norm = " + << prepared_test::global_norm(reference_action, communicator) + ); + INFO("Relative prepared-source error = " << relative_error); + + REQUIRE(prepared_operator.IsPrepared()); + CHECK_THAT(relative_error, WithinAbs(0.0, 2.0e-11)); + + if (deformation_scale == 0.0) { + identity_action = prepared_action; + } else { + deformed_action = prepared_action; + } + } + + const double geometry_change = prepared_test::relative_error( + deformed_action, identity_action, communicator + ); + + INFO("Relative source change under deformation = " << geometry_change); + + CHECK(prepared_operator.GetPreparationCount() == 2); + CHECK(geometry_change > 1.0e-5); +} + +TEST_CASE( + "Prepared Mapped Gravity Source Preserves Linearity And Excludes Vacuum", + tags::integration &tags::gravity &tags::prepared +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + operators::PreparedMappedGravitySourceOperator prepared_operator( + f, *f.domainMapperStateless + ); + REQUIRE(prepared_operator.Width() == f.densityFes->GetTrueVSize()); + REQUIRE( + prepared_operator.Height() == f.gravityPotentialFes->GetTrueVSize() + ); + const mfem::Vector displacement = prepared_test::make_displacement(f, 1.0); + prepared_operator.Prepare(displacement); + + const mfem::Vector first = prepared_test::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.27 + ); + const mfem::Vector second = prepared_test::make_deterministic_vector( + f.densityFes->GetTrueVSize(), 0.79 + ); + const mfem::Vector combination = + prepared_test::linear_combination(first, 1.3, second, -0.6); + const mfem::Vector stellar_density = + prepared_test::make_domain_supported_density(f, true); + const mfem::Vector vacuum_density = + prepared_test::make_domain_supported_density(f, false); + + mfem::Vector first_action; + mfem::Vector second_action; + mfem::Vector combination_action; + mfem::Vector stellar_action; + mfem::Vector vacuum_action; + + prepared_operator.Mult(first, first_action); + prepared_operator.Mult(second, second_action); + prepared_operator.Mult(combination, combination_action); + prepared_operator.Mult(stellar_density, stellar_action); + prepared_operator.Mult(vacuum_density, vacuum_action); + + const mfem::Vector expected_combination = prepared_test::linear_combination( + first_action, 1.3, second_action, -0.6 + ); + const MPI_Comm communicator = f.mesh->GetComm(); + + const double linearity_error = prepared_test::relative_error( + combination_action, expected_combination, communicator + ); + const double stellar_norm = + prepared_test::global_norm(stellar_action, communicator); + const double vacuum_norm = + prepared_test::global_norm(vacuum_action, communicator); + const std::uint64_t preparation_count = + prepared_operator.GetPreparationCount(); + + mfem::Vector repeated_action; + prepared_operator.Mult(first, repeated_action); + + INFO("Relative source linearity error = " << linearity_error); + INFO("Stellar source norm = " << stellar_norm); + INFO("Vacuum-only source norm = " << vacuum_norm); + + CHECK_THAT(linearity_error, WithinAbs(0.0, 2.0e-12)); + CHECK(stellar_norm > 0.0); + CHECK(vacuum_norm <= 1.0e-13 * stellar_norm); + CHECK( + prepared_test::relative_error( + repeated_action, first_action, communicator + ) < 2.0e-14 + ); + CHECK(prepared_operator.GetPreparationCount() == preparation_count); +} diff --git a/tests/operators/prepared_hdiv_mass.cpp b/tests/operators/prepared_hdiv_mass.cpp new file mode 100644 index 0000000..f19f6c3 --- /dev/null +++ b/tests/operators/prepared_hdiv_mass.cpp @@ -0,0 +1,164 @@ +#include +#include +#include + +import mean_field; +import test_helpers; + +using namespace mean_field; +using Catch::Matchers::WithinAbs; +namespace prepared_test = gravity_prepared_test_utils; + +TEST_CASE( + "Prepared Mapped Hdiv Mass Matches Stateless Kernel", + tags::integration &tags::mfem_operators &tags::prepared +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + operators::PreparedMappedHDivMassOperator prepared_operator( + f, *f.domainMapperStateless + ); + + const mfem::Vector gravity_gradient = + prepared_test::make_deterministic_vector( + f.gravityFluxFes->GetTrueVSize(), 0.21 + ); + const MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + mfem::Vector identity_action; + mfem::Vector deformed_action; + + for (const double deformation_scale : {0.0, 1.0}) { + const mfem::Vector displacement = + prepared_test::make_displacement(f, deformation_scale); + + prepared_operator.Prepare(displacement); + + mfem::Vector prepared_action; + mfem::Vector reference_action; + + prepared_operator.Mult(gravity_gradient, prepared_action); + operators::kernels::apply_mapped_hdiv_mass( + f, *f.domainMapperStateless, gravity_gradient, displacement, + reference_action + ); + + const double relative_error = prepared_test::relative_error( + prepared_action, reference_action, communicator + ); + + INFO("Deformation scale = " << deformation_scale); + INFO( + "Prepared action norm = " + << prepared_test::global_norm(prepared_action, communicator) + ); + INFO( + "Reference action norm = " + << prepared_test::global_norm(reference_action, communicator) + ); + INFO("Relative prepared-operator error = " << relative_error); + + REQUIRE(prepared_operator.IsPrepared()); + CHECK_THAT(relative_error, WithinAbs(0.0, 2.0e-11)); + + if (deformation_scale == 0.0) { + identity_action = prepared_action; + } else { + deformed_action = prepared_action; + } + } + + const double geometry_change = prepared_test::relative_error( + deformed_action, identity_action, communicator + ); + + INFO("Relative action change under deformation = " << geometry_change); + + CHECK(prepared_operator.GetPreparationCount() == 2); + CHECK(geometry_change > 1.0e-5); +} + +TEST_CASE( + "Prepared Mapped Hdiv Mass Preserves Operator Identities", + tags::integration &tags::gravity &tags::prepared +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + operators::PreparedMappedHDivMassOperator prepared_operator( + f, *f.domainMapperStateless + ); + const mfem::Vector displacement = prepared_test::make_displacement(f, 1.0); + prepared_operator.Prepare(displacement); + + const mfem::Vector first = prepared_test::make_deterministic_vector( + f.gravityFluxFes->GetTrueVSize(), 0.17 + ); + const mfem::Vector second = prepared_test::make_deterministic_vector( + f.gravityFluxFes->GetTrueVSize(), 0.83 + ); + const mfem::Vector combination = + prepared_test::linear_combination(first, 1.7, second, -0.4); + + mfem::Vector first_action; + mfem::Vector second_action; + mfem::Vector combination_action; + mfem::Vector zero_action; + + prepared_operator.Mult(first, first_action); + prepared_operator.Mult(second, second_action); + prepared_operator.Mult(combination, combination_action); + + mfem::Vector expected_combination = prepared_test::linear_combination( + first_action, 1.7, second_action, -0.4 + ); + + mfem::Vector zero(first.Size()); + zero = 0.0; + prepared_operator.Mult(zero, zero_action); + + const MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + const double first_second_product = + prepared_test::global_dot(first, second_action, communicator); + const double second_first_product = + prepared_test::global_dot(second, first_action, communicator); + const double symmetry_error = prepared_test::relative_scalar_error( + first_second_product, second_first_product + ); + const double linearity_error = prepared_test::relative_error( + combination_action, expected_combination, communicator + ); + const double first_energy = + prepared_test::global_dot(first, first_action, communicator); + const double second_energy = + prepared_test::global_dot(second, second_action, communicator); + const std::uint64_t preparation_count = + prepared_operator.GetPreparationCount(); + + mfem::Vector repeated_action; + prepared_operator.Mult(first, repeated_action); + + INFO("u^T M v = " << first_second_product); + INFO("v^T M u = " << second_first_product); + INFO("Relative symmetry error = " << symmetry_error); + INFO("Relative linearity error = " << linearity_error); + INFO("u^T M u = " << first_energy); + INFO("v^T M v = " << second_energy); + + CHECK_THAT(symmetry_error, WithinAbs(0.0, 2.0e-12)); + CHECK_THAT(linearity_error, WithinAbs(0.0, 2.0e-12)); + CHECK_THAT( + prepared_test::global_norm(zero_action, communicator), + WithinAbs(0.0, 1.0e-14) + ); + CHECK(first_energy > 0.0); + CHECK(second_energy > 0.0); + CHECK( + prepared_test::relative_error( + repeated_action, first_action, communicator + ) < 2.0e-14 + ); + CHECK(prepared_operator.GetPreparationCount() == preparation_count); +} \ No newline at end of file diff --git a/tests/operators/prepared_hydrostatic_equilibrium.cpp b/tests/operators/prepared_hydrostatic_equilibrium.cpp new file mode 100644 index 0000000..7d44708 --- /dev/null +++ b/tests/operators/prepared_hydrostatic_equilibrium.cpp @@ -0,0 +1,334 @@ +#include +#include + +import mean_field; +import test_helpers; + +namespace prepared_hydrostatic_test_utils { + static mean_field::operators::context::hydrostatic:: + HydrostaticEquilibriumDependencies + make_dependencies() { + return { + .discretization = {.identity = 211, .revision = 2}, + .enthalpy = {.identity = 223, .revision = 3}, + .gravityPotential = {.identity = 227, .revision = 5}, + .displacement = {.identity = 229, .revision = 7}, + .rotation = {.identity = 233, .revision = 11}, + .bernoulliConstant = {.identity = 239, .revision = 13} + }; + } + + mean_field::operators::context::hydrostatic::HydrostaticEquilibriumStateView + make_state( + const mfem::Vector &enthalpy, + const mfem::Vector &gravityPotential, + const mfem::Vector &displacement, + const double bernoulliConstant + ) { + return { + .enthalpy = enthalpy, + .gravityPotential = gravityPotential, + .displacement = displacement, + .bernoulliConstant = bernoulliConstant + }; + } + + mfem::Vector make_enthalpy( + const mean_field::fem::FEM &f, + const double phase = 0.19 + ) { + return gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), phase + ); + } + + mfem::Vector make_gravity_potential( + const mean_field::fem::FEM &f, + const double phase = 0.37 + ) { + return gravity_prepared_test_utils::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), phase + ); + } + + mean_field::physics::RigidRotation make_rotation(const double scale = 1.0) { + mfem::Vector angularVelocity(3); + + angularVelocity(0) = 0.17 * scale; + angularVelocity(1) = -0.11 * scale; + angularVelocity(2) = 0.43 * scale; + + mfem::Vector center(3); + + center(0) = 0.037; + center(1) = -0.029; + center(2) = 0.021; + + return mean_field::physics::RigidRotation(angularVelocity, center); + } +} // namespace prepared_hydrostatic_test_utils + +TEST_CASE( + "Prepared Hydrostatic Residual Matches Stateless Kernel", + tags::barotrope &tags::hydro &tags::prepared &tags::residuals &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + mean_field::operators::PreparedHydrostaticEquilibriumOperator + preparedOperator(f, *f.domainMapperStateless); + + const mfem::Vector enthalpy = + prepared_hydrostatic_test_utils::make_enthalpy(f); + + const mfem::Vector gravityPotential = + prepared_hydrostatic_test_utils::make_gravity_potential(f); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.73); + + constexpr double bernoulliConstant = 0.41; + + const mean_field::physics::RigidRotation rotation = + prepared_hydrostatic_test_utils::make_rotation(); + + const auto dependencies = + prepared_hydrostatic_test_utils::make_dependencies(); + + CHECK_FALSE(preparedOperator.IsPrepared()); + CHECK(preparedOperator.GetResidualPreparationCount() == 0); + CHECK(preparedOperator.GetResidualApplicationCount() == 0); + + const auto report = preparedOperator.Prepare( + prepared_hydrostatic_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, rotation + ); + + mfem::Vector preparedResidual; + mfem::Vector referenceResidual; + + preparedOperator.BuildResidual(preparedResidual); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, enthalpy, gravityPotential, + displacement, bernoulliConstant, referenceResidual + ); + + const double relativeError = gravity_prepared_test_utils::relative_error( + preparedResidual, referenceResidual, f.mesh->GetComm() + ); + + INFO("Prepared hydrostatic residual relative error = " << relativeError); + + const auto &statistics = preparedOperator.GetContextPreparationStatistics(); + + CHECK(preparedOperator.IsPrepared()); + CHECK(report.contextReport.preparedStaticDependencies); + CHECK(report.contextReport.preparedGeometryState); + CHECK(report.contextReport.preparedRotationDependencies); + CHECK(report.contextReport.preparedBaseState); + CHECK(report.updatedRotation); + CHECK(report.preparedResidual); + CHECK(report.DidAnyWork()); + + CHECK(preparedOperator.GetStellarElementCount() > 0); + CHECK(statistics.staticPreparations == 1); + CHECK(statistics.geometryPreparations == 1); + CHECK(statistics.rotationPreparations == 1); + CHECK(statistics.baseStatePreparations == 1); + CHECK(preparedOperator.GetResidualPreparationCount() == 1); + CHECK(preparedOperator.GetResidualApplicationCount() == 1); + + CHECK(relativeError < 2.0e-12); +} + +TEST_CASE( + "Prepared Hydrostatic Residual Reuses And Selectively Rebuilds Data", + tags::barotrope &tags::hydro &tags::prepared &tags::residuals &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + mean_field::operators::PreparedHydrostaticEquilibriumOperator + preparedOperator(f, *f.domainMapperStateless); + + mfem::Vector enthalpy = prepared_hydrostatic_test_utils::make_enthalpy(f); + + mfem::Vector gravityPotential = + prepared_hydrostatic_test_utils::make_gravity_potential(f); + + mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.42); + + double bernoulliConstant = 0.36; + + const mfem::Vector initialEnthalpy(enthalpy); + const mfem::Vector initialGravityPotential(gravityPotential); + const mfem::Vector initialDisplacement(displacement); + const double initialBernoulliConstant = bernoulliConstant; + + const mean_field::physics::RigidRotation initialRotation = + prepared_hydrostatic_test_utils::make_rotation(0.80); + + const mean_field::physics::RigidRotation changedRotation = + prepared_hydrostatic_test_utils::make_rotation(1.25); + + auto dependencies = prepared_hydrostatic_test_utils::make_dependencies(); + + preparedOperator.Prepare( + prepared_hydrostatic_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, initialRotation + ); + + mfem::Vector initialResidual; + preparedOperator.BuildResidual(initialResidual); + + enthalpy(0) += 0.29; + gravityPotential(0) -= 0.17; + displacement = gravity_prepared_test_utils::make_displacement(f, 0.73); + bernoulliConstant += 0.23; + + const auto unchangedReport = preparedOperator.Prepare( + prepared_hydrostatic_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, changedRotation + ); + + mfem::Vector unchangedResidual; + preparedOperator.BuildResidual(unchangedResidual); + + CHECK_FALSE(unchangedReport.DidAnyWork()); + CHECK_FALSE(unchangedReport.updatedRotation); + CHECK_FALSE(unchangedReport.preparedResidual); + CHECK( + gravity_prepared_test_utils::relative_error( + unchangedResidual, initialResidual, f.mesh->GetComm() + ) == 0.0 + ); + CHECK(preparedOperator.GetResidualPreparationCount() == 1); + + // Only the enthalpy stamp changes. The altered potential, + // displacement, constant, and rotation remain intentionally frozen. + ++dependencies.enthalpy.revision; + + const auto enthalpyReport = preparedOperator.Prepare( + prepared_hydrostatic_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, changedRotation + ); + + mfem::Vector enthalpyResidual; + mfem::Vector enthalpyReference; + + preparedOperator.BuildResidual(enthalpyResidual); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, initialRotation, enthalpy, + initialGravityPotential, initialDisplacement, initialBernoulliConstant, + enthalpyReference + ); + + CHECK_FALSE(enthalpyReport.contextReport.preparedStaticDependencies); + CHECK_FALSE(enthalpyReport.contextReport.preparedGeometryState); + CHECK_FALSE(enthalpyReport.contextReport.preparedRotationDependencies); + CHECK(enthalpyReport.contextReport.preparedBaseState); + CHECK_FALSE(enthalpyReport.updatedRotation); + CHECK(enthalpyReport.preparedResidual); + CHECK( + gravity_prepared_test_utils::relative_error( + enthalpyResidual, enthalpyReference, f.mesh->GetComm() + ) < 2.0e-12 + ); + + ++dependencies.rotation.revision; + + const auto rotationReport = preparedOperator.Prepare( + prepared_hydrostatic_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, changedRotation + ); + + mfem::Vector rotationResidual; + mfem::Vector rotationReference; + + preparedOperator.BuildResidual(rotationResidual); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, changedRotation, enthalpy, + initialGravityPotential, initialDisplacement, initialBernoulliConstant, + rotationReference + ); + + CHECK_FALSE(rotationReport.contextReport.preparedStaticDependencies); + CHECK_FALSE(rotationReport.contextReport.preparedGeometryState); + CHECK(rotationReport.contextReport.preparedRotationDependencies); + CHECK(rotationReport.contextReport.preparedBaseState); + CHECK(rotationReport.updatedRotation); + CHECK(rotationReport.preparedResidual); + CHECK( + gravity_prepared_test_utils::relative_error( + rotationResidual, rotationReference, f.mesh->GetComm() + ) < 2.0e-12 + ); + + ++dependencies.displacement.revision; + + const auto displacementReport = preparedOperator.Prepare( + prepared_hydrostatic_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, changedRotation + ); + + mfem::Vector displacementResidual; + mfem::Vector displacementReference; + + preparedOperator.BuildResidual(displacementResidual); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, changedRotation, enthalpy, + initialGravityPotential, displacement, initialBernoulliConstant, + displacementReference + ); + + CHECK_FALSE(displacementReport.contextReport.preparedStaticDependencies); + CHECK(displacementReport.contextReport.preparedGeometryState); + CHECK(displacementReport.contextReport.preparedRotationDependencies); + CHECK(displacementReport.contextReport.preparedBaseState); + CHECK_FALSE(displacementReport.updatedRotation); + CHECK(displacementReport.preparedResidual); + CHECK( + gravity_prepared_test_utils::relative_error( + displacementResidual, displacementReference, f.mesh->GetComm() + ) < 2.0e-12 + ); + + const auto &statistics = preparedOperator.GetContextPreparationStatistics(); + + CHECK(statistics.staticPreparations == 1); + CHECK(statistics.geometryPreparations == 2); + CHECK(statistics.rotationPreparations == 3); + CHECK(statistics.baseStatePreparations == 4); + CHECK(preparedOperator.GetResidualPreparationCount() == 4); + CHECK(preparedOperator.GetResidualApplicationCount() == 5); + + const double displacementEffect = + gravity_prepared_test_utils::relative_error( + displacementResidual, rotationResidual, f.mesh->GetComm() + ); + + INFO("Residual change after displacement update = " << displacementEffect); + + CHECK(displacementEffect > 1.0e-8); +} diff --git a/tests/operators/prepared_hydrostatic_equilibrium_analytic_accuracy.cpp b/tests/operators/prepared_hydrostatic_equilibrium_analytic_accuracy.cpp new file mode 100644 index 0000000..0e15b5d --- /dev/null +++ b/tests/operators/prepared_hydrostatic_equilibrium_analytic_accuracy.cpp @@ -0,0 +1,484 @@ +#include +#include +#include + +#include +#include + +import mean_field; +import test_helpers; + +namespace prepared_hydrostatic_analytic_solve_test_utils { + constexpr double bernoulliConstant = 0.83; + constexpr double enthalpyAmplitude = 0.61; + + struct AnalyticCase { + const char *name; + + std::array deformationScale; + std::array angularVelocity; + std::array rotationCenter; + }; + + class EnthalpyJacobianOperator final : public mfem::Operator { + public: + EnthalpyJacobianOperator( + const int enthalpySize, + const mean_field::operators::PreparedHydrostaticEquilibriumOperator + &preparedOperator + ) + : mfem::Operator(enthalpySize), + m_preparedOperator(preparedOperator) { + } + + void Mult( + const mfem::Vector &direction, + mfem::Vector &action + ) const override { + m_preparedOperator.ApplyEnthalpyJacobianAction(direction, action); + } + + private: + const mean_field::operators::PreparedHydrostaticEquilibriumOperator + &m_preparedOperator; + }; + + mean_field::operators::context::hydrostatic:: + HydrostaticEquilibriumDependencies + make_dependencies() { + return { + .discretization = {.identity = 701, .revision = 2}, + .enthalpy = {.identity = 709, .revision = 3}, + .gravityPotential = {.identity = 719, .revision = 5}, + .displacement = {.identity = 727, .revision = 7}, + .rotation = {.identity = 733, .revision = 11}, + .bernoulliConstant = {.identity = 739, .revision = 13} + }; + } + + mean_field::operators::context::hydrostatic::HydrostaticEquilibriumStateView + make_state( + const mfem::Vector &enthalpy, + const mfem::Vector &gravityPotential, + const mfem::Vector &displacement + ) { + return { + .enthalpy = enthalpy, + .gravityPotential = gravityPotential, + .displacement = displacement, + .bernoulliConstant = bernoulliConstant + }; + } + + mfem::Vector make_vector( + const std::array< + double, + 3> &values + ) { + mfem::Vector vector(3); + + for (int component = 0; component < 3; ++component) { + vector(component) = values[static_cast(component)]; + } + + return vector; + } + + mean_field::physics::RigidRotation + make_rotation(const AnalyticCase &analyticCase) { + return mean_field::physics::RigidRotation( + make_vector(analyticCase.angularVelocity), + make_vector(analyticCase.rotationCenter) + ); + } + + void map_to_physical( + const mfem::Vector &referencePosition, + const AnalyticCase &analyticCase, + mfem::Vector &physicalPosition + ) { + physicalPosition.SetSize(3); + + for (int component = 0; component < 3; ++component) { + physicalPosition(component) = + analyticCase + .deformationScale[static_cast(component)] * + referencePosition(component); + } + } + + double exact_enthalpy_value(const mfem::Vector &referencePosition) { + double normalizedRadiusSquared = 0.0; + + for (int component = 0; component < 3; ++component) { + const double normalizedCoordinate = + referencePosition(component) / mean_field::utils::RADIUS; + + normalizedRadiusSquared += + normalizedCoordinate * normalizedCoordinate; + } + + return enthalpyAmplitude * std::max(0.0, 1.0 - normalizedRadiusSquared); + } + + double exact_potential_value( + const mfem::Vector &referencePosition, + const AnalyticCase &analyticCase, + const mean_field::physics::RigidRotation &rotation + ) { + mfem::Vector physicalPosition; + + map_to_physical(referencePosition, analyticCase, physicalPosition); + + /* + * Construct Phi so that + * + * h + Phi - Psi_rotation - C = 0 + * + * analytically. + */ + return bernoulliConstant + rotation.potential(physicalPosition) - + exact_enthalpy_value(referencePosition); + } + + mfem::Array + make_stellar_element_marker(const mean_field::fem::FEM &f) { + mfem::Array stellarElementMarker(f.mesh->GetNE()); + + const int vacuumAttribute = + f.domainMapperStateless->GetVacuumElementAttribute(); + + for (int elementId = 0; elementId < f.mesh->GetNE(); ++elementId) { + stellarElementMarker[elementId] = + f.mesh->GetAttribute(elementId) != vacuumAttribute; + } + + return stellarElementMarker; + } +} // namespace prepared_hydrostatic_analytic_solve_test_utils + +TEST_CASE( + "Prepared Hydrostatic Operator Solves Analytic Bernoulli Equilibria", + tags::barotrope &tags::hydro &tags::prepared &tags::integration + &tags::solver &tags::convergence &tags::accuracy + &tags::analytic_comparison +) { + using prepared_hydrostatic_analytic_solve_test_utils::AnalyticCase; + + constexpr double deformationX = 1.08; + constexpr double deformationY = 0.96; + + /* + * The third scale makes the affine deformation + * volume-preserving: + * + * det(F) = sx * sy * sz = 1. + */ + constexpr double deformationZ = 1.0 / (deformationX * deformationY); + + const std::array analyticCases{ + {{.name = "spherical nonrotating equilibrium", + .deformationScale = {1.0, 1.0, 1.0}, + .angularVelocity = {0.0, 0.0, 0.0}, + .rotationCenter = {0.0, 0.0, 0.0}}, + {.name = "spherical rotating equilibrium", + .deformationScale = {1.0, 1.0, 1.0}, + .angularVelocity = {0.13, -0.09, 0.31}, + .rotationCenter = {0.04, -0.03, 0.02}}, + {.name = "volume-preserving deformed rotating equilibrium", + .deformationScale = {deformationX, deformationY, deformationZ}, + .angularVelocity = {0.17, -0.12, 0.43}, + .rotationCenter = {0.031, -0.024, 0.018}}} + }; + + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + const MPI_Comm communicator = f.mesh->GetComm(); + + const mfem::Array stellarElementMarker = + prepared_hydrostatic_analytic_solve_test_utils:: + make_stellar_element_marker(f); + + for (const AnalyticCase &analyticCase : analyticCases) { + DYNAMIC_SECTION(analyticCase.name) { + const double deformationDeterminant = + analyticCase.deformationScale[0] * + analyticCase.deformationScale[1] * + analyticCase.deformationScale[2]; + + REQUIRE(std::abs(deformationDeterminant - 1.0) < 2.0e-14); + + const mean_field::physics::RigidRotation rotation = + prepared_hydrostatic_analytic_solve_test_utils::make_rotation( + analyticCase + ); + + auto displacementFunction = [&analyticCase]( + const mfem::Vector + &referencePosition, + mfem::Vector &displacementValue + ) { + mfem::Vector physicalPosition; + + prepared_hydrostatic_analytic_solve_test_utils::map_to_physical( + referencePosition, analyticCase, physicalPosition + ); + + displacementValue.SetSize(3); + displacementValue = physicalPosition; + displacementValue -= referencePosition; + }; + + auto potentialFunction = [&analyticCase, &rotation]( + const mfem::Vector &referencePosition + ) { + return prepared_hydrostatic_analytic_solve_test_utils:: + exact_potential_value( + referencePosition, analyticCase, rotation + ); + }; + + auto enthalpyFunction = [](const mfem::Vector &referencePosition) { + return prepared_hydrostatic_analytic_solve_test_utils:: + exact_enthalpy_value(referencePosition); + }; + + mfem::VectorFunctionCoefficient displacementCoefficient( + f.mesh->Dimension(), displacementFunction + ); + + mfem::FunctionCoefficient potentialCoefficient(potentialFunction); + + mfem::FunctionCoefficient exactEnthalpyCoefficient( + enthalpyFunction + ); + + /* + * Project the prescribed geometry and potential. + */ + mfem::ParGridFunction displacementField(f.displacementFes.get()); + + mfem::ParGridFunction potentialField(f.gravityPotentialFes.get()); + + displacementField.ProjectCoefficient(displacementCoefficient); + + potentialField.ProjectCoefficient(potentialCoefficient); + + mfem::Vector displacement; + mfem::Vector gravityPotential; + + displacementField.GetTrueDofs(displacement); + potentialField.GetTrueDofs(gravityPotential); + + /* + * This projection is not used as the solution. It gives + * the best directly available representation baseline + * against which the solved field can be compared. + */ + mfem::ParGridFunction projectedEnthalpyField(f.enthalpyFes.get()); + + projectedEnthalpyField.ProjectCoefficient(exactEnthalpyCoefficient); + + mfem::ParGridFunction zeroEnthalpyField(f.enthalpyFes.get()); + + zeroEnthalpyField = 0.0; + + const double exactEnthalpyNorm = zeroEnthalpyField.ComputeL2Error( + exactEnthalpyCoefficient, nullptr, &stellarElementMarker + ); + + const double projectionError = + projectedEnthalpyField.ComputeL2Error( + exactEnthalpyCoefficient, nullptr, &stellarElementMarker + ); + + REQUIRE(exactEnthalpyNorm > 0.0); + + const double relativeProjectionError = + projectionError / exactEnthalpyNorm; + + /* + * Begin deliberately far from equilibrium. + */ + mfem::Vector enthalpy(f.enthalpyFes->GetTrueVSize()); + + enthalpy = 0.0; + + auto dependencies = prepared_hydrostatic_analytic_solve_test_utils:: + make_dependencies(); + + mean_field::operators::PreparedHydrostaticEquilibriumOperator + preparedOperator(f, *f.domainMapperStateless); + + const auto initialReport = preparedOperator.Prepare( + prepared_hydrostatic_analytic_solve_test_utils::make_state( + enthalpy, gravityPotential, displacement + ), + dependencies, rotation + ); + + REQUIRE(initialReport.preparedResidual); + REQUIRE(initialReport.preparedAlgebraicJacobianBlocks); + + mfem::Vector initialResidual; + + preparedOperator.BuildResidual(initialResidual); + + const double initialResidualNorm = + gravity_prepared_test_utils::global_norm( + initialResidual, communicator + ); + + REQUIRE(initialResidualNorm > 1.0e-12); + + /* + * One discrete Newton step: + * + * M_h delta_h = -R_h. + * + * The full four-block Bernoulli Jacobian is rectangular + * and underdetermined in isolation. Freezing Phi, C, + * rotation, and displacement makes this a well-defined + * enthalpy solve. + */ + prepared_hydrostatic_analytic_solve_test_utils:: + EnthalpyJacobianOperator enthalpyJacobian( + f.enthalpyFes->GetTrueVSize(), preparedOperator + ); + + mfem::Vector rightHandSide(initialResidual); + rightHandSide *= -1.0; + + mfem::Vector enthalpyCorrection(f.enthalpyFes->GetTrueVSize()); + + enthalpyCorrection = 0.0; + + /* + * The operator is positive definite on stellar-supported + * enthalpy DOFs and semidefinite on exterior-only DOFs. + * The RHS is in its range, so MINRES is appropriate for + * the compatible system. + */ + mfem::MINRESSolver linearSolver(communicator); + + linearSolver.SetOperator(enthalpyJacobian); + + linearSolver.SetRelTol(1.0e-13); + linearSolver.SetAbsTol(1.0e-14); + linearSolver.SetMaxIter(2000); + linearSolver.SetPrintLevel(0); + + linearSolver.Mult(rightHandSide, enthalpyCorrection); + + INFO("Linear solver converged = " << linearSolver.GetConverged()); + + INFO( + "Linear solver iterations = " << linearSolver.GetNumIterations() + ); + + INFO("Linear solver final norm = " << linearSolver.GetFinalNorm()); + + REQUIRE(linearSolver.GetConverged()); + + enthalpy += enthalpyCorrection; + + /* + * Only the enthalpy state changed. Geometry, rotation, + * and algebraic Jacobian data must remain reusable. + */ + ++dependencies.enthalpy.revision; + + const auto solvedReport = preparedOperator.Prepare( + prepared_hydrostatic_analytic_solve_test_utils::make_state( + enthalpy, gravityPotential, displacement + ), + dependencies, rotation + ); + + CHECK(solvedReport.contextReport.updatedEnthalpy); + + CHECK(solvedReport.contextReport.preparedBaseState); + + CHECK_FALSE(solvedReport.contextReport.preparedGeometryState); + + CHECK_FALSE(solvedReport.preparedAlgebraicJacobianBlocks); + + mfem::Vector solvedResidual; + + preparedOperator.BuildResidual(solvedResidual); + + const double solvedResidualNorm = + gravity_prepared_test_utils::global_norm( + solvedResidual, communicator + ); + + const double residualReduction = + solvedResidualNorm / initialResidualNorm; + + /* + * Compare the solved field with the continuum analytic + * enthalpy over stellar elements only. + * + * All three mappings have determinant one, so this + * normalized L2 error is also unchanged by the physical + * volume transformation. + */ + mfem::ParGridFunction solvedEnthalpyField(f.enthalpyFes.get()); + + solvedEnthalpyField.SetFromTrueDofs(enthalpy); + + const double solvedAnalyticError = + solvedEnthalpyField.ComputeL2Error( + exactEnthalpyCoefficient, nullptr, &stellarElementMarker + ); + + const double relativeSolvedAnalyticError = + solvedAnalyticError / exactEnthalpyNorm; + + INFO("Deformation determinant = " << deformationDeterminant); + + INFO("Initial weak residual norm = " << initialResidualNorm); + + INFO("Solved weak residual norm = " << solvedResidualNorm); + + INFO("Weak residual reduction = " << residualReduction); + + INFO( + "Relative analytic projection floor = " + << relativeProjectionError + ); + + INFO( + "Relative solved analytic L2 error = " + << relativeSolvedAnalyticError + ); + + /* + * The discrete Bernoulli equation must be solved essentially + * to the linear-solver floor. + */ + CHECK(residualReduction < 1.0e-10); + + /* + * The directly projected analytic enthalpy provides a lower + * representation bound, but it is not the expected solution + * of the cross-space discrete Bernoulli equation. The latter + * also contains potential-projection and mapped-space + * compatibility errors. + */ + CHECK( + relativeSolvedAnalyticError < + std::max(5.0 * relativeProjectionError, 1.25e-4) + ); + + /* + * Record that the analytic error remains within one order of + * magnitude of the direct enthalpy projection floor. + */ + CHECK(relativeSolvedAnalyticError / relativeProjectionError < 5.0); + } + } +} \ No newline at end of file diff --git a/tests/operators/prepared_hydrostatic_equilibrium_complete_jacobian.cpp b/tests/operators/prepared_hydrostatic_equilibrium_complete_jacobian.cpp new file mode 100644 index 0000000..b9d0d2d --- /dev/null +++ b/tests/operators/prepared_hydrostatic_equilibrium_complete_jacobian.cpp @@ -0,0 +1,436 @@ +#include +#include + +import mean_field; +import test_helpers; + +namespace prepared_hydrostatic_complete_test_utils { + mean_field::operators::context::hydrostatic:: + HydrostaticEquilibriumDependencies + make_dependencies() { + return { + .discretization = {.identity = 503, .revision = 2}, + .enthalpy = {.identity = 509, .revision = 3}, + .gravityPotential = {.identity = 521, .revision = 5}, + .displacement = {.identity = 523, .revision = 7}, + .rotation = {.identity = 541, .revision = 11}, + .bernoulliConstant = {.identity = 547, .revision = 13} + }; + } + + mean_field::operators::context::hydrostatic::HydrostaticEquilibriumStateView + make_state( + const mfem::Vector &enthalpy, + const mfem::Vector &gravityPotential, + const mfem::Vector &displacement, + const double bernoulliConstant + ) { + return { + .enthalpy = enthalpy, + .gravityPotential = gravityPotential, + .displacement = displacement, + .bernoulliConstant = bernoulliConstant + }; + } + + mean_field::physics::RigidRotation make_rotation() { + mfem::Vector angularVelocity(3); + + angularVelocity(0) = 0.18; + angularVelocity(1) = -0.13; + angularVelocity(2) = 0.49; + + mfem::Vector center(3); + + center(0) = 0.031; + center(1) = -0.024; + center(2) = 0.017; + + return mean_field::physics::RigidRotation(angularVelocity, center); + } + + mfem::Vector make_displacement_direction( + const mean_field::fem::FEM &f, + const double firstPhase, + const double secondPhase + ) { + mfem::Vector direction = + gravity_prepared_test_utils::make_displacement(f, firstPhase); + + const mfem::Vector secondField = + gravity_prepared_test_utils::make_displacement(f, secondPhase); + + direction -= secondField; + return direction; + } + + void centered_complete_difference( + const mean_field::fem::FEM &f, + const mean_field::physics::RigidRotation &rotation, + const mfem::Vector &baseEnthalpy, + const mfem::Vector &baseGravityPotential, + const mfem::Vector &baseDisplacement, + const double baseBernoulliConstant, + const mfem::Vector &enthalpyVariation, + const mfem::Vector &gravityPotentialVariation, + const mfem::Vector &displacementVariation, + const double bernoulliConstantVariation, + const double step, + mfem::Vector &difference + ) { + mfem::Vector enthalpyPlus(baseEnthalpy); + mfem::Vector enthalpyMinus(baseEnthalpy); + mfem::Vector gravityPotentialPlus(baseGravityPotential); + mfem::Vector gravityPotentialMinus(baseGravityPotential); + mfem::Vector displacementPlus(baseDisplacement); + mfem::Vector displacementMinus(baseDisplacement); + + enthalpyPlus.Add(step, enthalpyVariation); + enthalpyMinus.Add(-step, enthalpyVariation); + + gravityPotentialPlus.Add(step, gravityPotentialVariation); + + gravityPotentialMinus.Add(-step, gravityPotentialVariation); + + displacementPlus.Add(step, displacementVariation); + displacementMinus.Add(-step, displacementVariation); + + const double bernoulliConstantPlus = + baseBernoulliConstant + step * bernoulliConstantVariation; + + const double bernoulliConstantMinus = + baseBernoulliConstant - step * bernoulliConstantVariation; + + mfem::Vector residualPlus; + mfem::Vector residualMinus; + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, enthalpyPlus, + gravityPotentialPlus, displacementPlus, bernoulliConstantPlus, + residualPlus + ); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, enthalpyMinus, + gravityPotentialMinus, displacementMinus, bernoulliConstantMinus, + residualMinus + ); + + difference = residualPlus; + difference -= residualMinus; + difference /= 2.0 * step; + } + + void set_block( + mfem::Vector &packedDirection, + const mean_field::operators::HydrostaticJacobianBlockLayout &layout, + const mean_field::operators::HydrostaticJacobianInputBlock block, + const mfem::Vector &values + ) { + REQUIRE(layout.Size(block) == values.Size()); + + const int offset = layout.Offset(block); + + for (int entry = 0; entry < values.Size(); ++entry) { + packedDirection(offset + entry) = values(entry); + } + } +} // namespace prepared_hydrostatic_complete_test_utils + +TEST_CASE( + "Prepared Hydrostatic Complete Jacobian Matches Sum And Centered " + "Differences", + tags::barotrope &tags::hydro &tags::integration &tags::jacobian + &tags::prepared &tags::self_consistency +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + mean_field::operators::PreparedHydrostaticEquilibriumOperator + preparedOperator(f, *f.domainMapperStateless); + + const mfem::Vector enthalpy = + gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), 0.34 + ); + + const mfem::Vector gravityPotential = + gravity_prepared_test_utils::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), 0.57 + ); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.68); + + constexpr double bernoulliConstant = 0.43; + + const mean_field::physics::RigidRotation rotation = + prepared_hydrostatic_complete_test_utils::make_rotation(); + + preparedOperator.Prepare( + prepared_hydrostatic_complete_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + prepared_hydrostatic_complete_test_utils::make_dependencies(), rotation + ); + + const mfem::Vector enthalpyVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), 1.07 + ); + + const mfem::Vector gravityPotentialVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), 1.31 + ); + + const mfem::Vector displacementVariation = + prepared_hydrostatic_complete_test_utils::make_displacement_direction( + f, 1.19, 0.38 + ); + + constexpr double bernoulliConstantVariation = -0.37; + + mfem::Vector enthalpyAction; + mfem::Vector gravityPotentialAction; + mfem::Vector bernoulliConstantAction; + mfem::Vector displacementAction; + mfem::Vector completeAction; + + preparedOperator.ApplyEnthalpyJacobianAction( + enthalpyVariation, enthalpyAction + ); + + preparedOperator.ApplyGravityPotentialJacobianAction( + gravityPotentialVariation, gravityPotentialAction + ); + + preparedOperator.ApplyBernoulliConstantJacobianAction( + bernoulliConstantVariation, bernoulliConstantAction + ); + + preparedOperator.ApplyDisplacementJacobianAction( + displacementVariation, displacementAction + ); + + preparedOperator.ApplyCompleteJacobianAction( + enthalpyVariation, gravityPotentialVariation, + bernoulliConstantVariation, displacementVariation, completeAction + ); + + mfem::Vector summedAction(enthalpyAction); + summedAction += gravityPotentialAction; + summedAction += bernoulliConstantAction; + summedAction += displacementAction; + + constexpr double finiteDifferenceStep = 1.0e-5; + + mfem::Vector centeredDifference; + + prepared_hydrostatic_complete_test_utils::centered_complete_difference( + f, rotation, enthalpy, gravityPotential, displacement, + bernoulliConstant, enthalpyVariation, gravityPotentialVariation, + displacementVariation, bernoulliConstantVariation, finiteDifferenceStep, + centeredDifference + ); + + const double summationError = gravity_prepared_test_utils::relative_error( + completeAction, summedAction, f.mesh->GetComm() + ); + + const double centeredDifferenceError = + gravity_prepared_test_utils::relative_error( + completeAction, centeredDifference, f.mesh->GetComm() + ); + + INFO("Complete-action summation error = " << summationError); + + INFO( + "Complete-action centered-difference error = " + << centeredDifferenceError + ); + + CHECK(preparedOperator.GetCompleteJacobianStatistics().applications == 1); + + CHECK(summationError < 5.0e-12); + CHECK(centeredDifferenceError < 2.0e-7); +} + +TEST_CASE( + "Prepared Hydrostatic MFEM Adapter Uses Four Block Layout And Reuses " + "Preparation", + tags::barotrope &tags::hydro &tags::integration &tags::jacobian + &tags::mfem_operators &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + mean_field::operators::PreparedHydrostaticEquilibriumOperator + preparedOperator(f, *f.domainMapperStateless); + + const mfem::Vector enthalpy = + gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), 0.41 + ); + + const mfem::Vector gravityPotential = + gravity_prepared_test_utils::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), 0.63 + ); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.74); + + constexpr double bernoulliConstant = 0.38; + + preparedOperator.Prepare( + prepared_hydrostatic_complete_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + prepared_hydrostatic_complete_test_utils::make_dependencies(), + prepared_hydrostatic_complete_test_utils::make_rotation() + ); + + mean_field::operators::PreparedHydrostaticEquilibriumJacobianOperator + adapter(f, preparedOperator); + + const auto &layout = adapter.GetLayout(); + + CHECK( + layout.Offset( + mean_field::operators::HydrostaticJacobianInputBlock::enthalpy + ) == 0 + ); + + CHECK( + layout.Offset( + mean_field::operators::HydrostaticJacobianInputBlock:: + gravityPotential + ) == f.enthalpyFes->GetTrueVSize() + ); + + CHECK( + layout.Size( + mean_field::operators::HydrostaticJacobianInputBlock:: + bernoulliConstant + ) == 1 + ); + + CHECK(adapter.Width() == layout.GetTotalSize()); + CHECK(adapter.Height() == layout.GetResidualSize()); + CHECK(adapter.Height() == f.enthalpyFes->GetTrueVSize()); + + const mfem::Vector enthalpyVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), 1.12 + ); + + const mfem::Vector gravityPotentialVariation = + gravity_prepared_test_utils::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), 1.39 + ); + + const mfem::Vector displacementVariation = + prepared_hydrostatic_complete_test_utils::make_displacement_direction( + f, 1.28, 0.49 + ); + + constexpr double bernoulliConstantVariation = 0.29; + + mfem::Vector packedDirection(adapter.Width()); + packedDirection = 0.0; + + prepared_hydrostatic_complete_test_utils::set_block( + packedDirection, layout, + mean_field::operators::HydrostaticJacobianInputBlock::enthalpy, + enthalpyVariation + ); + + prepared_hydrostatic_complete_test_utils::set_block( + packedDirection, layout, + mean_field::operators::HydrostaticJacobianInputBlock::gravityPotential, + gravityPotentialVariation + ); + + prepared_hydrostatic_complete_test_utils::set_block( + packedDirection, layout, + mean_field::operators::HydrostaticJacobianInputBlock::displacement, + displacementVariation + ); + + packedDirection(layout.Offset( + mean_field::operators::HydrostaticJacobianInputBlock::bernoulliConstant + )) = bernoulliConstantVariation; + + mfem::Vector directAction; + mfem::Vector adapterAction; + + preparedOperator.ApplyCompleteJacobianAction( + enthalpyVariation, gravityPotentialVariation, + bernoulliConstantVariation, displacementVariation, directAction + ); + + adapter.Mult(packedDirection, adapterAction); + + const double adapterError = gravity_prepared_test_utils::relative_error( + adapterAction, directAction, f.mesh->GetComm() + ); + + const auto contextStatisticsBefore = + preparedOperator.GetContextPreparationStatistics(); + + const auto algebraicStatisticsBefore = + preparedOperator.GetAlgebraicJacobianStatistics(); + + const auto displacementStatisticsBefore = + preparedOperator.GetDisplacementJacobianStatistics(); + + mfem::Vector secondPackedDirection(packedDirection); + secondPackedDirection *= -0.61; + + mfem::Vector secondAdapterAction; + adapter.Mult(secondPackedDirection, secondAdapterAction); + + mfem::Vector expectedSecondAction(adapterAction); + expectedSecondAction *= -0.61; + + const double adapterLinearityError = + gravity_prepared_test_utils::relative_error( + secondAdapterAction, expectedSecondAction, f.mesh->GetComm() + ); + + const auto &contextStatisticsAfter = + preparedOperator.GetContextPreparationStatistics(); + + const auto &algebraicStatisticsAfter = + preparedOperator.GetAlgebraicJacobianStatistics(); + + const auto &displacementStatisticsAfter = + preparedOperator.GetDisplacementJacobianStatistics(); + + INFO("MFEM adapter/direct-action error = " << adapterError); + + INFO("MFEM adapter linearity error = " << adapterLinearityError); + + CHECK(adapterError < 5.0e-12); + CHECK(adapterLinearityError < 5.0e-12); + CHECK(secondAdapterAction.Size() == adapter.Height()); + + CHECK(contextStatisticsAfter == contextStatisticsBefore); + + CHECK( + algebraicStatisticsAfter.preparations == + algebraicStatisticsBefore.preparations + ); + + CHECK( + displacementStatisticsAfter.preparations == + displacementStatisticsBefore.preparations + ); + + CHECK(preparedOperator.GetCompleteJacobianStatistics().applications == 3); +} diff --git a/tests/operators/prepared_hydrostatic_equilibrium_displacement_jacobian.cpp b/tests/operators/prepared_hydrostatic_equilibrium_displacement_jacobian.cpp new file mode 100644 index 0000000..7d74c1d --- /dev/null +++ b/tests/operators/prepared_hydrostatic_equilibrium_displacement_jacobian.cpp @@ -0,0 +1,423 @@ +#include +#include + +import mean_field; +import test_helpers; + +namespace prepared_hydrostatic_displacement_test_utils { + mean_field::operators::context::hydrostatic:: + HydrostaticEquilibriumDependencies + make_dependencies() { + return { + .discretization = {.identity = 401, .revision = 2}, + .enthalpy = {.identity = 409, .revision = 3}, + .gravityPotential = {.identity = 419, .revision = 5}, + .displacement = {.identity = 421, .revision = 7}, + .rotation = {.identity = 431, .revision = 11}, + .bernoulliConstant = {.identity = 433, .revision = 13} + }; + } + + mean_field::operators::context::hydrostatic::HydrostaticEquilibriumStateView + make_state( + const mfem::Vector &enthalpy, + const mfem::Vector &gravityPotential, + const mfem::Vector &displacement, + const double bernoulliConstant + ) { + return { + .enthalpy = enthalpy, + .gravityPotential = gravityPotential, + .displacement = displacement, + .bernoulliConstant = bernoulliConstant + }; + } + + mfem::Vector make_enthalpy( + const mean_field::fem::FEM &f, + const double phase = 0.29 + ) { + return gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), phase + ); + } + + mfem::Vector make_gravity_potential( + const mean_field::fem::FEM &f, + const double phase = 0.47 + ) { + return gravity_prepared_test_utils::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), phase + ); + } + + mfem::Vector make_displacement_direction( + const mean_field::fem::FEM &f, + const double firstPhase, + const double secondPhase + ) { + mfem::Vector direction = + gravity_prepared_test_utils::make_displacement(f, firstPhase); + + const mfem::Vector secondField = + gravity_prepared_test_utils::make_displacement(f, secondPhase); + + direction -= secondField; + return direction; + } + + mean_field::physics::RigidRotation make_rotation(const double scale = 1.0) { + mfem::Vector angularVelocity(3); + + angularVelocity(0) = 0.16 * scale; + angularVelocity(1) = -0.14 * scale; + angularVelocity(2) = 0.46 * scale; + + mfem::Vector center(3); + + center(0) = 0.034; + center(1) = -0.026; + center(2) = 0.019; + + return mean_field::physics::RigidRotation(angularVelocity, center); + } + + void centered_displacement_difference( + const mean_field::fem::FEM &f, + const mean_field::physics::RigidRotation &rotation, + const mfem::Vector &enthalpy, + const mfem::Vector &gravityPotential, + const mfem::Vector &baseDisplacement, + const mfem::Vector &displacementVariation, + const double bernoulliConstant, + const double step, + mfem::Vector &difference + ) { + mfem::Vector displacementPlus(baseDisplacement); + mfem::Vector displacementMinus(baseDisplacement); + + displacementPlus.Add(step, displacementVariation); + displacementMinus.Add(-step, displacementVariation); + + mfem::Vector residualPlus; + mfem::Vector residualMinus; + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, enthalpy, gravityPotential, + displacementPlus, bernoulliConstant, residualPlus + ); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, enthalpy, gravityPotential, + displacementMinus, bernoulliConstant, residualMinus + ); + + difference = residualPlus; + difference -= residualMinus; + difference /= 2.0 * step; + } + + double relative_error( + const mfem::Vector &actual, + const mfem::Vector &expected, + const MPI_Comm communicator + ) { + return gravity_prepared_test_utils::relative_error( + actual, expected, communicator + ); + } +} // namespace prepared_hydrostatic_displacement_test_utils + +TEST_CASE( + "Prepared Hydrostatic Displacement Jacobian Matches Centered Differences", + tags::barotrope &tags::hydro &tags::jacobian &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + mean_field::operators::PreparedHydrostaticEquilibriumOperator + preparedOperator(f, *f.domainMapperStateless); + + const mfem::Vector enthalpy = + prepared_hydrostatic_displacement_test_utils::make_enthalpy(f); + + const mfem::Vector gravityPotential = + prepared_hydrostatic_displacement_test_utils::make_gravity_potential(f); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.73); + + constexpr double bernoulliConstant = 0.39; + + const mean_field::physics::RigidRotation rotation = + prepared_hydrostatic_displacement_test_utils::make_rotation(0.9); + + const auto dependencies = + prepared_hydrostatic_displacement_test_utils::make_dependencies(); + + const auto report = preparedOperator.Prepare( + prepared_hydrostatic_displacement_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, rotation + ); + + const mfem::Vector firstVariation = + prepared_hydrostatic_displacement_test_utils:: + make_displacement_direction(f, 1.17, 0.31); + + const mfem::Vector secondVariation = + prepared_hydrostatic_displacement_test_utils:: + make_displacement_direction(f, 1.43, 0.58); + + mfem::Vector combinedVariation(firstVariation); + combinedVariation += secondVariation; + + mfem::Vector firstAction; + mfem::Vector secondAction; + mfem::Vector combinedAction; + + preparedOperator.ApplyDisplacementJacobianAction( + firstVariation, firstAction + ); + + preparedOperator.ApplyDisplacementJacobianAction( + secondVariation, secondAction + ); + + preparedOperator.ApplyDisplacementJacobianAction( + combinedVariation, combinedAction + ); + + constexpr double finiteDifferenceStep = 1.0e-5; + + mfem::Vector centeredDifference; + + prepared_hydrostatic_displacement_test_utils:: + centered_displacement_difference( + f, rotation, enthalpy, gravityPotential, displacement, + firstVariation, bernoulliConstant, finiteDifferenceStep, + centeredDifference + ); + + mfem::Vector sumOfActions(firstAction); + sumOfActions += secondAction; + + const double centeredDifferenceError = + prepared_hydrostatic_displacement_test_utils::relative_error( + firstAction, centeredDifference, f.mesh->GetComm() + ); + + const double linearityError = + prepared_hydrostatic_displacement_test_utils::relative_error( + combinedAction, sumOfActions, f.mesh->GetComm() + ); + + INFO( + "Prepared displacement centered-difference error = " + << centeredDifferenceError + ); + + INFO("Prepared displacement linearity error = " << linearityError); + + const auto &statistics = + preparedOperator.GetDisplacementJacobianStatistics(); + + CHECK(report.preparedDisplacementJacobianData); + CHECK(statistics.preparations == 1); + CHECK(statistics.applications == 3); + CHECK(centeredDifferenceError < 2.0e-7); + CHECK(linearityError < 5.0e-12); +} + +TEST_CASE( + "Prepared Hydrostatic Displacement Jacobian Reuses And Refreshes Frozen " + "Data", + tags::barotrope &tags::hydro &tags::jacobian &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + mean_field::operators::PreparedHydrostaticEquilibriumOperator + preparedOperator(f, *f.domainMapperStateless); + + const mfem::Vector enthalpy = + prepared_hydrostatic_displacement_test_utils::make_enthalpy(f, 0.37); + + const mfem::Vector gravityPotential = + prepared_hydrostatic_displacement_test_utils::make_gravity_potential( + f, 0.53 + ); + + mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.42); + + constexpr double bernoulliConstant = 0.36; + + mean_field::physics::RigidRotation rotation = + prepared_hydrostatic_displacement_test_utils::make_rotation(0.75); + + auto dependencies = + prepared_hydrostatic_displacement_test_utils::make_dependencies(); + + preparedOperator.Prepare( + prepared_hydrostatic_displacement_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, rotation + ); + + const mfem::Vector displacementVariation = + prepared_hydrostatic_displacement_test_utils:: + make_displacement_direction(f, 1.09, 0.27); + + const mfem::Vector secondVariation = + prepared_hydrostatic_displacement_test_utils:: + make_displacement_direction(f, 1.36, 0.64); + + mfem::Vector initialAction; + mfem::Vector secondDirectionAction; + + preparedOperator.ApplyDisplacementJacobianAction( + displacementVariation, initialAction + ); + + preparedOperator.ApplyDisplacementJacobianAction( + secondVariation, secondDirectionAction + ); + + CHECK( + preparedOperator.GetDisplacementJacobianStatistics().preparations == 1 + ); + + rotation = + prepared_hydrostatic_displacement_test_utils::make_rotation(1.45); + + ++dependencies.rotation.revision; + + const auto rotationReport = preparedOperator.Prepare( + prepared_hydrostatic_displacement_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, rotation + ); + + mfem::Vector rotationUpdatedAction; + + preparedOperator.ApplyDisplacementJacobianAction( + displacementVariation, rotationUpdatedAction + ); + + constexpr double finiteDifferenceStep = 1.0e-5; + + mfem::Vector rotationReference; + + prepared_hydrostatic_displacement_test_utils:: + centered_displacement_difference( + f, rotation, enthalpy, gravityPotential, displacement, + displacementVariation, bernoulliConstant, finiteDifferenceStep, + rotationReference + ); + + const double rotationReferenceError = + prepared_hydrostatic_displacement_test_utils::relative_error( + rotationUpdatedAction, rotationReference, f.mesh->GetComm() + ); + + const double rotationEffect = + prepared_hydrostatic_displacement_test_utils::relative_error( + rotationUpdatedAction, initialAction, f.mesh->GetComm() + ); + + CHECK_FALSE(rotationReport.contextReport.preparedGeometryState); + CHECK(rotationReport.contextReport.preparedRotationDependencies); + CHECK(rotationReport.contextReport.preparedBaseState); + CHECK(rotationReport.updatedRotation); + CHECK(rotationReport.preparedDisplacementJacobianData); + CHECK_FALSE(rotationReport.preparedAlgebraicJacobianBlocks); + CHECK(rotationReferenceError < 2.0e-7); + CHECK(rotationEffect > 1.0e-8); + + displacement = gravity_prepared_test_utils::make_displacement(f, 0.91); + + ++dependencies.displacement.revision; + + const auto geometryReport = preparedOperator.Prepare( + prepared_hydrostatic_displacement_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, rotation + ); + + mfem::Vector geometryUpdatedAction; + + preparedOperator.ApplyDisplacementJacobianAction( + displacementVariation, geometryUpdatedAction + ); + + mfem::Vector geometryReference; + + prepared_hydrostatic_displacement_test_utils:: + centered_displacement_difference( + f, rotation, enthalpy, gravityPotential, displacement, + displacementVariation, bernoulliConstant, finiteDifferenceStep, + geometryReference + ); + + const double geometryReferenceError = + prepared_hydrostatic_displacement_test_utils::relative_error( + geometryUpdatedAction, geometryReference, f.mesh->GetComm() + ); + + const double geometryEffect = + prepared_hydrostatic_displacement_test_utils::relative_error( + geometryUpdatedAction, rotationUpdatedAction, f.mesh->GetComm() + ); + + INFO( + "Rotation-updated displacement Jacobian error = " + << rotationReferenceError + ); + + INFO( + "Displacement Jacobian change after rotation update = " + << rotationEffect + ); + + INFO( + "Geometry-updated displacement Jacobian error = " + << geometryReferenceError + ); + + INFO( + "Displacement Jacobian change after geometry update = " + << geometryEffect + ); + + const auto &contextStatistics = + preparedOperator.GetContextPreparationStatistics(); + + const auto &displacementStatistics = + preparedOperator.GetDisplacementJacobianStatistics(); + + CHECK(geometryReport.contextReport.preparedGeometryState); + CHECK(geometryReport.contextReport.preparedRotationDependencies); + CHECK(geometryReport.contextReport.preparedBaseState); + CHECK_FALSE(geometryReport.updatedRotation); + CHECK(geometryReport.preparedAlgebraicJacobianBlocks); + CHECK(geometryReport.preparedDisplacementJacobianData); + + CHECK(contextStatistics.staticPreparations == 1); + CHECK(contextStatistics.geometryPreparations == 2); + CHECK(contextStatistics.rotationPreparations == 3); + CHECK(contextStatistics.baseStatePreparations == 3); + + CHECK(displacementStatistics.preparations == 3); + CHECK(displacementStatistics.applications == 4); + CHECK(geometryReferenceError < 2.0e-7); + CHECK(geometryEffect > 1.0e-8); +} diff --git a/tests/operators/prepared_hydrostatic_equilibrium_jacobian.cpp b/tests/operators/prepared_hydrostatic_equilibrium_jacobian.cpp new file mode 100644 index 0000000..8d89388 --- /dev/null +++ b/tests/operators/prepared_hydrostatic_equilibrium_jacobian.cpp @@ -0,0 +1,472 @@ +#include +#include + +import mean_field; +import test_helpers; + +namespace prepared_hydrostatic_jacobian_test_utils { + mean_field::operators::context::hydrostatic:: + HydrostaticEquilibriumDependencies + make_dependencies() { + return { + .discretization = {.identity = 307, .revision = 2}, + .enthalpy = {.identity = 311, .revision = 3}, + .gravityPotential = {.identity = 313, .revision = 5}, + .displacement = {.identity = 317, .revision = 7}, + .rotation = {.identity = 331, .revision = 11}, + .bernoulliConstant = {.identity = 337, .revision = 13} + }; + } + + mean_field::operators::context::hydrostatic::HydrostaticEquilibriumStateView + make_state( + const mfem::Vector &enthalpy, + const mfem::Vector &gravityPotential, + const mfem::Vector &displacement, + const double bernoulliConstant + ) { + return { + .enthalpy = enthalpy, + .gravityPotential = gravityPotential, + .displacement = displacement, + .bernoulliConstant = bernoulliConstant + }; + } + + mfem::Vector make_enthalpy( + const mean_field::fem::FEM &f, + const double phase = 0.23 + ) { + return gravity_prepared_test_utils::make_deterministic_vector( + f.enthalpyFes->GetTrueVSize(), phase + ); + } + + mfem::Vector make_gravity_potential( + const mean_field::fem::FEM &f, + const double phase = 0.41 + ) { + return gravity_prepared_test_utils::make_deterministic_vector( + f.gravityPotentialFes->GetTrueVSize(), phase + ); + } + + mean_field::physics::RigidRotation make_rotation(const double scale = 1.0) { + mfem::Vector angularVelocity(3); + + angularVelocity(0) = 0.13 * scale; + angularVelocity(1) = -0.19 * scale; + angularVelocity(2) = 0.47 * scale; + + mfem::Vector center(3); + + center(0) = 0.031; + center(1) = -0.023; + center(2) = 0.017; + + return mean_field::physics::RigidRotation(angularVelocity, center); + } + + void centered_residual_difference( + const mean_field::fem::FEM &f, + const mean_field::physics::RigidRotation &rotation, + const mfem::Vector &enthalpyPlus, + const mfem::Vector &enthalpyMinus, + const mfem::Vector &gravityPotentialPlus, + const mfem::Vector &gravityPotentialMinus, + const mfem::Vector &displacement, + const double bernoulliConstantPlus, + const double bernoulliConstantMinus, + mfem::Vector &difference + ) { + mfem::Vector residualPlus; + mfem::Vector residualMinus; + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, enthalpyPlus, + gravityPotentialPlus, displacement, bernoulliConstantPlus, + residualPlus + ); + + mean_field::operators::kernels::apply_hydrostatic_equilibrium( + f, *f.domainMapperStateless, rotation, enthalpyMinus, + gravityPotentialMinus, displacement, bernoulliConstantMinus, + residualMinus + ); + + // The two states are separated by one complete variation: + // x_+ = x + 0.5 dx and x_- = x - 0.5 dx. + difference = residualPlus; + difference -= residualMinus; + } + + double relative_error( + const mfem::Vector &actual, + const mfem::Vector &expected, + MPI_Comm communicator + ) { + return gravity_prepared_test_utils::relative_error( + actual, expected, communicator + ); + } +} // namespace prepared_hydrostatic_jacobian_test_utils + +TEST_CASE( + "Prepared Hydrostatic Algebraic Jacobian Matches Centered Residual " + "Differences", + tags::barotrope &tags::hydro &tags::jacobian &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + mean_field::operators::PreparedHydrostaticEquilibriumOperator + preparedOperator(f, *f.domainMapperStateless); + + const mfem::Vector enthalpy = + prepared_hydrostatic_jacobian_test_utils::make_enthalpy(f); + + const mfem::Vector gravityPotential = + prepared_hydrostatic_jacobian_test_utils::make_gravity_potential(f); + + const mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.73); + + constexpr double bernoulliConstant = 0.39; + + const mean_field::physics::RigidRotation rotation = + prepared_hydrostatic_jacobian_test_utils::make_rotation(); + + const auto report = preparedOperator.Prepare( + prepared_hydrostatic_jacobian_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + prepared_hydrostatic_jacobian_test_utils::make_dependencies(), rotation + ); + + const mfem::Vector enthalpyVariation = + prepared_hydrostatic_jacobian_test_utils::make_enthalpy(f, 0.71); + + const mfem::Vector gravityPotentialVariation = + prepared_hydrostatic_jacobian_test_utils::make_gravity_potential( + f, 0.83 + ); + + constexpr double bernoulliConstantVariation = -0.31; + + mfem::Vector enthalpyAction; + mfem::Vector gravityPotentialAction; + mfem::Vector bernoulliConstantAction; + mfem::Vector combinedAction; + + preparedOperator.ApplyEnthalpyJacobianAction( + enthalpyVariation, enthalpyAction + ); + + preparedOperator.ApplyGravityPotentialJacobianAction( + gravityPotentialVariation, gravityPotentialAction + ); + + preparedOperator.ApplyBernoulliConstantJacobianAction( + bernoulliConstantVariation, bernoulliConstantAction + ); + + preparedOperator.ApplyAlgebraicJacobianAction( + enthalpyVariation, gravityPotentialVariation, + bernoulliConstantVariation, combinedAction + ); + + mfem::Vector enthalpyPlus(enthalpy); + mfem::Vector enthalpyMinus(enthalpy); + mfem::Vector gravityPotentialPlus(gravityPotential); + mfem::Vector gravityPotentialMinus(gravityPotential); + + enthalpyPlus.Add(0.5, enthalpyVariation); + enthalpyMinus.Add(-0.5, enthalpyVariation); + + mfem::Vector enthalpyReference; + + prepared_hydrostatic_jacobian_test_utils::centered_residual_difference( + f, rotation, enthalpyPlus, enthalpyMinus, gravityPotential, + gravityPotential, displacement, bernoulliConstant, bernoulliConstant, + enthalpyReference + ); + + enthalpyPlus = enthalpy; + enthalpyMinus = enthalpy; + + gravityPotentialPlus.Add(0.5, gravityPotentialVariation); + + gravityPotentialMinus.Add(-0.5, gravityPotentialVariation); + + mfem::Vector gravityPotentialReference; + + prepared_hydrostatic_jacobian_test_utils::centered_residual_difference( + f, rotation, enthalpy, enthalpy, gravityPotentialPlus, + gravityPotentialMinus, displacement, bernoulliConstant, + bernoulliConstant, gravityPotentialReference + ); + + gravityPotentialPlus = gravityPotential; + gravityPotentialMinus = gravityPotential; + + mfem::Vector bernoulliConstantReference; + + prepared_hydrostatic_jacobian_test_utils::centered_residual_difference( + f, rotation, enthalpy, enthalpy, gravityPotential, gravityPotential, + displacement, bernoulliConstant + 0.5 * bernoulliConstantVariation, + bernoulliConstant - 0.5 * bernoulliConstantVariation, + bernoulliConstantReference + ); + + enthalpyPlus.Add(0.5, enthalpyVariation); + enthalpyMinus.Add(-0.5, enthalpyVariation); + + gravityPotentialPlus.Add(0.5, gravityPotentialVariation); + + gravityPotentialMinus.Add(-0.5, gravityPotentialVariation); + + mfem::Vector combinedReference; + + prepared_hydrostatic_jacobian_test_utils::centered_residual_difference( + f, rotation, enthalpyPlus, enthalpyMinus, gravityPotentialPlus, + gravityPotentialMinus, displacement, + bernoulliConstant + 0.5 * bernoulliConstantVariation, + bernoulliConstant - 0.5 * bernoulliConstantVariation, combinedReference + ); + + mfem::Vector sumOfBlocks(enthalpyAction); + sumOfBlocks += gravityPotentialAction; + sumOfBlocks += bernoulliConstantAction; + + const double enthalpyError = + prepared_hydrostatic_jacobian_test_utils::relative_error( + enthalpyAction, enthalpyReference, f.mesh->GetComm() + ); + + const double gravityPotentialError = + prepared_hydrostatic_jacobian_test_utils::relative_error( + gravityPotentialAction, gravityPotentialReference, f.mesh->GetComm() + ); + + const double bernoulliConstantError = + prepared_hydrostatic_jacobian_test_utils::relative_error( + bernoulliConstantAction, bernoulliConstantReference, + f.mesh->GetComm() + ); + + const double combinedError = + prepared_hydrostatic_jacobian_test_utils::relative_error( + combinedAction, combinedReference, f.mesh->GetComm() + ); + + const double blockSumError = + prepared_hydrostatic_jacobian_test_utils::relative_error( + combinedAction, sumOfBlocks, f.mesh->GetComm() + ); + + INFO("Enthalpy block error = " << enthalpyError); + INFO("Gravity-potential block error = " << gravityPotentialError); + INFO("Bernoulli-constant block error = " << bernoulliConstantError); + INFO("Combined algebraic action error = " << combinedError); + INFO("Combined-versus-summed-block error = " << blockSumError); + + const auto &statistics = preparedOperator.GetAlgebraicJacobianStatistics(); + + CHECK(report.preparedAlgebraicJacobianBlocks); + CHECK(statistics.preparations == 1); + CHECK(statistics.enthalpyApplications == 1); + CHECK(statistics.gravityPotentialApplications == 1); + CHECK(statistics.bernoulliConstantApplications == 1); + CHECK(statistics.combinedApplications == 1); + + CHECK(enthalpyError < 5.0e-12); + CHECK(gravityPotentialError < 5.0e-12); + CHECK(bernoulliConstantError < 5.0e-12); + CHECK(combinedError < 5.0e-12); + CHECK(blockSumError < 5.0e-13); +} + +TEST_CASE( + "Prepared Hydrostatic Algebraic Jacobian Reuses And Rebuilds Only With " + "Geometry", + tags::barotrope &tags::hydro &tags::jacobian &tags::prepared &tags::unit +) { + auto args = test_utils::setup_args(); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + mean_field::operators::PreparedHydrostaticEquilibriumOperator + preparedOperator(f, *f.domainMapperStateless); + + mfem::Vector enthalpy = + prepared_hydrostatic_jacobian_test_utils::make_enthalpy(f); + + mfem::Vector gravityPotential = + prepared_hydrostatic_jacobian_test_utils::make_gravity_potential(f); + + mfem::Vector displacement = + gravity_prepared_test_utils::make_displacement(f, 0.42); + + double bernoulliConstant = 0.37; + + mean_field::physics::RigidRotation rotation = + prepared_hydrostatic_jacobian_test_utils::make_rotation(0.8); + + auto dependencies = + prepared_hydrostatic_jacobian_test_utils::make_dependencies(); + + preparedOperator.Prepare( + prepared_hydrostatic_jacobian_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, rotation + ); + + const mfem::Vector enthalpyVariation = + prepared_hydrostatic_jacobian_test_utils::make_enthalpy(f, 0.67); + + const mfem::Vector gravityPotentialVariation = + prepared_hydrostatic_jacobian_test_utils::make_gravity_potential( + f, 0.79 + ); + + constexpr double bernoulliConstantVariation = 0.28; + + mfem::Vector initialAction; + + preparedOperator.ApplyAlgebraicJacobianAction( + enthalpyVariation, gravityPotentialVariation, + bernoulliConstantVariation, initialAction + ); + + enthalpy = prepared_hydrostatic_jacobian_test_utils::make_enthalpy(f, 1.13); + + gravityPotential = + prepared_hydrostatic_jacobian_test_utils::make_gravity_potential( + f, 1.31 + ); + + bernoulliConstant = 0.62; + rotation = prepared_hydrostatic_jacobian_test_utils::make_rotation(1.4); + + ++dependencies.enthalpy.revision; + ++dependencies.gravityPotential.revision; + ++dependencies.bernoulliConstant.revision; + ++dependencies.rotation.revision; + + const auto baseStateReport = preparedOperator.Prepare( + prepared_hydrostatic_jacobian_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, rotation + ); + + mfem::Vector baseStateChangedAction; + + preparedOperator.ApplyAlgebraicJacobianAction( + enthalpyVariation, gravityPotentialVariation, + bernoulliConstantVariation, baseStateChangedAction + ); + + CHECK_FALSE(baseStateReport.contextReport.preparedGeometryState); + CHECK(baseStateReport.contextReport.preparedRotationDependencies); + CHECK(baseStateReport.contextReport.preparedBaseState); + CHECK_FALSE(baseStateReport.preparedAlgebraicJacobianBlocks); + CHECK(preparedOperator.GetAlgebraicJacobianStatistics().preparations == 1); + CHECK( + prepared_hydrostatic_jacobian_test_utils::relative_error( + baseStateChangedAction, initialAction, f.mesh->GetComm() + ) == 0.0 + ); + + const mfem::Vector secondEnthalpyVariation = + prepared_hydrostatic_jacobian_test_utils::make_enthalpy(f, 1.57); + + const mfem::Vector secondGravityPotentialVariation = + prepared_hydrostatic_jacobian_test_utils::make_gravity_potential( + f, 1.73 + ); + + mfem::Vector secondDirectionAction; + + preparedOperator.ApplyAlgebraicJacobianAction( + secondEnthalpyVariation, secondGravityPotentialVariation, -0.19, + secondDirectionAction + ); + + CHECK(preparedOperator.GetAlgebraicJacobianStatistics().preparations == 1); + + displacement = gravity_prepared_test_utils::make_displacement(f, 0.73); + + ++dependencies.displacement.revision; + + const auto geometryReport = preparedOperator.Prepare( + prepared_hydrostatic_jacobian_test_utils::make_state( + enthalpy, gravityPotential, displacement, bernoulliConstant + ), + dependencies, rotation + ); + + mfem::Vector geometryChangedAction; + + preparedOperator.ApplyAlgebraicJacobianAction( + enthalpyVariation, gravityPotentialVariation, + bernoulliConstantVariation, geometryChangedAction + ); + + mfem::Vector enthalpyPlus(enthalpy); + mfem::Vector enthalpyMinus(enthalpy); + mfem::Vector gravityPotentialPlus(gravityPotential); + mfem::Vector gravityPotentialMinus(gravityPotential); + + enthalpyPlus.Add(0.5, enthalpyVariation); + enthalpyMinus.Add(-0.5, enthalpyVariation); + + gravityPotentialPlus.Add(0.5, gravityPotentialVariation); + + gravityPotentialMinus.Add(-0.5, gravityPotentialVariation); + + mfem::Vector geometryReference; + + prepared_hydrostatic_jacobian_test_utils::centered_residual_difference( + f, rotation, enthalpyPlus, enthalpyMinus, gravityPotentialPlus, + gravityPotentialMinus, displacement, + bernoulliConstant + 0.5 * bernoulliConstantVariation, + bernoulliConstant - 0.5 * bernoulliConstantVariation, geometryReference + ); + + const double geometryReferenceError = + prepared_hydrostatic_jacobian_test_utils::relative_error( + geometryChangedAction, geometryReference, f.mesh->GetComm() + ); + + const double geometryEffect = + prepared_hydrostatic_jacobian_test_utils::relative_error( + geometryChangedAction, initialAction, f.mesh->GetComm() + ); + + INFO( + "Geometry-updated algebraic Jacobian error = " << geometryReferenceError + ); + + INFO( + "Algebraic Jacobian change after deformation update = " + << geometryEffect + ); + + const auto &statistics = preparedOperator.GetAlgebraicJacobianStatistics(); + + CHECK(geometryReport.contextReport.preparedGeometryState); + CHECK(geometryReport.preparedAlgebraicJacobianBlocks); + CHECK(statistics.preparations == 2); + CHECK(statistics.enthalpyApplications == 0); + CHECK(statistics.gravityPotentialApplications == 0); + CHECK(statistics.bernoulliConstantApplications == 0); + CHECK(statistics.combinedApplications == 4); + + CHECK(geometryReferenceError < 5.0e-12); + CHECK(geometryEffect > 1.0e-8); +} diff --git a/tests/physics/barotrope.cpp b/tests/physics/barotrope.cpp new file mode 100644 index 0000000..63999e9 --- /dev/null +++ b/tests/physics/barotrope.cpp @@ -0,0 +1,144 @@ +#include +#include +#include + +#include +#include + +import mean_field; +import test_helpers; + +TEST_CASE( + "Polytropic Barotrope Satisfies Its Analytic Identities", + tags::hydro &tags::unit &tags::barotrope +) { + constexpr double polytropic_index = 3.0; + constexpr double polytropic_constant = 1.5; + + const mean_field::physics::PolytropicBarotrope barotrope( + polytropic_index, polytropic_constant + ); + + const std::array densities{1.0e-6, 1.0e-3, 0.1, 0.7, 2.0}; + + for (const double density : densities) { + const double pressure = barotrope.pressure_from_density(density); + + const double enthalpy = barotrope.enthalpy_from_density(density); + + const double reconstructed_density = + barotrope.density_from_enthalpy(enthalpy); + + const double reconstructed_pressure = + barotrope.pressure_from_enthalpy(enthalpy); + + CHECK_THAT( + reconstructed_density, Catch::Matchers::WithinRel(density, 2.0e-14) + ); + + CHECK_THAT( + reconstructed_pressure, + Catch::Matchers::WithinRel(pressure, 2.0e-14) + ); + + CHECK_THAT( + pressure, Catch::Matchers::WithinRel( + density * enthalpy / (polytropic_index + 1.0), 2.0e-14 + ) + ); + + CHECK_THAT( + barotrope.pressure_derivative_from_enthalpy(enthalpy), + Catch::Matchers::WithinRel(density, 2.0e-14) + ); + + CHECK_THAT( + barotrope.pressure_derivative_from_density(density), + Catch::Matchers::WithinRel(enthalpy / polytropic_index, 2.0e-14) + ); + } +} + +TEST_CASE( + "Polytropic Barotrope Derivatives Match Centered Differences", + tags::hydro &tags::jacobian &tags::unit &tags::barotrope +) { + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + const std::array enthalpies{0.05, 0.2, 0.7, 1.4}; + + for (const double enthalpy : enthalpies) { + const double step = 1.0e-6 * std::max(1.0, enthalpy); + + const double density_difference = + (barotrope.density_from_enthalpy(enthalpy + step) - + barotrope.density_from_enthalpy(enthalpy - step)) / + (2.0 * step); + + const double pressure_difference = + (barotrope.pressure_from_enthalpy(enthalpy + step) - + barotrope.pressure_from_enthalpy(enthalpy - step)) / + (2.0 * step); + + CHECK_THAT( + density_difference, + Catch::Matchers::WithinRel( + barotrope.density_derivative_from_enthalpy(enthalpy), 5.0e-10 + ) + ); + + CHECK_THAT( + pressure_difference, + Catch::Matchers::WithinRel( + barotrope.pressure_derivative_from_enthalpy(enthalpy), 5.0e-10 + ) + ); + } +} + +TEST_CASE( + "Polytropic Barotrope Has An Exact Zero Density Surface", + tags::hydro &tags::unit &tags::barotrope +) { + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.5); + + CHECK(barotrope.density_from_enthalpy(-1.0) == 0.0); + CHECK(barotrope.density_from_enthalpy(0.0) == 0.0); + + CHECK(barotrope.pressure_from_enthalpy(-1.0) == 0.0); + CHECK(barotrope.pressure_from_enthalpy(0.0) == 0.0); + + CHECK(barotrope.density_derivative_from_enthalpy(-1.0) == 0.0); + + CHECK(barotrope.density_derivative_from_enthalpy(0.0) == 0.0); + + CHECK(barotrope.pressure_derivative_from_enthalpy(0.0) == 0.0); +} + +TEST_CASE( + "Polytropic Barotrope Rejects Invalid Material Parameters", + tags::hydro &tags::unit +) { + CHECK_THROWS_AS( + mean_field::physics::PolytropicBarotrope(0.5, 1.0), + std::invalid_argument + ); + + CHECK_THROWS_AS( + mean_field::physics::PolytropicBarotrope(3.0, 0.0), + std::invalid_argument + ); + + CHECK_THROWS_AS( + mean_field::physics::PolytropicBarotrope( + std::numeric_limits::infinity(), 1.0 + ), + std::invalid_argument + ); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 1.0); + + CHECK_THROWS_AS(barotrope.pressure_from_density(-1.0), std::domain_error); + + CHECK_THROWS_AS(barotrope.enthalpy_from_density(-1.0), std::domain_error); +} \ No newline at end of file diff --git a/tests/physics/barotrope_pressure.cpp b/tests/physics/barotrope_pressure.cpp new file mode 100644 index 0000000..a5fd127 --- /dev/null +++ b/tests/physics/barotrope_pressure.cpp @@ -0,0 +1,699 @@ +#include +#include +#include +#include +#include +#include + +#include +#include + +#include + +import mean_field; +import test_helpers; + +namespace polytropic_barotrope_test_utils { + template + double centered_derivative( + Function &&function, + const double position, + const double step + ) { + return (function(position + step) - function(position - step)) / + (2.0 * step); + } + + template + double integrate_cube( + const mfem::IntegrationRule &integrationRule, + Integrand &&integrand + ) { + double integral = 0.0; + + for (int pointIndex = 0; pointIndex < integrationRule.GetNPoints(); + ++pointIndex) { + const mfem::IntegrationPoint &integrationPoint = + integrationRule.IntPoint(pointIndex); + + integral += integrationPoint.weight * integrand(integrationPoint); + } + + return integral; + } +} // namespace polytropic_barotrope_test_utils + +TEST_CASE( + "Polytropic Barotrope Satisfies Its Thermodynamic Identities", + tags::barotrope &tags::physics &tags::unit +) { + constexpr std::array polytropicIndices{1.0, 1.5, 3.0}; + + constexpr std::array densities{1.0e-4, 0.02, 0.37, 2.4}; + + constexpr double polytropicConstant = 0.73; + + for (const double polytropicIndex : polytropicIndices) { + DYNAMIC_SECTION("polytropic index n = " << polytropicIndex) { + const mean_field::physics::PolytropicBarotrope barotrope( + polytropicIndex, polytropicConstant + ); + + const double expectedEnthalpyScale = + (polytropicIndex + 1.0) * polytropicConstant; + + CHECK(barotrope.polytropic_index() == polytropicIndex); + + CHECK(barotrope.polytropic_constant() == polytropicConstant); + + CHECK(barotrope.enthalpy_scale() == expectedEnthalpyScale); + + for (const double density : densities) { + CAPTURE(polytropicIndex, polytropicConstant, density); + + const double expectedPressure = + polytropicConstant * + std::pow(density, 1.0 + 1.0 / polytropicIndex); + + const double expectedEnthalpy = + expectedEnthalpyScale * + std::pow(density, 1.0 / polytropicIndex); + + const double pressureFromDensity = + barotrope.pressure_from_density(density); + + const double enthalpyFromDensity = + barotrope.enthalpy_from_density(density); + + const double recoveredDensity = + barotrope.density_from_enthalpy(enthalpyFromDensity); + + const double pressureFromEnthalpy = + barotrope.pressure_from_enthalpy(enthalpyFromDensity); + + CHECK_THAT( + pressureFromDensity, + Catch::Matchers::WithinRel(expectedPressure, 2.0e-13) + ); + + CHECK_THAT( + enthalpyFromDensity, + Catch::Matchers::WithinRel(expectedEnthalpy, 2.0e-13) + ); + + CHECK_THAT( + recoveredDensity, + Catch::Matchers::WithinRel(density, 5.0e-13) + ); + + CHECK_THAT( + pressureFromEnthalpy, + Catch::Matchers::WithinRel(expectedPressure, 5.0e-13) + ); + + /* + * Polytropic identity: + * + * P = rho h / (n + 1). + */ + CHECK_THAT( + pressureFromEnthalpy, + Catch::Matchers::WithinRel( + density * enthalpyFromDensity / (polytropicIndex + 1.0), + 5.0e-13 + ) + ); + + /* + * Polytropic identity: + * + * dP / dh = rho. + * + * The implementation should return the same + * value as density_from_enthalpy(). + */ + CHECK( + barotrope.pressure_derivative_from_enthalpy( + enthalpyFromDensity + ) == barotrope.density_from_enthalpy(enthalpyFromDensity) + ); + + /* + * Since + * + * h = (n + 1) K rho^(1/n), + * + * it follows that + * + * dP / d rho = h / n. + */ + CHECK_THAT( + barotrope.pressure_derivative_from_density(density), + Catch::Matchers::WithinRel( + enthalpyFromDensity / polytropicIndex, 5.0e-13 + ) + ); + } + } + } +} + +TEST_CASE( + "Polytropic Barotrope Pressure Derivatives Match Centered Differences", + tags::barotrope &tags::physics &tags::unit &tags::jacobian &tags::pressure +) { + constexpr std::array polytropicIndices{1.0, 1.5, 3.0}; + + constexpr std::array positiveValues{0.2, 0.73, 1.8}; + + constexpr double polytropicConstant = 0.61; + + for (const double polytropicIndex : polytropicIndices) { + const mean_field::physics::PolytropicBarotrope barotrope( + polytropicIndex, polytropicConstant + ); + + DYNAMIC_SECTION("polytropic index n = " << polytropicIndex) { + for (const double enthalpy : positiveValues) { + const double step = 2.0e-6 * std::max(1.0, std::abs(enthalpy)); + + const double numericalDerivative = + polytropic_barotrope_test_utils::centered_derivative( + [&barotrope](const double perturbedEnthalpy) { + return barotrope.pressure_from_enthalpy( + perturbedEnthalpy + ); + }, + enthalpy, step + ); + + const double analyticDerivative = + barotrope.pressure_derivative_from_enthalpy(enthalpy); + + CAPTURE( + polytropicIndex, enthalpy, step, numericalDerivative, + analyticDerivative + ); + + CHECK_THAT( + numericalDerivative, + Catch::Matchers::WithinRel(analyticDerivative, 5.0e-8) + ); + } + + for (const double density : positiveValues) { + const double step = 2.0e-6 * std::max(1.0, std::abs(density)); + + const double numericalDerivative = + polytropic_barotrope_test_utils::centered_derivative( + [&barotrope](const double perturbedDensity) { + return barotrope.pressure_from_density( + perturbedDensity + ); + }, + density, step + ); + + const double analyticDerivative = + barotrope.pressure_derivative_from_density(density); + + CAPTURE( + polytropicIndex, density, step, numericalDerivative, + analyticDerivative + ); + + CHECK_THAT( + numericalDerivative, + Catch::Matchers::WithinRel(analyticDerivative, 5.0e-8) + ); + } + } + } +} + +TEST_CASE( + "Polytropic Barotrope Density Derivative Matches Centered Differences", + tags::barotrope &tags::physics &tags::unit &tags::jacobian &tags::pressure +) { + constexpr std::array polytropicIndices{1.0, 1.5, 3.0}; + + constexpr std::array enthalpies{0.2, 0.73, 1.8}; + + constexpr double polytropicConstant = 0.61; + + for (const double polytropicIndex : polytropicIndices) { + const mean_field::physics::PolytropicBarotrope barotrope( + polytropicIndex, polytropicConstant + ); + + DYNAMIC_SECTION("polytropic index n = " << polytropicIndex) { + for (const double enthalpy : enthalpies) { + const double step = 2.0e-6 * std::max(1.0, std::abs(enthalpy)); + + const double numericalDerivative = + polytropic_barotrope_test_utils::centered_derivative( + [&barotrope](const double perturbedEnthalpy) { + return barotrope.density_from_enthalpy( + perturbedEnthalpy + ); + }, + enthalpy, step + ); + + const double analyticDerivative = + barotrope.density_derivative_from_enthalpy(enthalpy); + + CAPTURE( + polytropicIndex, enthalpy, step, numericalDerivative, + analyticDerivative + ); + + CHECK_THAT( + numericalDerivative, + Catch::Matchers::WithinRel(analyticDerivative, 5.0e-8) + ); + } + } + } +} + +TEST_CASE( + "Polytropic Barotrope Defines Consistent Surface And Exterior Behavior", + tags::barotrope &tags::physics &tags::unit &tags::pressure +) { + constexpr std::array polytropicIndices{1.0, 1.5, 3.0}; + + constexpr double polytropicConstant = 0.47; + constexpr double exteriorEnthalpy = -0.3; + + for (const double polytropicIndex : polytropicIndices) { + const mean_field::physics::PolytropicBarotrope barotrope( + polytropicIndex, polytropicConstant + ); + + DYNAMIC_SECTION("polytropic index n = " << polytropicIndex) { + /* + * Exact surface values. + */ + CHECK(barotrope.density_from_enthalpy(0.0) == 0.0); + + CHECK(barotrope.pressure_from_enthalpy(0.0) == 0.0); + + CHECK(barotrope.pressure_derivative_from_enthalpy(0.0) == 0.0); + + CHECK(barotrope.pressure_from_density(0.0) == 0.0); + + CHECK(barotrope.enthalpy_from_density(0.0) == 0.0); + + CHECK(barotrope.pressure_derivative_from_density(0.0) == 0.0); + + /* + * Positive-part extension into h < 0. + */ + CHECK(barotrope.density_from_enthalpy(exteriorEnthalpy) == 0.0); + + CHECK(barotrope.pressure_from_enthalpy(exteriorEnthalpy) == 0.0); + + CHECK( + barotrope.density_derivative_from_enthalpy(exteriorEnthalpy) == + 0.0 + ); + + CHECK( + barotrope.pressure_derivative_from_enthalpy(exteriorEnthalpy) == + 0.0 + ); + + /* + * At h = 0, rho(h) has a nonzero right + * derivative only for n = 1. + */ + const double expectedSurfaceDensityDerivative = + polytropicIndex == 1.0 ? 1.0 / barotrope.enthalpy_scale() : 0.0; + + CHECK( + barotrope.density_derivative_from_enthalpy(0.0) == + expectedSurfaceDensityDerivative + ); + } + } +} + +TEST_CASE( + "Polytropic Barotrope Rejects Invalid Physical Inputs", + tags::barotrope &tags::physics &tags::unit &tags::pressure +) { + CHECK_THROWS_AS( + mean_field::physics::PolytropicBarotrope(0.999, 1.0), + std::invalid_argument + ); + + CHECK_THROWS_AS( + mean_field::physics::PolytropicBarotrope( + std::numeric_limits::infinity(), 1.0 + ), + std::invalid_argument + ); + + CHECK_THROWS_AS( + mean_field::physics::PolytropicBarotrope(3.0, 0.0), + std::invalid_argument + ); + + CHECK_THROWS_AS( + mean_field::physics::PolytropicBarotrope(3.0, -1.0), + std::invalid_argument + ); + + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 0.75); + + CHECK_THROWS_AS(barotrope.pressure_from_density(-0.1), std::domain_error); + + CHECK_THROWS_AS(barotrope.enthalpy_from_density(-0.1), std::domain_error); + + CHECK_THROWS_AS( + barotrope.pressure_derivative_from_density(-0.1), std::domain_error + ); + + constexpr std::array nonfiniteValues{ + std::numeric_limits::infinity(), + -std::numeric_limits::infinity(), + std::numeric_limits::quiet_NaN() + }; + + for (const double nonfiniteValue : nonfiniteValues) { + CAPTURE(nonfiniteValue); + + CHECK_THROWS_AS( + barotrope.density_from_enthalpy(nonfiniteValue), std::domain_error + ); + + CHECK_THROWS_AS( + barotrope.pressure_from_enthalpy(nonfiniteValue), std::domain_error + ); + + CHECK_THROWS_AS( + barotrope.density_derivative_from_enthalpy(nonfiniteValue), + std::domain_error + ); + + CHECK_THROWS_AS( + barotrope.pressure_derivative_from_enthalpy(nonfiniteValue), + std::domain_error + ); + } +} + +TEST_CASE( + "Pressure Force And Pressure Integral Have Distinct Registered Forms", + tags::barotrope &tags::pressure &tags::pressure_gradient &tags::quadrature + &tags::unit +) { + using EnthalpyField = mean_field::field::Field; + + /* + * For the registered H1 order p = 3 and n = 3: + * + * h has degree p, + * P(h) has degree 4p, + * + * so the nonlinear EOS contributes an additional + * + * 4p - p = 3p = 9 + * + * beyond the registered enthalpy operand. + */ + constexpr int enthalpyOrder = + mean_field::field::Enthalpy::Scalar::familyOrder; + + constexpr int pressureExtraOrder = 3 * enthalpyOrder; + + constexpr int geometryWeightOrder = 2; + + constexpr mean_field::quadrature::Query pressureIntegralQuery = + EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::PressureIntegral>( + mean_field::quadrature::QuadratureRole::diagnostic, + geometryWeightOrder, std::array{pressureExtraOrder}, + mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + constexpr mean_field::quadrature::Query pressureForceQuery = + EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::PressureForce>( + mean_field::quadrature::QuadratureRole::discretization, + geometryWeightOrder, std::array{pressureExtraOrder}, + mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::general + ); + + STATIC_CHECK( + mean_field::field::Enthalpy::Form::PressureIntegral:: + dynamicOrderCount == 1 + ); + + STATIC_CHECK( + mean_field::field::Enthalpy::Form::PressureForce::dynamicOrderCount == 1 + ); + + STATIC_CHECK( + mean_field::field::Enthalpy::Form::PressureIntegral::policyKey != + mean_field::field::Enthalpy::Form::PressureForce::policyKey + ); + + REQUIRE(pressureIntegralQuery.base_order.has_value()); + + REQUIRE(pressureForceQuery.base_order.has_value()); + + /* + * Pressure integral: + * + * degree(P) + degree(J) + * = 12 + 2 + * = 14. + */ + CHECK(*pressureIntegralQuery.base_order == 14); + + /* + * Pressure force: + * + * degree(P) + * + degree(grad w) + * + degree(J) + * + * = 12 + 2 + 2 + * = 16. + */ + CHECK(*pressureForceQuery.base_order == 16); + + CHECK( + pressureIntegralQuery.term == + mean_field::quadrature::Term::pressure_integral + ); + + CHECK( + pressureForceQuery.term == mean_field::quadrature::Term::pressure_force + ); + + CHECK( + pressureIntegralQuery.role == + mean_field::quadrature::QuadratureRole::diagnostic + ); + + CHECK( + pressureForceQuery.role == + mean_field::quadrature::QuadratureRole::discretization + ); + + CHECK(pressureIntegralQuery.domain == mean_field::utils::DOMAINS::STELLAR); + + CHECK(pressureForceQuery.domain == mean_field::utils::DOMAINS::STELLAR); + + /* + * Verify that the two terms route to independent policy + * controls. + */ + mean_field::quadrature::RuleSet ruleSet = + mean_field::quadrature::make_rule_set( + mean_field::quadrature::Mode::production + ); + + ruleSet.pressure_integral.boost = 3; + ruleSet.pressure_force.boost = 5; + + const mean_field::quadrature::Policy policy(std::move(ruleSet)); + + const mean_field::quadrature::Resolution pressureIntegralResolution = + policy.resolve(pressureIntegralQuery); + + const mean_field::quadrature::Resolution pressureForceResolution = + policy.resolve(pressureForceQuery); + + CHECK(pressureIntegralResolution.base_order == 14); + + CHECK(pressureIntegralResolution.boost == 3); + + CHECK(pressureIntegralResolution.order == 17); + + CHECK(pressureForceResolution.base_order == 16); + + CHECK(pressureForceResolution.boost == 5); + + CHECK(pressureForceResolution.order == 21); +} + +TEST_CASE( + "Stage Four Pressure Quadrature Exactly Integrates An N Three Polynomial", + tags::barotrope &tags::pressure &tags::pressure_gradient &tags::quadrature + &tags::accuracy +) { + using EnthalpyField = mean_field::field::Field; + + constexpr int enthalpyOrder = + mean_field::field::Enthalpy::Scalar::familyOrder; + + constexpr int pressureExtraOrder = 3 * enthalpyOrder; + + /* + * K = 1/4 and n = 3 give + * + * (n + 1) K = 1, + * rho(h) = h^3, + * P(h) = h^4 / 4. + */ + const mean_field::physics::PolytropicBarotrope barotrope(3.0, 0.25); + + constexpr mean_field::quadrature::Query pressureIntegralQuery = + EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::PressureIntegral>( + mean_field::quadrature::QuadratureRole::diagnostic, 0, + std::array{pressureExtraOrder}, + mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::affine + ); + + constexpr mean_field::quadrature::Query pressureForceQuery = + EnthalpyField::make_query< + mean_field::field::Enthalpy::Form::PressureForce>( + mean_field::quadrature::QuadratureRole::discretization, 0, + std::array{pressureExtraOrder}, + mean_field::utils::DOMAINS::STELLAR, + mean_field::quadrature::MappingKind::affine + ); + + const mean_field::quadrature::RuleFactory ruleFactory{ + mean_field::quadrature::Policy( + mean_field::quadrature::make_rule_set( + mean_field::quadrature::Mode::production + ) + ) + }; + + const mean_field::quadrature::MfemRule pressureIntegralRule = + ruleFactory.get(pressureIntegralQuery, mfem::Geometry::CUBE); + + const mean_field::quadrature::MfemRule pressureForceRule = + ruleFactory.get(pressureForceQuery, mfem::Geometry::CUBE); + + /* + * On the reference cube [0,1]^3 choose + * + * h = x^3 y^3 z^3. + * + * This is representable by the order-three H1 space. + * Then + * + * P = x^12 y^12 z^12 / 4. + */ + const double numericalPressureIntegral = + polytropic_barotrope_test_utils::integrate_cube( + *pressureIntegralRule.integration_rule, + [&barotrope](const mfem::IntegrationPoint &integrationPoint) { + const double coordinateProduct = integrationPoint.x * + integrationPoint.y * + integrationPoint.z; + + const double enthalpy = std::pow(coordinateProduct, 3.0); + + return barotrope.pressure_from_enthalpy(enthalpy); + } + ); + + const double analyticPressureIntegral = 0.25 / std::pow(13.0, 3.0); + + /* + * Choose a representable vector test function whose + * divergence is + * + * div(w) = x^2 y^2 z^2. + * + * Therefore + * + * -P div(w) + * = -x^14 y^14 z^14 / 4. + */ + const double numericalPressureForceIntegral = + polytropic_barotrope_test_utils::integrate_cube( + *pressureForceRule.integration_rule, + [&barotrope](const mfem::IntegrationPoint &integrationPoint) { + const double coordinateProduct = integrationPoint.x * + integrationPoint.y * + integrationPoint.z; + + const double enthalpy = std::pow(coordinateProduct, 3.0); + + const double pressure = + barotrope.pressure_from_enthalpy(enthalpy); + + const double testDivergence = + integrationPoint.x * integrationPoint.x * + integrationPoint.y * integrationPoint.y * + integrationPoint.z * integrationPoint.z; + + return -pressure * testDivergence; + } + ); + + const double analyticPressureForceIntegral = -0.25 / std::pow(15.0, 3.0); + + INFO( + "Pressure-integral quadrature order = " + << pressureIntegralRule.resolution.order + ); + + INFO( + "Pressure-force quadrature order = " + << pressureForceRule.resolution.order + ); + + INFO("Numerical pressure integral = " << numericalPressureIntegral); + + INFO("Analytic pressure integral = " << analyticPressureIntegral); + + INFO( + "Numerical pressure-force integral = " << numericalPressureForceIntegral + ); + + INFO( + "Analytic pressure-force integral = " << analyticPressureForceIntegral + ); + + CHECK(pressureIntegralRule.resolution.base_order == 12); + + CHECK(pressureIntegralRule.resolution.order == 12); + + CHECK(pressureForceRule.resolution.base_order == 14); + + CHECK(pressureForceRule.resolution.order == 14); + + CHECK_THAT( + numericalPressureIntegral, + Catch::Matchers::WithinAbs(analyticPressureIntegral, 5.0e-14) + ); + + CHECK_THAT( + numericalPressureForceIntegral, + Catch::Matchers::WithinAbs(analyticPressureForceIntegral, 5.0e-14) + ); +} \ No newline at end of file diff --git a/tests/physics/gravity.cpp b/tests/physics/gravity.cpp index ef42e0e..60d736e 100644 --- a/tests/physics/gravity.cpp +++ b/tests/physics/gravity.cpp @@ -2,9 +2,11 @@ #include #include -#include -#include +#include #include +#include +#include +#include #include #include @@ -16,6 +18,46 @@ import test_helpers; using namespace mean_field; namespace { + double global_vector_norm( + const mfem::Vector &vector, + MPI_Comm communicator + ) { + const double local_norm_squared = vector * vector; + double global_norm_squared = 0.0; + MPI_Allreduce( + &local_norm_squared, &global_norm_squared, 1, MPI_DOUBLE, MPI_SUM, + communicator + ); + return std::sqrt(global_norm_squared); + } + + double global_vector_dot( + const mfem::Vector &lhs, + const mfem::Vector &rhs, + MPI_Comm communicator + ) { + const double local_dot = lhs * rhs; + double global_dot = 0.0; + MPI_Allreduce( + &local_dot, &global_dot, 1, MPI_DOUBLE, MPI_SUM, communicator + ); + return global_dot; + } + + double global_relative_vector_error( + const mfem::Vector &computed, + const mfem::Vector &reference, + MPI_Comm communicator + ) { + mfem::Vector difference(computed); + difference -= reference; + return global_vector_norm(difference, communicator) / + std::max( + global_vector_norm(reference, communicator), + std::numeric_limits::epsilon() + ); + } + struct GravitationalEnergies { double binding; double virial; @@ -28,12 +70,73 @@ namespace { double energy_kernel; }; + class HomogeneousEllipsoidHDivCoefficient : public mfem::VectorCoefficient { + public: + HomogeneousEllipsoidHDivCoefficient( + const mapping::DomainMapper &domain_mapping, + const double density, + const HomogeneousEllipsoidAnalytic &analytic + ) + : VectorCoefficient(3), + domain_mapping(domain_mapping), + density(density), + coefficient_x(analytic.coefficient_x), + coefficient_y(analytic.coefficient_y), + coefficient_z(analytic.coefficient_z) { + } + + void Eval( + mfem::Vector &value, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point + ) override { + transformation.SetIntPoint(&integration_point); + + mfem::Vector x_physical(3); + mfem::Vector field_physical(3); + mfem::DenseMatrix map_jacobian(3, 3); + mfem::DenseMatrix inverse_map_jacobian(3, 3); + + domain_mapping.GetPhysicalPoint( + transformation, integration_point, x_physical + ); + + field_physical(0) = + 2.0 * M_PI * utils::G * density * coefficient_x * x_physical(0); + field_physical(1) = + 2.0 * M_PI * utils::G * density * coefficient_y * x_physical(1); + field_physical(2) = + 2.0 * M_PI * utils::G * density * coefficient_z * x_physical(2); + + domain_mapping.ComputeJacobian(transformation, map_jacobian); + const double map_determinant = map_jacobian.Det(); + MFEM_VERIFY( + map_determinant > 0.0, + "Domain mapping has a non-positive Jacobian determinant." + ); + + mfem::CalcInverse(map_jacobian, inverse_map_jacobian); + inverse_map_jacobian.Mult(field_physical, value); + value *= map_determinant; + } + + private: + const mapping::DomainMapper &domain_mapping; + double density; + double coefficient_x; + double coefficient_y; + double coefficient_z; + }; + template - GravitationalEnergies compute_gravitational_energies(fem::FEM& f, const mfem::GridFunction& rho, - const GravitySolutionType& gravity_solution, - const int quadrature_order) { - const int dim = f.mesh->Dimension(); - double local_bind_integral = 0.0; + GravitationalEnergies compute_gravitational_energies( + fem::FEM &f, + const mfem::GridFunction &rho, + const GravitySolutionType &gravity_solution, + const int quadrature_order + ) { + const int dim = f.mesh->Dimension(); + double local_bind_integral = 0.0; double local_virial_integral = 0.0; mfem::Vector x_physical(dim); @@ -46,85 +149,120 @@ namespace { continue; } - mfem::ElementTransformation* transformation = f.mesh->GetElementTransformation(elem_id); - const mfem::IntegrationRule& integration_rule = - mfem::IntRules.Get(transformation->GetGeometryType(), quadrature_order); + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(elem_id); + const mfem::IntegrationRule &integration_rule = mfem::IntRules.Get( + transformation->GetGeometryType(), quadrature_order + ); for (int q = 0; q < integration_rule.GetNPoints(); ++q) { - const mfem::IntegrationPoint& integration_point = integration_rule.IntPoint(q); + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); transformation->SetIntPoint(&integration_point); - double weight = transformation->Weight() * integration_point.weight; + double weight = + transformation->Weight() * integration_point.weight; if (f.has_mapping()) { - const double map_determinant = f.mapping->ComputeDetJ(*transformation, integration_point); - MFEM_VERIFY(map_determinant > 0.0, "Domain mapping has a non-positive Jacobian determinant."); + const double map_determinant = f.mapping->ComputeDetJ( + *transformation, integration_point + ); + MFEM_VERIFY( + map_determinant > 0.0, + "Domain mapping has a non-positive Jacobian " + "determinant." + ); weight *= map_determinant; - f.mapping->GetPhysicalPoint(*transformation, integration_point, x_physical); - gravity_solution.gradPhi.GetVectorValue(elem_id, integration_point, grad_phi_element); + f.mapping->GetPhysicalPoint( + *transformation, integration_point, x_physical + ); + gravity_solution.gradPhi.GetVectorValue( + elem_id, integration_point, grad_phi_element + ); f.mapping->ComputeJacobian(*transformation, map_jacobian); map_jacobian.Mult(grad_phi_element, grad_phi_physical); grad_phi_physical /= map_determinant; } else { transformation->Transform(integration_point, x_physical); - gravity_solution.gradPhi.GetVectorValue(elem_id, integration_point, grad_phi_physical); + gravity_solution.gradPhi.GetVectorValue( + elem_id, integration_point, grad_phi_physical + ); } - const double rho_value = rho.GetValue(elem_id, integration_point); - const double phi_value = gravity_solution.phi.GetValue(elem_id, integration_point); + const double rho_value = + rho.GetValue(elem_id, integration_point); + const double phi_value = + gravity_solution.phi.GetValue(elem_id, integration_point); double radius_dot_gradient = 0.0; for (int d = 0; d < dim; ++d) { - radius_dot_gradient += (x_physical(d) - f.com(d)) * grad_phi_physical(d); + radius_dot_gradient += + (x_physical(d) - f.com(d)) * grad_phi_physical(d); } local_bind_integral += rho_value * phi_value * weight; - local_virial_integral += rho_value * radius_dot_gradient * weight; + local_virial_integral += + rho_value * radius_dot_gradient * weight; } } const double local_w_bind = 0.5 * local_bind_integral; - const double local_w_vir = -local_virial_integral; - double global_w_bind = 0.0; - double global_w_vir = 0.0; - MPI_Comm communicator = f.L2_fes->GetComm(); + const double local_w_vir = -local_virial_integral; + double global_w_bind = 0.0; + double global_w_vir = 0.0; + MPI_Comm communicator = f.densityFes->GetComm(); - MPI_Allreduce(&local_w_bind, &global_w_bind, 1, MPI_DOUBLE, MPI_SUM, communicator); - MPI_Allreduce(&local_w_vir, &global_w_vir, 1, MPI_DOUBLE, MPI_SUM, communicator); + MPI_Allreduce( + &local_w_bind, &global_w_bind, 1, MPI_DOUBLE, MPI_SUM, communicator + ); + MPI_Allreduce( + &local_w_vir, &global_w_vir, 1, MPI_DOUBLE, MPI_SUM, communicator + ); return {.binding = global_w_bind, .virial = global_w_vir}; } - void zero_vacuum_density(const fem::FEM& f, mfem::GridFunction& rho) { - for (int i = 0; i < f.vacuum_tdof_rho.Size(); ++i) { - rho(f.vacuum_tdof_rho[i]) = 0.0; + void zero_vacuum_density( + const fem::FEM &f, + mfem::GridFunction &rho + ) { + for (int i = 0; i < f.vacuumDensityTdofs.Size(); ++i) { + rho(f.vacuumDensityTdofs[i]) = 0.0; } } - int get_gravity_quadrature_order(const fem::FEM& f) { - return 2 * std::max(f.L2_fes->GetMaxElementOrder(), f.RT_fes->GetMaxElementOrder()) + 8; + int get_gravity_quadrature_order(const fem::FEM &f) { + return 2 * std::max( + f.gravityPotentialFes->GetMaxElementOrder(), + f.gravityFluxFes->GetMaxElementOrder() + ) + + 8; } - double compute_ellipsoid_coefficient(const double normalized_axis_x, const double normalized_axis_y, - const double normalized_axis_z, const double target_axis_squared) { + double compute_ellipsoid_coefficient( + const double normalized_axis_x, + const double normalized_axis_y, + const double normalized_axis_z, + const double target_axis_squared + ) { auto integrand = [=](const double t) { if (t <= 0.0 || t >= 1.0) { return 0.0; } - const double one_minus_t = 1.0 - t; - const double s = t / one_minus_t; - const double s_squared = s * s; + const double one_minus_t = 1.0 - t; + const double s = t / one_minus_t; + const double s_squared = s * s; const double ds_squared_dt = 2.0 * s / (one_minus_t * one_minus_t); - const double delta = std::sqrt( + const double delta = std::sqrt( (normalized_axis_x * normalized_axis_x + s_squared) * (normalized_axis_y * normalized_axis_y + s_squared) * (normalized_axis_z * normalized_axis_z + s_squared) ); - return normalized_axis_x * normalized_axis_y * normalized_axis_z * ds_squared_dt / - ((target_axis_squared + s_squared) * delta); + return normalized_axis_x * normalized_axis_y * normalized_axis_z * + ds_squared_dt / ((target_axis_squared + s_squared) * delta); }; double integration_error = 0.0; @@ -133,8 +271,12 @@ namespace { ); } - double compute_ellipsoid_energy_kernel(const double normalized_axis_x, const double normalized_axis_y, - const double normalized_axis_z, const double length_scale) { + double compute_ellipsoid_energy_kernel( + const double normalized_axis_x, + const double normalized_axis_y, + const double normalized_axis_z, + const double length_scale + ) { auto integrand = [=](const double t) { if (t <= 0.0) { return 0.0; @@ -143,11 +285,11 @@ namespace { return 2.0; } - const double one_minus_t = 1.0 - t; - const double s = t / one_minus_t; - const double s_squared = s * s; + const double one_minus_t = 1.0 - t; + const double s = t / one_minus_t; + const double s_squared = s * s; const double ds_squared_dt = 2.0 * s / (one_minus_t * one_minus_t); - const double delta = std::sqrt( + const double delta = std::sqrt( (normalized_axis_x * normalized_axis_x + s_squared) * (normalized_axis_y * normalized_axis_y + s_squared) * (normalized_axis_z * normalized_axis_z + s_squared) @@ -157,31 +299,39 @@ namespace { }; double integration_error = 0.0; - const double dimensionless_integral = boost::math::quadrature::gauss_kronrod::integrate( - integrand, 0.0, 1.0, 15, 1.0e-13, &integration_error - ); + const double dimensionless_integral = + boost::math::quadrature::gauss_kronrod::integrate( + integrand, 0.0, 1.0, 15, 1.0e-13, &integration_error + ); return dimensionless_integral / length_scale; } HomogeneousEllipsoidAnalytic compute_homogeneous_ellipsoid_analytic( - const double semi_axis_x, const double semi_axis_y, const double semi_axis_z + const double semi_axis_x, + const double semi_axis_y, + const double semi_axis_z ) { - const double length_scale = std::cbrt(semi_axis_x * semi_axis_y * semi_axis_z); + const double length_scale = + std::cbrt(semi_axis_x * semi_axis_y * semi_axis_z); const double normalized_axis_x = semi_axis_x / length_scale; const double normalized_axis_y = semi_axis_y / length_scale; const double normalized_axis_z = semi_axis_z / length_scale; - const double coefficient_x = compute_ellipsoid_coefficient( - normalized_axis_x, normalized_axis_y, normalized_axis_z, normalized_axis_x * normalized_axis_x + const double coefficient_x = compute_ellipsoid_coefficient( + normalized_axis_x, normalized_axis_y, normalized_axis_z, + normalized_axis_x * normalized_axis_x ); const double coefficient_y = compute_ellipsoid_coefficient( - normalized_axis_x, normalized_axis_y, normalized_axis_z, normalized_axis_y * normalized_axis_y + normalized_axis_x, normalized_axis_y, normalized_axis_z, + normalized_axis_y * normalized_axis_y ); const double coefficient_z = compute_ellipsoid_coefficient( - normalized_axis_x, normalized_axis_y, normalized_axis_z, normalized_axis_z * normalized_axis_z + normalized_axis_x, normalized_axis_y, normalized_axis_z, + normalized_axis_z * normalized_axis_z ); const double energy_kernel = compute_ellipsoid_energy_kernel( - normalized_axis_x, normalized_axis_y, normalized_axis_z, length_scale + normalized_axis_x, normalized_axis_y, normalized_axis_z, + length_scale ); return { @@ -191,198 +341,1269 @@ namespace { .energy_kernel = energy_kernel }; } -} -TEST_CASE("Uniform Potential Matches Analytic", tags::gravity & tags::analytic_comparison) { - auto args = test_utils::setup_args(); + struct GravitySolutionComparison { + double relative_gradient_difference; + double relative_potential_difference; + }; + + template < + typename LeftGravitySolution, + typename RightGravitySolution> + GravitySolutionComparison compare_gravity_solutions( + fem::FEM &f, + const LeftGravitySolution &left_solution, + const RightGravitySolution &right_solution, + const int quadrature_order + ) { + const int dimension = f.mesh->Dimension(); + + double local_gradient_difference_squared = 0.0; + double local_left_gradient_norm_squared = 0.0; + double local_right_gradient_norm_squared = 0.0; + double local_potential_difference_squared = 0.0; + double local_left_potential_norm_squared = 0.0; + double local_right_potential_norm_squared = 0.0; + + mfem::Vector left_gradient_element(dimension); + mfem::Vector right_gradient_element(dimension); + mfem::Vector left_gradient_physical(dimension); + mfem::Vector right_gradient_physical(dimension); + mfem::Vector gradient_difference(dimension); + mfem::DenseMatrix map_jacobian(dimension, dimension); + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + if (f.mesh->GetAttribute(element_id) == 3) { + continue; + } + + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + const mfem::IntegrationRule &integration_rule = mfem::IntRules.Get( + transformation->GetGeometryType(), quadrature_order + ); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + transformation->SetIntPoint(&integration_point); + + double weight = + transformation->Weight() * integration_point.weight; + + left_solution.gradPhi.GetVectorValue( + element_id, integration_point, left_gradient_element + ); + right_solution.gradPhi.GetVectorValue( + element_id, integration_point, right_gradient_element + ); + + if (f.has_mapping()) { + const double map_determinant = f.mapping->ComputeDetJ( + *transformation, integration_point + ); + MFEM_VERIFY( + map_determinant > 0.0, + "Domain mapping has a non-positive Jacobian " + "determinant." + ); + + weight *= map_determinant; + f.mapping->ComputeJacobian(*transformation, map_jacobian); + + map_jacobian.Mult( + left_gradient_element, left_gradient_physical + ); + map_jacobian.Mult( + right_gradient_element, right_gradient_physical + ); + + left_gradient_physical /= map_determinant; + right_gradient_physical /= map_determinant; + } else { + left_gradient_physical = left_gradient_element; + right_gradient_physical = right_gradient_element; + } + + gradient_difference = left_gradient_physical; + gradient_difference -= right_gradient_physical; + + local_gradient_difference_squared += + (gradient_difference * gradient_difference) * weight; + local_left_gradient_norm_squared += + (left_gradient_physical * left_gradient_physical) * weight; + local_right_gradient_norm_squared += + (right_gradient_physical * right_gradient_physical) * + weight; + + const double left_potential = + left_solution.phi.GetValue(element_id, integration_point); + const double right_potential = + right_solution.phi.GetValue(element_id, integration_point); + const double potential_difference = + left_potential - right_potential; + + local_potential_difference_squared += + potential_difference * potential_difference * weight; + local_left_potential_norm_squared += + left_potential * left_potential * weight; + local_right_potential_norm_squared += + right_potential * right_potential * weight; + } + } + + const std::array local_values{ + local_gradient_difference_squared, + local_left_gradient_norm_squared, + local_right_gradient_norm_squared, + local_potential_difference_squared, + local_left_potential_norm_squared, + local_right_potential_norm_squared + }; + + std::array global_values{}; + + MPI_Allreduce( + local_values.data(), global_values.data(), + static_cast(local_values.size()), MPI_DOUBLE, MPI_SUM, + f.densityFes->GetComm() + ); + + const double gradient_scale_squared = + 0.5 * (global_values[1] + global_values[2]); + const double potential_scale_squared = + 0.5 * (global_values[4] + global_values[5]); + + MFEM_VERIFY( + gradient_scale_squared > 0.0, + "Cannot compare gravity solutions with zero gradient norm." + ); + MFEM_VERIFY( + potential_scale_squared > 0.0, + "Cannot compare gravity solutions with zero potential norm." + ); + + return { + .relative_gradient_difference = + std::sqrt(global_values[0] / gradient_scale_squared), + .relative_potential_difference = + std::sqrt(global_values[3] / potential_scale_squared) + }; + } + + struct GravityResidualMetrics { + double relative_total; + double relative_gradient; + double relative_poisson; + }; + + double gravity_test_global_norm( + const mfem::Vector &vector, + MPI_Comm communicator + ) { + const double local_norm_squared = vector * vector; + double global_norm_squared = 0.0; + MPI_Allreduce( + &local_norm_squared, &global_norm_squared, 1, MPI_DOUBLE, MPI_SUM, + communicator + ); + return std::sqrt(global_norm_squared); + } + + void gravity_test_get_true_dofs( + const mfem::ParFiniteElementSpace &finite_element_space, + const mfem::GridFunction &grid_function, + mfem::Vector &true_dofs + ) { + MFEM_VERIFY( + grid_function.Size() == finite_element_space.GetVSize(), + "Grid function has the wrong local size." + ); + + true_dofs.SetSize(finite_element_space.GetTrueVSize()); + + const mfem::Operator *restriction = + finite_element_space.GetRestrictionMatrix(); + + if (restriction != nullptr) { + restriction->Mult(grid_function, true_dofs); + } else { + MFEM_VERIFY( + grid_function.Size() == true_dofs.Size(), + "Local and true sizes do not match." + ); + true_dofs = grid_function; + } + } + + GravityResidualMetrics measure_gravity_residual( + const mfem::Vector &residual, + const mfem::Array &offsets, + const double right_hand_side_norm, + MPI_Comm communicator + ) { + MFEM_VERIFY( + offsets.Size() == 3, "Gravity residual must contain two blocks." + ); + MFEM_VERIFY( + residual.Size() == offsets.Last(), + "Gravity residual has the wrong size." + ); + MFEM_VERIFY( + right_hand_side_norm > 0.0, + "Gravity right-hand side must be nonzero." + ); + + mfem::Vector gradient_residual(offsets[1] - offsets[0]); + mfem::Vector poisson_residual(offsets[2] - offsets[1]); + + for (int i = 0; i < gradient_residual.Size(); ++i) { + gradient_residual(i) = residual(offsets[0] + i); + } + + for (int i = 0; i < poisson_residual.Size(); ++i) { + poisson_residual(i) = residual(offsets[1] + i); + } + + return { + .relative_total = gravity_test_global_norm(residual, communicator) / + right_hand_side_norm, + .relative_gradient = + gravity_test_global_norm(gradient_residual, communicator) / + right_hand_side_norm, + .relative_poisson = + gravity_test_global_norm(poisson_residual, communicator) / + right_hand_side_norm + }; + } + + enum class ExteriorMonopoleMapping { legacy, stateless }; + + struct ExteriorMonopoleShellMetrics { + long long quadrature_points{0}; + double minimum_radius{std::numeric_limits::infinity()}; + double maximum_radius{0.0}; + double potential_rms_error{0.0}; + double radial_field_rms_error{0.0}; + double tangential_field_rms{0.0}; + }; + + struct ExteriorMonopoleShellAccumulator { + long long quadrature_points{0}; + double minimum_radius{std::numeric_limits::infinity()}; + double maximum_radius{0.0}; + double reference_weight{0.0}; + double potential_error_squared{0.0}; + double radial_field_error_squared{0.0}; + double tangential_field_squared{0.0}; + }; + + constexpr std::array exterior_shell_boundaries{0.0, 0.25, 0.50, + 0.75, 0.90, 1.0}; + + int get_exterior_shell(const double compactification_coordinate) { + REQUIRE(std::isfinite(compactification_coordinate)); + REQUIRE(compactification_coordinate >= -1.0e-12); + REQUIRE(compactification_coordinate <= 1.0 + 1.0e-12); + + const double coordinate = std::clamp( + compactification_coordinate, 0.0, std::nextafter(1.0, 0.0) + ); + + for (int shell = 0; + shell < static_cast(exterior_shell_boundaries.size()) - 1; + ++shell) { + if (coordinate < exterior_shell_boundaries[shell + 1]) { + return shell; + } + } + + return static_cast(exterior_shell_boundaries.size()) - 2; + } + + std::array< + ExteriorMonopoleShellMetrics, + 5> + measure_exterior_monopole_shells( + fem::FEM &f, + const physics::GravitySolution &solution, + const mfem::GridFunction &displacement, + const ExteriorMonopoleMapping mapping_path, + const double mass + ) { + REQUIRE(f.mesh != nullptr); + REQUIRE(f.gravityFluxFes != nullptr); + REQUIRE(f.displacementFes != nullptr); + REQUIRE(f.compactificationFes != nullptr); + REQUIRE(f.compactificationCoordinate != nullptr); + REQUIRE(f.mapping != nullptr); + REQUIRE(f.domainMapperStateless != nullptr); + + constexpr int shell_count = + static_cast(exterior_shell_boundaries.size()) - 1; + + std::array + local_shells{}; + + mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + const int vacuum_attribute = + f.domainMapperStateless->GetVacuumElementAttribute(); + + const int quadrature_order = get_gravity_quadrature_order(f); + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + + REQUIRE(transformation != nullptr); + + if (transformation->Attribute != vacuum_attribute) { + continue; + } + + const mfem::FiniteElement &displacement_element = + *f.displacementFes->GetFE(element_id); + + const mfem::FiniteElement &compactification_element = + *f.compactificationFes->GetFE(element_id); + + mfem::Array displacement_dofs; + mfem::Array compactification_dofs; + + mfem::DofTransformation *displacement_dof_transformation = + f.displacementFes->GetElementVDofs( + element_id, displacement_dofs + ); + + mfem::DofTransformation *compactification_dof_transformation = + f.compactificationFes->GetElementDofs( + element_id, compactification_dofs + ); + + mfem::Vector element_displacement; + mfem::Vector element_compactification; + + displacement.GetSubVector(displacement_dofs, element_displacement); + + f.compactificationCoordinate->GetSubVector( + compactification_dofs, element_compactification + ); + + if (displacement_dof_transformation != nullptr) { + displacement_dof_transformation->InvTransformPrimal( + element_displacement + ); + } + + if (compactification_dof_transformation != nullptr) { + compactification_dof_transformation->InvTransformPrimal( + element_compactification + ); + } + + const mapping::ElementDisplacementData displacement_data( + displacement_element, element_displacement, + f.displacementFes->GetOrdering() + ); + + const mapping::ElementCompactificationData compactification_data( + compactification_element, element_compactification + ); + + const mapping::ElementMappingData mapping_data{ + .displacement = displacement_data, + .compactification = compactification_data + }; + + mfem::Vector compactification_shape( + compactification_element.GetDof() + ); + + const mfem::IntegrationRule &integration_rule = mfem::IntRules.Get( + transformation->GetGeometryType(), quadrature_order + ); + + for (int q = 0; q < integration_rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); + + transformation->SetIntPoint(&integration_point); + + compactification_element.CalcShape( + integration_point, compactification_shape + ); + + const double compactification_coordinate = + element_compactification * compactification_shape; + + const int shell = + get_exterior_shell(compactification_coordinate); + + mfem::Vector reference_field(3); + mfem::Vector physical_field(3); + mfem::Vector physical_position(3); + + solution.gradPhi.GetVectorValue( + element_id, integration_point, reference_field + ); + + if (mapping_path == ExteriorMonopoleMapping::stateless) { + mapping::VolumeMappingContext mapping_context; + + const mapping::MappingStatus status = + f.domainMapperStateless->EvaluateVolume( + mapping_data, *transformation, integration_point, + workspace, mapping_context + ); + + CAPTURE( + element_id, q, compactification_coordinate, + static_cast(status) + ); + + REQUIRE( + status == mean_field::mapping::MappingStatus::valid + ); + + physical_position = + mapping_context.mapping.physical_position; + + mean_field::mapping::MapHDivFluxToPhysical( + mapping_context.mapping, reference_field, physical_field + ); + } else { + /* + * The legacy path intentionally does not use the exterior + * coordinate to construct its physical mapping. + */ + f.mapping->GetPhysicalPoint( + *transformation, integration_point, physical_position + ); + + mfem::DenseMatrix mapping_jacobian(3); + f.mapping->ComputeJacobian( + *transformation, mapping_jacobian + ); + + const double mapping_determinant = mapping_jacobian.Det(); + + REQUIRE(std::isfinite(mapping_determinant)); + REQUIRE(mapping_determinant > 0.0); + + mapping_jacobian.Mult(reference_field, physical_field); + + physical_field /= mapping_determinant; + } + + const double radius = physical_position.Norml2(); + + CAPTURE( + element_id, q, shell, compactification_coordinate, radius + ); + + REQUIRE(std::isfinite(radius)); + REQUIRE(radius > 0.0); + + mfem::Vector radial_unit_vector(physical_position); + radial_unit_vector /= radius; + + const double numerical_radial_field = + physical_field * radial_unit_vector; + + mfem::Vector tangential_field(physical_field); + tangential_field.Add( + -numerical_radial_field, radial_unit_vector + ); + + const double numerical_potential = + solution.phi.GetValue(element_id, integration_point); + + /* + * For an exterior monopole: + * + * phi = -GM/r + * grad(phi) = GM r_hat/r^2 + * + * These scaled quantities should therefore be one, one, and + * zero respectively. They remain well-conditioned as r -> inf. + */ + const double scaled_potential = + -radius * numerical_potential / (utils::G * mass); + + const double scaled_radial_field = radius * radius * + numerical_radial_field / + (utils::G * mass); + + const double scaled_tangential_field = + radius * radius * tangential_field.Norml2() / + (utils::G * mass); + + REQUIRE(std::isfinite(scaled_potential)); + REQUIRE(std::isfinite(scaled_radial_field)); + REQUIRE(std::isfinite(scaled_tangential_field)); + + /* + * Use the finite reference-domain measure for averaging. A + * physical L2 norm of phi over an infinite three-dimensional + * exterior domain is not finite. + */ + const double reference_weight = + integration_point.weight * transformation->Weight(); + + ExteriorMonopoleShellAccumulator &accumulator = + local_shells[shell]; + + ++accumulator.quadrature_points; + + accumulator.minimum_radius = + std::min(accumulator.minimum_radius, radius); + + accumulator.maximum_radius = + std::max(accumulator.maximum_radius, radius); + + accumulator.reference_weight += reference_weight; + + accumulator.potential_error_squared += + reference_weight * std::pow(scaled_potential - 1.0, 2); + + accumulator.radial_field_error_squared += + reference_weight * std::pow(scaled_radial_field - 1.0, 2); + + accumulator.tangential_field_squared += + reference_weight * scaled_tangential_field * + scaled_tangential_field; + } + } + + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + std::array metrics{}; + + for (int shell = 0; shell < shell_count; ++shell) { + long long global_points = 0; + + MPI_Allreduce( + &local_shells[shell].quadrature_points, &global_points, 1, + MPI_LONG_LONG, MPI_SUM, communicator + ); + + double local_sums[4]{ + local_shells[shell].reference_weight, + local_shells[shell].potential_error_squared, + local_shells[shell].radial_field_error_squared, + local_shells[shell].tangential_field_squared + }; + + double global_sums[4]{}; + + MPI_Allreduce( + local_sums, global_sums, 4, MPI_DOUBLE, MPI_SUM, communicator + ); + + double global_minimum_radius = 0.0; + double global_maximum_radius = 0.0; + + MPI_Allreduce( + &local_shells[shell].minimum_radius, &global_minimum_radius, 1, + MPI_DOUBLE, MPI_MIN, communicator + ); + + MPI_Allreduce( + &local_shells[shell].maximum_radius, &global_maximum_radius, 1, + MPI_DOUBLE, MPI_MAX, communicator + ); + + REQUIRE(global_points > 0); + REQUIRE(global_sums[0] > 0.0); + + metrics[shell] = { + .quadrature_points = global_points, + .minimum_radius = global_minimum_radius, + .maximum_radius = global_maximum_radius, + .potential_rms_error = + std::sqrt(global_sums[1] / global_sums[0]), + .radial_field_rms_error = + std::sqrt(global_sums[2] / global_sums[0]), + .tangential_field_rms = + std::sqrt(global_sums[3] / global_sums[0]) + }; + } + + return metrics; + } + + class StatelessProjectionGeometry { + public: + StatelessProjectionGeometry( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::GridFunction &displacement + ) + : m_fem(f), + m_domain_mapper(domain_mapper), + m_displacement(displacement), + m_workspace(f.mesh->Dimension()) { + } + + mapping::MappingStatus Evaluate( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + mapping::MappingPointContext &context, + const bool permit_infinity_limit + ) { + m_last_evaluation_used_infinity_limit = false; + + const int element_id = transformation.ElementNo; + + MFEM_VERIFY( + element_id >= 0, + "Projection coefficient received an invalid element number." + ); + + const mfem::FiniteElement &displacement_element = + *m_fem.displacementFes->GetFE(element_id); + + const mfem::FiniteElement &compactification_element = + *m_fem.compactificationFes->GetFE(element_id); + + mfem::Array displacement_dofs; + mfem::Array compactification_dofs; + + mfem::DofTransformation *displacement_dof_transformation = + m_fem.displacementFes->GetElementVDofs( + element_id, displacement_dofs + ); + + mfem::DofTransformation *compactification_dof_transformation = + m_fem.compactificationFes->GetElementDofs( + element_id, compactification_dofs + ); + + mfem::Vector element_displacement; + mfem::Vector element_compactification; + + m_displacement.GetSubVector( + displacement_dofs, element_displacement + ); + + m_fem.compactificationCoordinate->GetSubVector( + compactification_dofs, element_compactification + ); + + if (displacement_dof_transformation != nullptr) { + displacement_dof_transformation->InvTransformPrimal( + element_displacement + ); + } + + if (compactification_dof_transformation != nullptr) { + compactification_dof_transformation->InvTransformPrimal( + element_compactification + ); + } + + const mapping::ElementDisplacementData displacement_data( + displacement_element, element_displacement, + m_fem.displacementFes->GetOrdering() + ); + + const mapping::ElementCompactificationData compactification_data( + compactification_element, element_compactification + ); + + mfem::Vector requested_compactification_shape( + compactification_element.GetDof() + ); + + compactification_element.CalcShape( + integration_point, requested_compactification_shape + ); + + const double requested_compactification_coordinate = + element_compactification * requested_compactification_shape; + + constexpr double infinity_candidate_tolerance = 1.0e-8; + + const bool requested_infinity_limit = + std::isfinite(requested_compactification_coordinate) && + requested_compactification_coordinate >= + 1.0 - infinity_candidate_tolerance; + + const mapping::ElementMappingData mapping_data{ + .displacement = displacement_data, + .compactification = compactification_data + }; + + mapping::MappingStatus status = m_domain_mapper.EvaluatePoint( + mapping_data, transformation, integration_point, m_workspace, + context + ); + + if (status == mapping::MappingStatus::valid) { + transformation.SetIntPoint(&integration_point); + return status; + } + + if (!permit_infinity_limit || + !m_domain_mapper.IsCompactifiedElement(transformation)) { + transformation.SetIntPoint(&integration_point); + return status; + } + + const bool retryable_boundary_status = + status == mapping::MappingStatus::at_compactified_infinity || + status == mapping::MappingStatus::outside_reference_domain || + status == mapping::MappingStatus::non_finite_result || + (requested_infinity_limit && + status == mapping::MappingStatus::non_positive_determinant); + + if (!retryable_boundary_status) { + transformation.SetIntPoint(&integration_point); + return status; + } + + const mfem::IntegrationPoint &element_center = + mfem::Geometries.GetCenter(transformation.GetGeometryType()); + + /* + * Use the nearest admissible point. Starting extremely close to + * the requested point preserves the limiting RT trace, while the + * larger fallbacks accommodate the mapper's infinity guard. + */ + constexpr std::array inward_fractions{ + 1.0e-12, 1.0e-11, 1.0e-10, 1.0e-9, 1.0e-8, + 1.0e-7, 1.0e-6, 1.0e-5, 1.0e-4 + }; + + for (const double inward_fraction : inward_fractions) { + mfem::IntegrationPoint inward_point; + + inward_point.x = (1.0 - inward_fraction) * integration_point.x + + inward_fraction * element_center.x; + + inward_point.y = (1.0 - inward_fraction) * integration_point.y + + inward_fraction * element_center.y; + + inward_point.z = (1.0 - inward_fraction) * integration_point.z + + inward_fraction * element_center.z; + + inward_point.weight = integration_point.weight; + + status = m_domain_mapper.EvaluatePoint( + mapping_data, transformation, inward_point, m_workspace, + context + ); + + if (status == mapping::MappingStatus::valid) { + m_last_evaluation_used_infinity_limit = true; + transformation.SetIntPoint(&integration_point); + return status; + } + + const bool still_retryable = + status == + mapping::MappingStatus::at_compactified_infinity || + status == + mapping::MappingStatus::outside_reference_domain || + status == mapping::MappingStatus::non_finite_result || + (requested_infinity_limit && + status == + mapping::MappingStatus::non_positive_determinant); + if (!still_retryable) { + break; + } + } + + transformation.SetIntPoint(&integration_point); + return status; + } + + [[nodiscard]] + bool LastEvaluationUsedInfinityLimit() const noexcept { + return m_last_evaluation_used_infinity_limit; + } + + private: + const fem::FEM &m_fem; + const mapping::DomainMapperStateless &m_domain_mapper; + const mfem::GridFunction &m_displacement; + mapping::DomainMapperStateless::Workspace m_workspace; + bool m_last_evaluation_used_infinity_limit{false}; + }; + class StatelessMonopolePotentialCoefficient final + : public mfem::Coefficient { + public: + StatelessMonopolePotentialCoefficient( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::GridFunction &displacement, + const double mass, + const double stellar_radius + ) + : m_geometry( + f, + domain_mapper, + displacement + ), + m_vacuum_attribute(domain_mapper.GetVacuumElementAttribute()), + m_mass(mass), + m_stellar_radius(stellar_radius) { + } + + double Eval( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point + ) override { + mapping::MappingPointContext context; + + const mapping::MappingStatus status = m_geometry.Evaluate( + transformation, integration_point, context, true + ); + + MFEM_VERIFY( + status == mean_field::mapping::MappingStatus::valid, + "Stateless monopole-potential projection failed." + << "\nMapping status = " << static_cast(status) + << "\nElement ID = " << transformation.ElementNo + << "\nElement attribute = " << transformation.Attribute + << "\nIntegration point = <" << integration_point.x << ", " + << integration_point.y << ", " << integration_point.z << ">" + ); + + if (m_geometry.LastEvaluationUsedInfinityLimit()) { + return 0.0; + } + + const double radius = context.physical_position.Norml2(); + + MFEM_VERIFY( + std::isfinite(radius) && radius > 0.0, + "Monopole projection encountered an invalid physical radius." + ); + + if (transformation.Attribute == m_vacuum_attribute) { + return -utils::G * m_mass / radius; + } + + return -utils::G * m_mass / + (2.0 * m_stellar_radius * m_stellar_radius * + m_stellar_radius) * + (3.0 * m_stellar_radius * m_stellar_radius - + radius * radius); + } + + private: + StatelessProjectionGeometry m_geometry; + int m_vacuum_attribute; + double m_mass; + double m_stellar_radius; + }; + + class StatelessMonopoleHDivCoefficient final + : public mfem::VectorCoefficient { + public: + StatelessMonopoleHDivCoefficient( + const fem::FEM &f, + const mapping::DomainMapperStateless &domain_mapper, + const mfem::GridFunction &displacement, + const double mass, + const double stellar_radius + ) + : VectorCoefficient(f.mesh->Dimension()), + m_geometry( + f, + domain_mapper, + displacement + ), + m_vacuum_attribute(domain_mapper.GetVacuumElementAttribute()), + m_mass(mass), + m_stellar_radius(stellar_radius) { + } + + void Eval( + mfem::Vector &value, + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point + ) override { + mapping::MappingPointContext context; + + const mapping::MappingStatus status = m_geometry.Evaluate( + transformation, integration_point, context, true + ); + + MFEM_VERIFY( + status == mean_field::mapping::MappingStatus::valid, + "Stateless monopole H(div) projection failed." + << "\nMapping status = " << static_cast(status) + << "\nElement ID = " << transformation.ElementNo + << "\nElement attribute = " << transformation.Attribute + << "\nIntegration point = <" << integration_point.x << ", " + << integration_point.y << ", " << integration_point.z << ">" + << "\nInfinity-limit evaluation attempted = " + << m_geometry.LastEvaluationUsedInfinityLimit() + ); + const mfem::Vector &displaced_position = context.displaced_position; + + const double computational_radius = displaced_position.Norml2(); + + MFEM_VERIFY( + std::isfinite(computational_radius) && + computational_radius > 0.0, + "Monopole H(div) projection encountered an invalid displaced " + "computational radius." + ); + + const double displacement_determinant = + context.displacement_jacobian.Det(); + + MFEM_VERIFY( + std::isfinite(displacement_determinant) && + displacement_determinant > 0.0, + "Monopole H(div) projection encountered an invalid " + "displacement " + "Jacobian determinant." + ); + + mfem::DenseMatrix inverse_displacement_jacobian; + + inverse_displacement_jacobian.SetSize( + context.displacement_jacobian.Height(), + context.displacement_jacobian.Width() + ); + + mfem::CalcInverse( + context.displacement_jacobian, inverse_displacement_jacobian + ); + + /* + * Pull the radial field back only through the regular displacement + * map. + * + * In the compactified vacuum, the Kelvin scale and its radial + * derivative cancel exactly from the three-dimensional H(div) Piola + * pullback of the inverse-square monopole field: + * + * det(J) J^{-1} (GM x / |x|^3) + * = GM det(A) A^{-1} y / |y|^3. + * + * This is also the finite reference-space limit at compactified + * infinity. + */ + inverse_displacement_jacobian.Mult(displaced_position, value); + + double radial_denominator = 0.0; + + if (transformation.Attribute == m_vacuum_attribute) { + radial_denominator = computational_radius * + computational_radius * + computational_radius; + } else { + radial_denominator = + m_stellar_radius * m_stellar_radius * m_stellar_radius; + } + + value *= mean_field::utils::G * m_mass * displacement_determinant / + radial_denominator; + + for (int component = 0; component < value.Size(); ++component) { + MFEM_VERIFY( + std::isfinite(value(component)), + "Monopole H(div) projection produced a non-finite " + "reference flux." + ); + } + } + + private: + StatelessProjectionGeometry m_geometry; + int m_vacuum_attribute; + double m_mass; + double m_stellar_radius; + }; + +} // namespace + +TEST_CASE( + "Uniform Potential Matches Analytic", + tags::gravity &tags::analytic_comparison &tags::initialization +) { + auto args = test_utils::setup_args(); fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); f.mapping->ResetDisplacement(); physics::update_stiffness_matrix(f); - const double radius = utils::RADIUS; - const double mass = utils::MASS; + const double radius = utils::RADIUS; + const double mass = utils::MASS; const double analytic_volume = (4.0 / 3.0) * M_PI * std::pow(radius, 3.0); - const double density = mass / analytic_volume; + const double density = mass / analytic_volume; - mfem::GridFunction rho_uniform(f.L2_fes.get()); + mfem::GridFunction rho_uniform(f.densityFes.get()); rho_uniform = density; zero_vacuum_density(f, rho_uniform); analysis::conserve_mass(f, rho_uniform, mass); f.com = analysis::get_com(f, rho_uniform); - f.Q = physics::compute_quadrupole_moment_tensor(f, rho_uniform, f.com); + f.Q = physics::compute_quadrupole_moment_tensor(f, rho_uniform, f.com); const auto gravity_solution = physics::grav_potential(f, args, rho_uniform); - constexpr double potential_tolerance = utils::APPROX_MAX_ACCEPTABLE_POTENTIAL_ERROR_SI_BURNING; - double local_max_abs_error = 0.0; - double local_max_rel_error = 0.0; + constexpr double potential_tolerance = + utils::APPROX_MAX_ACCEPTABLE_POTENTIAL_ERROR_SI_BURNING; + double local_max_abs_error = 0.0; + double local_max_rel_error = 0.0; const int num_elements_to_test = std::min(30, f.mesh->GetNE()); for (int elem_id = 0; elem_id < num_elements_to_test; ++elem_id) { - mfem::ElementTransformation* transformation = f.mesh->GetElementTransformation(elem_id); - const mfem::IntegrationRule& integration_rule = mfem::IntRules.Get(transformation->GetGeometryType(), 2); - const mfem::IntegrationPoint& integration_point = integration_rule.IntPoint(0); + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(elem_id); + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 2); + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(0); transformation->SetIntPoint(&integration_point); mfem::Vector x_physical; - f.mapping->GetPhysicalPoint(*transformation, integration_point, x_physical); + f.mapping->GetPhysicalPoint( + *transformation, integration_point, x_physical + ); const double radial_coordinate = x_physical.Norml2(); if (radial_coordinate < 1.0e-9) { continue; } - const double phi_analytic = -(utils::G * mass / (2.0 * std::pow(radius, 3.0))) * - (3.0 * radius * radius - radial_coordinate * radial_coordinate); - const double phi_fem = gravity_solution.phi.GetValue(elem_id, integration_point); + const double phi_analytic = + -(utils::G * mass / (2.0 * std::pow(radius, 3.0))) * + (3.0 * radius * radius - radial_coordinate * radial_coordinate); + const double phi_fem = + gravity_solution.phi.GetValue(elem_id, integration_point); const double absolute_error = std::abs(phi_fem - phi_analytic); const double relative_error = absolute_error / std::abs(phi_analytic); local_max_abs_error = std::max(local_max_abs_error, absolute_error); local_max_rel_error = std::max(local_max_rel_error, relative_error); - CHECK_THAT(relative_error, Catch::Matchers::WithinAbs(0.0, 0.1 * potential_tolerance)); + CHECK_THAT( + relative_error, + Catch::Matchers::WithinAbs(0.0, 0.1 * potential_tolerance) + ); } double global_max_abs_error = 0.0; double global_max_rel_error = 0.0; - MPI_Comm communicator = f.L2_fes->GetComm(); - MPI_Allreduce(&local_max_abs_error, &global_max_abs_error, 1, MPI_DOUBLE, MPI_MAX, communicator); - MPI_Allreduce(&local_max_rel_error, &global_max_rel_error, 1, MPI_DOUBLE, MPI_MAX, communicator); + MPI_Comm communicator = f.densityFes->GetComm(); + MPI_Allreduce( + &local_max_abs_error, &global_max_abs_error, 1, MPI_DOUBLE, MPI_MAX, + communicator + ); + MPI_Allreduce( + &local_max_rel_error, &global_max_rel_error, 1, MPI_DOUBLE, MPI_MAX, + communicator + ); - const int quadrature_order = get_gravity_quadrature_order(f); - const GravitationalEnergies energies = compute_gravitational_energies(f, rho_uniform, gravity_solution, quadrature_order); - const double analytic_binding_energy = -(3.0 / 5.0) * utils::G * mass * mass / radius; - const double relative_binding_error = std::abs(energies.binding - analytic_binding_energy) / std::abs(analytic_binding_energy); - const double relative_virial_error = std::abs(energies.virial - analytic_binding_energy) / std::abs(analytic_binding_energy); - const double relative_consistency_error = std::abs(energies.binding - energies.virial) / std::abs(energies.binding); + const int quadrature_order = get_gravity_quadrature_order(f); + const GravitationalEnergies energies = compute_gravitational_energies( + f, rho_uniform, gravity_solution, quadrature_order + ); + const double analytic_binding_energy = + -(3.0 / 5.0) * utils::G * mass * mass / radius; + const double relative_binding_error = + std::abs(energies.binding - analytic_binding_energy) / + std::abs(analytic_binding_energy); + const double relative_virial_error = + std::abs(energies.virial - analytic_binding_energy) / + std::abs(analytic_binding_energy); + const double relative_consistency_error = + std::abs(energies.binding - energies.virial) / + std::abs(energies.binding); INFO("Analytic binding energy = " << analytic_binding_energy); INFO("Computed binding energy = " << energies.binding); INFO("Computed virial energy = " << energies.virial); INFO("Relative virial consistency error = " << relative_consistency_error); - constexpr double energy_tolerance = 1.0e-5; + constexpr double energy_tolerance = 1.0e-5; constexpr double consistency_tolerance = 1.0e-6; - CHECK_THAT(global_max_rel_error, Catch::Matchers::WithinAbs(0.0, 0.1 * potential_tolerance)); - CHECK_THAT(global_max_abs_error, Catch::Matchers::WithinAbs(0.0, 0.1 * potential_tolerance)); - CHECK_THAT(relative_binding_error, Catch::Matchers::WithinAbs(0.0, energy_tolerance)); - CHECK_THAT(relative_virial_error, Catch::Matchers::WithinAbs(0.0, energy_tolerance)); - CHECK_THAT(relative_consistency_error, Catch::Matchers::WithinAbs(0.0, consistency_tolerance)); + CHECK_THAT( + global_max_rel_error, + Catch::Matchers::WithinAbs(0.0, 0.1 * potential_tolerance) + ); + CHECK_THAT( + global_max_abs_error, + Catch::Matchers::WithinAbs(0.0, 0.1 * potential_tolerance) + ); + CHECK_THAT( + relative_binding_error, + Catch::Matchers::WithinAbs(0.0, energy_tolerance) + ); + CHECK_THAT( + relative_virial_error, Catch::Matchers::WithinAbs(0.0, energy_tolerance) + ); + CHECK_THAT( + relative_consistency_error, + Catch::Matchers::WithinAbs(0.0, consistency_tolerance) + ); } -TEST_CASE("Parabolic Density Virial Self-Consistency", tags::gravity & tags::analytic_comparison) { - auto args = test_utils::setup_args(); +TEST_CASE( + "Parabolic Density Virial Self-Consistency", + tags::gravity &tags::analytic_comparison &tags::initialization +) { + auto args = test_utils::setup_args(); fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); f.mapping->ResetDisplacement(); physics::update_stiffness_matrix(f); const double radius = utils::RADIUS; - const double mass = utils::MASS; - const double central_density = (15.0 * mass) / (8.0 * M_PI * std::pow(radius, 3.0)); + const double mass = utils::MASS; + const double central_density = + (15.0 * mass) / (8.0 * M_PI * std::pow(radius, 3.0)); - auto parabolic_rho = [central_density, radius](const mfem::Vector& x) { + auto parabolic_rho = [central_density, radius](const mfem::Vector &x) { const double radial_coordinate = x.Norml2(); - return central_density * (1.0 - radial_coordinate * radial_coordinate / (radius * radius)); + return central_density * (1.0 - radial_coordinate * radial_coordinate / + (radius * radius)); }; std::unique_ptr rho_coeff; if (f.has_mapping()) { - rho_coeff = std::make_unique(*f.mapping, parabolic_rho); + rho_coeff = + std::make_unique( + *f.mapping, parabolic_rho + ); } else { rho_coeff = std::make_unique(parabolic_rho); } - mfem::GridFunction rho_grid(f.L2_fes.get()); + mfem::GridFunction rho_grid(f.densityFes.get()); rho_grid.ProjectCoefficient(*rho_coeff); zero_vacuum_density(f, rho_grid); analysis::conserve_mass(f, rho_grid, mass); f.com = analysis::get_com(f, rho_grid); - f.Q = physics::compute_quadrupole_moment_tensor(f, rho_grid, f.com); + f.Q = physics::compute_quadrupole_moment_tensor(f, rho_grid, f.com); const auto gravity_solution = physics::grav_potential(f, args, rho_grid); - const int quadrature_order = get_gravity_quadrature_order(f); - const GravitationalEnergies energies = compute_gravitational_energies(f, rho_grid, gravity_solution, quadrature_order); - const double analytic_binding_energy = -(5.0 / 7.0) * utils::G * mass * mass / radius; - const double relative_binding_error = std::abs(energies.binding - analytic_binding_energy) / std::abs(analytic_binding_energy); - const double relative_virial_error = std::abs(energies.virial - analytic_binding_energy) / std::abs(analytic_binding_energy); - const double relative_consistency_error = std::abs(energies.binding - energies.virial) / std::abs(energies.binding); + const int quadrature_order = get_gravity_quadrature_order(f); + const GravitationalEnergies energies = compute_gravitational_energies( + f, rho_grid, gravity_solution, quadrature_order + ); + const double analytic_binding_energy = + -(5.0 / 7.0) * utils::G * mass * mass / radius; + const double relative_binding_error = + std::abs(energies.binding - analytic_binding_energy) / + std::abs(analytic_binding_energy); + const double relative_virial_error = + std::abs(energies.virial - analytic_binding_energy) / + std::abs(analytic_binding_energy); + const double relative_consistency_error = + std::abs(energies.binding - energies.virial) / + std::abs(energies.binding); INFO("Analytic binding energy = " << analytic_binding_energy); INFO("Computed binding energy = " << energies.binding); INFO("Computed virial energy = " << energies.virial); INFO("Relative virial consistency error = " << relative_consistency_error); - constexpr double analytic_tolerance = 1.0e-5; + constexpr double analytic_tolerance = 1.0e-5; constexpr double consistency_tolerance = 1.0e-6; - CHECK_THAT(relative_binding_error, Catch::Matchers::WithinAbs(0.0, analytic_tolerance)); - CHECK_THAT(relative_virial_error, Catch::Matchers::WithinAbs(0.0, analytic_tolerance)); - CHECK_THAT(relative_consistency_error, Catch::Matchers::WithinAbs(0.0, consistency_tolerance)); + CHECK_THAT( + relative_binding_error, + Catch::Matchers::WithinAbs(0.0, analytic_tolerance) + ); + CHECK_THAT( + relative_virial_error, + Catch::Matchers::WithinAbs(0.0, analytic_tolerance) + ); + CHECK_THAT( + relative_consistency_error, + Catch::Matchers::WithinAbs(0.0, consistency_tolerance) + ); } -TEST_CASE("Rational Density Virial Self-Consistency", tags::gravity & tags::self_consistency) { - auto args = test_utils::setup_args(); +TEST_CASE( + "Rational Density Virial Self-Consistency", + tags::gravity &tags::self_consistency &tags::initialization +) { + auto args = test_utils::setup_args(); fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); f.mapping->ResetDisplacement(); physics::update_stiffness_matrix(f); - const double radius = utils::RADIUS; - const double mass = utils::MASS; + const double radius = utils::RADIUS; + const double mass = utils::MASS; - // Larger values are more centrally concentrated and generally harder for a polynomial to represent. - // A regression would be considered if this test does not pass for concentrations <= 16.0. + // Larger values are more centrally concentrated and generally harder for a + // polynomial to represent. A regression would be considered if this test + // does not pass for concentrations <= 16.0. constexpr double concentration = 16.0; - const double density_scale = mass / std::pow(radius, 3.0); + const double density_scale = mass / std::pow(radius, 3.0); - auto rational_rho = [radius, density_scale](const mfem::Vector& x) { + auto rational_rho = [radius, density_scale](const mfem::Vector &x) { const double normalized_radius_squared = (x * x) / (radius * radius); if (normalized_radius_squared >= 1.0) { return 0.0; } - const double denominator = 1.0 + concentration * normalized_radius_squared; - return density_scale * (1.0 - normalized_radius_squared) / (denominator * denominator); + const double denominator = + 1.0 + concentration * normalized_radius_squared; + return density_scale * (1.0 - normalized_radius_squared) / + (denominator * denominator); }; std::unique_ptr rho_coeff; if (f.has_mapping()) { - rho_coeff = std::make_unique(*f.mapping, rational_rho); + rho_coeff = + std::make_unique( + *f.mapping, rational_rho + ); } else { rho_coeff = std::make_unique(rational_rho); } - mfem::GridFunction rho_grid(f.L2_fes.get()); + mfem::GridFunction rho_grid(f.densityFes.get()); rho_grid.ProjectCoefficient(*rho_coeff); zero_vacuum_density(f, rho_grid); analysis::conserve_mass(f, rho_grid, mass); f.com = analysis::get_com(f, rho_grid); - f.Q = physics::compute_quadrupole_moment_tensor(f, rho_grid, f.com); + f.Q = physics::compute_quadrupole_moment_tensor(f, rho_grid, f.com); const auto gravity_solution = physics::grav_potential(f, args, rho_grid); - const int quadrature_order = get_gravity_quadrature_order(f); - const GravitationalEnergies energies = compute_gravitational_energies(f, rho_grid, gravity_solution, quadrature_order); + const int quadrature_order = get_gravity_quadrature_order(f); + const GravitationalEnergies energies = compute_gravitational_energies( + f, rho_grid, gravity_solution, quadrature_order + ); REQUIRE(energies.binding < 0.0); REQUIRE(energies.virial < 0.0); - const double relative_consistency_error = std::abs(energies.binding - energies.virial) / std::abs(energies.binding); + const double relative_consistency_error = + std::abs(energies.binding - energies.virial) / + std::abs(energies.binding); INFO("W_bind = " << energies.binding); INFO("W_vir = " << energies.virial); INFO("Relative virial consistency error = " << relative_consistency_error); constexpr double virial_tolerance = 1.0e-5; - CHECK_THAT(relative_consistency_error, Catch::Matchers::WithinAbs(0.0, virial_tolerance)); + CHECK_THAT( + relative_consistency_error, + Catch::Matchers::WithinAbs(0.0, virial_tolerance) + ); } -TEST_CASE("Homogeneous Ellipsoid Analytic Gravity", tags::gravity & tags::analytic_comparison) { - auto args = test_utils::setup_args(); - fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); +TEST_CASE( + "Homogeneous Ellipsoid Analytic Gravity", + tags::gravity &tags::analytic_comparison &tags::initialization +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); - const double radius = utils::RADIUS; - const double mass = utils::MASS; + const double radius = utils::RADIUS; + const double mass = utils::MASS; constexpr double x_scale = 1.15; constexpr double y_scale = 0.95; constexpr double z_scale = 1.0 / (x_scale * y_scale); @@ -392,7 +1613,8 @@ TEST_CASE("Homogeneous Ellipsoid Analytic Gravity", tags::gravity & tags::analyt const double semi_axis_y = y_scale * radius; const double semi_axis_z = z_scale * radius; - auto affine_displacement = [](const mfem::Vector& x, mfem::Vector& displacement_value) { + auto affine_displacement = [](const mfem::Vector &x, + mfem::Vector &displacement_value) { displacement_value.SetSize(3); displacement_value(0) = (x_scale - 1.0) * x(0); displacement_value(1) = (y_scale - 1.0) * x(1); @@ -400,28 +1622,35 @@ TEST_CASE("Homogeneous Ellipsoid Analytic Gravity", tags::gravity & tags::analyt }; mfem::VectorFunctionCoefficient displacement_coeff(3, affine_displacement); - mfem::ParGridFunction displacement(f.Vec_H1_fes.get()); + mfem::ParGridFunction displacement(f.displacementFes.get()); displacement.ProjectCoefficient(displacement_coeff); f.mapping->SetDisplacement(displacement); physics::update_stiffness_matrix(f); - const double analytic_volume = (4.0 / 3.0) * M_PI * semi_axis_x * semi_axis_y * semi_axis_z; + const double analytic_volume = + (4.0 / 3.0) * M_PI * semi_axis_x * semi_axis_y * semi_axis_z; const double density = mass / analytic_volume; - mfem::GridFunction rho_grid(f.L2_fes.get()); + mfem::GridFunction rho_grid(f.densityFes.get()); rho_grid = density; zero_vacuum_density(f, rho_grid); - const double projected_mass = analysis::domain_integrate_grid_function(f, rho_grid, utils::DOMAINS::STELLAR); + const double projected_mass = analysis::domain_integrate_grid_function( + f, rho_grid, utils::DOMAINS::STELLAR + ); const double numerical_density = density * mass / projected_mass; analysis::conserve_mass(f, rho_grid, mass); f.com = analysis::get_com(f, rho_grid); - f.Q = physics::compute_quadrupole_moment_tensor(f, rho_grid, f.com); + f.Q = physics::compute_quadrupole_moment_tensor(f, rho_grid, f.com); const HomogeneousEllipsoidAnalytic analytic = - compute_homogeneous_ellipsoid_analytic(semi_axis_x, semi_axis_y, semi_axis_z); - const double coefficient_sum = analytic.coefficient_x + analytic.coefficient_y + analytic.coefficient_z; + compute_homogeneous_ellipsoid_analytic( + semi_axis_x, semi_axis_y, semi_axis_z + ); + const double coefficient_sum = analytic.coefficient_x + + analytic.coefficient_y + + analytic.coefficient_z; INFO("A_x = " << analytic.coefficient_x); INFO("A_y = " << analytic.coefficient_y); @@ -431,73 +1660,178 @@ TEST_CASE("Homogeneous Ellipsoid Analytic Gravity", tags::gravity & tags::analyt mfem::DenseMatrix analytic_quadrupole(3, 3); analytic_quadrupole = 0.0; - analytic_quadrupole(0, 0) = (mass / 5.0) * (2.0 * semi_axis_x * semi_axis_x - semi_axis_y * semi_axis_y - semi_axis_z * semi_axis_z); - analytic_quadrupole(1, 1) = (mass / 5.0) * (2.0 * semi_axis_y * semi_axis_y - semi_axis_x * semi_axis_x - semi_axis_z * semi_axis_z); - analytic_quadrupole(2, 2) = (mass / 5.0) * (2.0 * semi_axis_z * semi_axis_z - semi_axis_x * semi_axis_x - semi_axis_y * semi_axis_y); + analytic_quadrupole(0, 0) = + (mass / 5.0) * (2.0 * semi_axis_x * semi_axis_x - + semi_axis_y * semi_axis_y - semi_axis_z * semi_axis_z); + analytic_quadrupole(1, 1) = + (mass / 5.0) * (2.0 * semi_axis_y * semi_axis_y - + semi_axis_x * semi_axis_x - semi_axis_z * semi_axis_z); + analytic_quadrupole(2, 2) = + (mass / 5.0) * (2.0 * semi_axis_z * semi_axis_z - + semi_axis_x * semi_axis_x - semi_axis_y * semi_axis_y); mfem::DenseMatrix quadrupole_difference(f.Q); quadrupole_difference -= analytic_quadrupole; - const double relative_quadrupole_error = quadrupole_difference.FNorm() / analytic_quadrupole.FNorm(); + const double relative_quadrupole_error = + quadrupole_difference.FNorm() / analytic_quadrupole.FNorm(); INFO("Relative quadrupole error = " << relative_quadrupole_error); + HomogeneousEllipsoidHDivCoefficient analytic_field_coefficient( + *f.mapping, numerical_density, analytic + ); + mfem::ParGridFunction analytic_field_projection(f.gravityFluxFes.get()); + analytic_field_projection = 0.0; + + for (int i = 0; i < f.mesh->attributes.Size(); ++i) { + const int attribute = f.mesh->attributes[i]; + + if (attribute != 3) { + analytic_field_projection.ProjectCoefficient( + analytic_field_coefficient, attribute + ); + } + } + const auto gravity_solution = physics::grav_potential(f, args, rho_grid); - const int quadrature_order = get_gravity_quadrature_order(f); - double local_field_error_squared = 0.0; - double local_field_norm_squared = 0.0; + const int quadrature_order = get_gravity_quadrature_order(f); + double local_field_error_squared = 0.0; + double local_field_norm_squared = 0.0; + double local_projection_error_squared = 0.0; + double local_gravity_projection_difference_squared = 0.0; mfem::Vector x_physical(3); mfem::Vector grad_phi_element(3); mfem::Vector grad_phi_physical(3); mfem::Vector grad_phi_analytic(3); mfem::Vector grad_phi_difference(3); + mfem::Vector projected_field_element(3); + mfem::Vector projected_field_physical(3); + mfem::Vector projected_field_difference(3); mfem::DenseMatrix map_jacobian(3, 3); + mfem::Vector gravity_projection_difference(3); for (int elem_id = 0; elem_id < f.mesh->GetNE(); ++elem_id) { if (f.mesh->GetAttribute(elem_id) == 3) { continue; } - mfem::ElementTransformation* transformation = f.mesh->GetElementTransformation(elem_id); - const mfem::IntegrationRule& integration_rule = - mfem::IntRules.Get(transformation->GetGeometryType(), quadrature_order); + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(elem_id); + const mfem::IntegrationRule &integration_rule = mfem::IntRules.Get( + transformation->GetGeometryType(), quadrature_order + ); for (int q = 0; q < integration_rule.GetNPoints(); ++q) { - const mfem::IntegrationPoint& integration_point = integration_rule.IntPoint(q); + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(q); transformation->SetIntPoint(&integration_point); - const double map_determinant = f.mapping->ComputeDetJ(*transformation, integration_point); - MFEM_VERIFY(map_determinant > 0.0, "Domain mapping has a non-positive Jacobian determinant."); + const double map_determinant = + f.mapping->ComputeDetJ(*transformation, integration_point); + MFEM_VERIFY( + map_determinant > 0.0, + "Domain mapping has a non-positive Jacobian determinant." + ); - const double weight = transformation->Weight() * integration_point.weight * map_determinant; - f.mapping->GetPhysicalPoint(*transformation, integration_point, x_physical); - gravity_solution.gradPhi.GetVectorValue(elem_id, integration_point, grad_phi_element); + const double weight = transformation->Weight() * + integration_point.weight * map_determinant; + f.mapping->GetPhysicalPoint( + *transformation, integration_point, x_physical + ); + gravity_solution.gradPhi.GetVectorValue( + elem_id, integration_point, grad_phi_element + ); f.mapping->ComputeJacobian(*transformation, map_jacobian); map_jacobian.Mult(grad_phi_element, grad_phi_physical); grad_phi_physical /= map_determinant; - grad_phi_analytic(0) = 2.0 * M_PI * utils::G * numerical_density * analytic.coefficient_x * x_physical(0); - grad_phi_analytic(1) = 2.0 * M_PI * utils::G * numerical_density * analytic.coefficient_y * x_physical(1); - grad_phi_analytic(2) = 2.0 * M_PI * utils::G * numerical_density * analytic.coefficient_z * x_physical(2); + analytic_field_projection.GetVectorValue( + elem_id, integration_point, projected_field_element + ); + map_jacobian.Mult( + projected_field_element, projected_field_physical + ); + projected_field_physical /= map_determinant; + + grad_phi_analytic(0) = 2.0 * M_PI * utils::G * numerical_density * + analytic.coefficient_x * x_physical(0); + grad_phi_analytic(1) = 2.0 * M_PI * utils::G * numerical_density * + analytic.coefficient_y * x_physical(1); + grad_phi_analytic(2) = 2.0 * M_PI * utils::G * numerical_density * + analytic.coefficient_z * x_physical(2); + + projected_field_difference = projected_field_physical; + projected_field_difference -= grad_phi_analytic; + local_projection_error_squared += + (projected_field_difference * projected_field_difference) * + weight; + + gravity_projection_difference = grad_phi_physical; + gravity_projection_difference -= projected_field_physical; + local_gravity_projection_difference_squared += + (gravity_projection_difference * + gravity_projection_difference) * + weight; grad_phi_difference = grad_phi_physical; grad_phi_difference -= grad_phi_analytic; - local_field_error_squared += (grad_phi_difference * grad_phi_difference) * weight; - local_field_norm_squared += (grad_phi_analytic * grad_phi_analytic) * weight; + local_field_error_squared += + (grad_phi_difference * grad_phi_difference) * weight; + local_field_norm_squared += + (grad_phi_analytic * grad_phi_analytic) * weight; } } - double global_field_error_squared = 0.0; - double global_field_norm_squared = 0.0; - MPI_Comm communicator = f.L2_fes->GetComm(); - MPI_Allreduce(&local_field_error_squared, &global_field_error_squared, 1, MPI_DOUBLE, MPI_SUM, communicator); - MPI_Allreduce(&local_field_norm_squared, &global_field_norm_squared, 1, MPI_DOUBLE, MPI_SUM, communicator); + double global_field_error_squared = 0.0; + double global_field_norm_squared = 0.0; + double global_projection_error_squared = 0.0; + double global_gravity_projection_difference_squared = 0.0; + MPI_Comm communicator = f.densityFes->GetComm(); + MPI_Allreduce( + &local_field_error_squared, &global_field_error_squared, 1, MPI_DOUBLE, + MPI_SUM, communicator + ); + MPI_Allreduce( + &local_field_norm_squared, &global_field_norm_squared, 1, MPI_DOUBLE, + MPI_SUM, communicator + ); + MPI_Allreduce( + &local_projection_error_squared, &global_projection_error_squared, 1, + MPI_DOUBLE, MPI_SUM, communicator + ); + MPI_Allreduce( + &local_gravity_projection_difference_squared, + &global_gravity_projection_difference_squared, 1, MPI_DOUBLE, MPI_SUM, + communicator + ); - const double relative_field_error = std::sqrt(global_field_error_squared / global_field_norm_squared); - const GravitationalEnergies energies = compute_gravitational_energies(f, rho_grid, gravity_solution, quadrature_order); - const double analytic_binding_energy = -(3.0 / 10.0) * utils::G * mass * mass * analytic.energy_kernel; - const double relative_binding_energy_error = std::abs(energies.binding - analytic_binding_energy) / std::abs(analytic_binding_energy); - const double relative_virial_energy_error = std::abs(energies.virial - analytic_binding_energy) / std::abs(analytic_binding_energy); - const double relative_consistency_error = std::abs(energies.binding - energies.virial) / std::abs(energies.binding); + const double relative_field_error = + std::sqrt(global_field_error_squared / global_field_norm_squared); + const GravitationalEnergies energies = compute_gravitational_energies( + f, rho_grid, gravity_solution, quadrature_order + ); + const double analytic_binding_energy = + -(3.0 / 10.0) * utils::G * mass * mass * analytic.energy_kernel; + const double relative_binding_energy_error = + std::abs(energies.binding - analytic_binding_energy) / + std::abs(analytic_binding_energy); + const double relative_virial_energy_error = + std::abs(energies.virial - analytic_binding_energy) / + std::abs(analytic_binding_energy); + const double relative_consistency_error = + std::abs(energies.binding - energies.virial) / + std::abs(energies.binding); + const double relative_projection_error = + std::sqrt(global_projection_error_squared / global_field_norm_squared); + const double gravity_to_projection_error_ratio = + relative_projection_error > 0.0 + ? relative_field_error / relative_projection_error + : std::numeric_limits::infinity(); + const double relative_gravity_projection_difference = std::sqrt( + global_gravity_projection_difference_squared / global_field_norm_squared + ); + const double projection_gap_ratio = + relative_gravity_projection_difference / relative_projection_error; INFO("Analytic binding energy = " << analytic_binding_energy); INFO("Computed binding energy = " << energies.binding); @@ -506,25 +1840,54 @@ TEST_CASE("Homogeneous Ellipsoid Analytic Gravity", tags::gravity & tags::analyt INFO("Relative binding energy error = " << relative_binding_energy_error); INFO("Relative virial energy error = " << relative_virial_energy_error); INFO("Relative virial consistency error = " << relative_consistency_error); + INFO( + "Relative gravity-to-RT-projection difference = " + << relative_gravity_projection_difference + ); + INFO("Gravity-to-projection gap ratio = " << projection_gap_ratio); - constexpr double quadrupole_tolerance = 2.0e-4; - constexpr double field_tolerance = 1.0e-5; - constexpr double energy_tolerance = 1.0e-5; + INFO("Relative RT projection L2 error = " << relative_projection_error); + INFO( + "Gravity-to-projection error ratio = " + << gravity_to_projection_error_ratio + ); + REQUIRE(std::isfinite(relative_projection_error)); + + constexpr double quadrupole_tolerance = 2.0e-4; + constexpr double field_tolerance = 1.0e-5; + constexpr double energy_tolerance = 1.0e-5; constexpr double consistency_tolerance = 1.0e-5; - CHECK_THAT(relative_quadrupole_error, Catch::Matchers::WithinAbs(0.0, quadrupole_tolerance)); - CHECK_THAT(relative_field_error, Catch::Matchers::WithinAbs(0.0, field_tolerance)); - CHECK_THAT(relative_binding_energy_error, Catch::Matchers::WithinAbs(0.0, energy_tolerance)); - CHECK_THAT(relative_virial_energy_error, Catch::Matchers::WithinAbs(0.0, energy_tolerance)); - CHECK_THAT(relative_consistency_error, Catch::Matchers::WithinAbs(0.0, consistency_tolerance)); + CHECK_THAT( + relative_quadrupole_error, + Catch::Matchers::WithinAbs(0.0, quadrupole_tolerance) + ); + CHECK_THAT( + relative_field_error, Catch::Matchers::WithinAbs(0.0, field_tolerance) + ); + CHECK_THAT( + relative_binding_energy_error, + Catch::Matchers::WithinAbs(0.0, energy_tolerance) + ); + CHECK_THAT( + relative_virial_energy_error, + Catch::Matchers::WithinAbs(0.0, energy_tolerance) + ); + CHECK_THAT( + relative_consistency_error, + Catch::Matchers::WithinAbs(0.0, consistency_tolerance) + ); } -TEST_CASE("Deformed Rational Density Virial Self-Consistency", tags::gravity & tags::self_consistency) { - auto args = test_utils::setup_args(); - fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); +TEST_CASE( + "Deformed Rational Density Virial Self-Consistency", + tags::gravity &tags::self_consistency &tags::initialization +) { + auto args = test_utils::setup_args(); + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); - const double radius = utils::RADIUS; - const double mass = utils::MASS; + const double radius = utils::RADIUS; + const double mass = utils::MASS; constexpr double x_scale = 1.15; constexpr double y_scale = 0.95; constexpr double z_scale = 1.0 / (x_scale * y_scale); @@ -534,7 +1897,8 @@ TEST_CASE("Deformed Rational Density Virial Self-Consistency", tags::gravity & t const double semi_axis_y = y_scale * radius; const double semi_axis_z = z_scale * radius; - auto affine_displacement = [](const mfem::Vector& x, mfem::Vector& displacement_value) { + auto affine_displacement = [](const mfem::Vector &x, + mfem::Vector &displacement_value) { displacement_value.SetSize(3); displacement_value(0) = (x_scale - 1.0) * x(0); displacement_value(1) = (y_scale - 1.0) * x(1); @@ -542,15 +1906,16 @@ TEST_CASE("Deformed Rational Density Virial Self-Consistency", tags::gravity & t }; mfem::VectorFunctionCoefficient displacement_coeff(3, affine_displacement); - mfem::ParGridFunction displacement(f.Vec_H1_fes.get()); + mfem::ParGridFunction displacement(f.displacementFes.get()); displacement.ProjectCoefficient(displacement_coeff); f.mapping->SetDisplacement(displacement); physics::update_stiffness_matrix(f); constexpr double concentration = 16.0; - const double density_scale = mass / std::pow(radius, 3.0); + const double density_scale = mass / std::pow(radius, 3.0); - auto ellipsoidal_rho = [semi_axis_x, semi_axis_y, semi_axis_z, density_scale](const mfem::Vector& x) { + auto ellipsoidal_rho = [semi_axis_x, semi_axis_y, semi_axis_z, + density_scale](const mfem::Vector &x) { const double ellipsoidal_radius_squared = x(0) * x(0) / (semi_axis_x * semi_axis_x) + x(1) * x(1) / (semi_axis_y * semi_axis_y) + @@ -560,41 +1925,2041 @@ TEST_CASE("Deformed Rational Density Virial Self-Consistency", tags::gravity & t return 0.0; } - const double denominator = 1.0 + concentration * ellipsoidal_radius_squared; - return density_scale * (1.0 - ellipsoidal_radius_squared) / (denominator * denominator); + const double denominator = + 1.0 + concentration * ellipsoidal_radius_squared; + return density_scale * (1.0 - ellipsoidal_radius_squared) / + (denominator * denominator); }; std::unique_ptr rho_coeff; if (f.has_mapping()) { - rho_coeff = std::make_unique(*f.mapping, ellipsoidal_rho); + rho_coeff = + std::make_unique( + *f.mapping, ellipsoidal_rho + ); } else { - rho_coeff = std::make_unique(ellipsoidal_rho); + rho_coeff = + std::make_unique(ellipsoidal_rho); } - mfem::GridFunction rho_grid(f.L2_fes.get()); + mfem::GridFunction rho_grid(f.densityFes.get()); rho_grid.ProjectCoefficient(*rho_coeff); zero_vacuum_density(f, rho_grid); analysis::conserve_mass(f, rho_grid, mass); f.com = analysis::get_com(f, rho_grid); - f.Q = physics::compute_quadrupole_moment_tensor(f, rho_grid, f.com); + f.Q = physics::compute_quadrupole_moment_tensor(f, rho_grid, f.com); const double normalized_quadrupole = f.Q.FNorm() / (mass * radius * radius); INFO("Normalized quadrupole = " << normalized_quadrupole); REQUIRE(normalized_quadrupole > 1.0e-3); const auto gravity_solution = physics::grav_potential(f, args, rho_grid); - const int quadrature_order = get_gravity_quadrature_order(f); - const GravitationalEnergies energies = compute_gravitational_energies(f, rho_grid, gravity_solution, quadrature_order); + const int quadrature_order = get_gravity_quadrature_order(f); + const GravitationalEnergies energies = compute_gravitational_energies( + f, rho_grid, gravity_solution, quadrature_order + ); REQUIRE(energies.binding < 0.0); REQUIRE(energies.virial < 0.0); - const double relative_consistency_error = std::abs(energies.binding - energies.virial) / std::abs(energies.binding); + const double relative_consistency_error = + std::abs(energies.binding - energies.virial) / + std::abs(energies.binding); INFO("W_bind = " << energies.binding); INFO("W_vir = " << energies.virial); INFO("Relative virial consistency error = " << relative_consistency_error); constexpr double virial_tolerance = 1.0e-5; - CHECK_THAT(relative_consistency_error, Catch::Matchers::WithinAbs(0.0, virial_tolerance)); -} \ No newline at end of file + CHECK_THAT( + relative_consistency_error, + Catch::Matchers::WithinAbs(0.0, virial_tolerance) + ); +} + +TEST_CASE( + "New Gravity Potential Matches Uniform Sphere Analytic", + tags::gravity &tags::analytic_comparison &tags::initialization + &tags::integration +) { + auto args = test_utils::setup_args(); + args.p.rtol = 1.0e-13; + args.p.max_iters = std::max(args.p.max_iters, 1000); + + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + f.mapping->ResetDisplacement(); + physics::update_stiffness_matrix(f); + + mfem::ParGridFunction displacement(f.displacementFes.get()); + displacement = 0.0; + + const double radius = utils::RADIUS; + const double mass = utils::MASS; + const double analytic_volume = (4.0 / 3.0) * M_PI * std::pow(radius, 3.0); + const double density = mass / analytic_volume; + + mfem::GridFunction rho_uniform(f.densityFes.get()); + rho_uniform = density; + zero_vacuum_density(f, rho_uniform); + analysis::conserve_mass(f, rho_uniform, mass); + + f.com = analysis::get_com(f, rho_uniform); + f.Q = physics::compute_quadrupole_moment_tensor(f, rho_uniform, f.com); + + const physics::GravitySolution gravity_solution = + physics::grav_potential_new(f, args, rho_uniform, displacement); + + constexpr double potential_tolerance = + utils::APPROX_MAX_ACCEPTABLE_POTENTIAL_ERROR_SI_BURNING; + double local_maximum_absolute_error = 0.0; + double local_maximum_relative_error = 0.0; + + const int elements_to_test = std::min(30, f.mesh->GetNE()); + + for (int element_id = 0; element_id < elements_to_test; ++element_id) { + if (f.mesh->GetAttribute(element_id) == 3) { + continue; + } + + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + const mfem::IntegrationRule &integration_rule = + mfem::IntRules.Get(transformation->GetGeometryType(), 2); + const mfem::IntegrationPoint &integration_point = + integration_rule.IntPoint(0); + transformation->SetIntPoint(&integration_point); + + mfem::Vector physical_position; + f.mapping->GetPhysicalPoint( + *transformation, integration_point, physical_position + ); + + const double radial_coordinate = physical_position.Norml2(); + + if (radial_coordinate < 1.0e-9) { + continue; + } + + const double analytic_potential = + -(utils::G * mass / (2.0 * std::pow(radius, 3.0))) * + (3.0 * radius * radius - radial_coordinate * radial_coordinate); + + const double computed_potential = + gravity_solution.phi.GetValue(element_id, integration_point); + const double absolute_error = + std::abs(computed_potential - analytic_potential); + const double relative_error = + absolute_error / std::abs(analytic_potential); + + local_maximum_absolute_error = + std::max(local_maximum_absolute_error, absolute_error); + local_maximum_relative_error = + std::max(local_maximum_relative_error, relative_error); + } + + double global_maximum_absolute_error = 0.0; + double global_maximum_relative_error = 0.0; + + MPI_Allreduce( + &local_maximum_absolute_error, &global_maximum_absolute_error, 1, + MPI_DOUBLE, MPI_MAX, f.densityFes->GetComm() + ); + + MPI_Allreduce( + &local_maximum_relative_error, &global_maximum_relative_error, 1, + MPI_DOUBLE, MPI_MAX, f.densityFes->GetComm() + ); + + const int quadrature_order = get_gravity_quadrature_order(f); + const GravitationalEnergies energies = compute_gravitational_energies( + f, rho_uniform, gravity_solution, quadrature_order + ); + const double analytic_binding_energy = + -(3.0 / 5.0) * utils::G * mass * mass / radius; + const double relative_binding_error = + std::abs(energies.binding - analytic_binding_energy) / + std::abs(analytic_binding_energy); + const double relative_virial_error = + std::abs(energies.virial - analytic_binding_energy) / + std::abs(analytic_binding_energy); + const double relative_consistency_error = + std::abs(energies.binding - energies.virial) / + std::abs(energies.binding); + + INFO( + "Global maximum absolute potential error = " + << global_maximum_absolute_error + ); + INFO( + "Global maximum relative potential error = " + << global_maximum_relative_error + ); + INFO("Analytic binding energy = " << analytic_binding_energy); + INFO("New-solver binding energy = " << energies.binding); + INFO("New-solver virial energy = " << energies.virial); + INFO("Relative binding-energy error = " << relative_binding_error); + INFO("Relative virial-energy error = " << relative_virial_error); + INFO("Relative virial consistency error = " << relative_consistency_error); + + REQUIRE(energies.binding < 0.0); + REQUIRE(energies.virial < 0.0); + + constexpr double energy_tolerance = 1.0e-5; + constexpr double consistency_tolerance = 1.0e-6; + + CHECK_THAT( + global_maximum_relative_error, + Catch::Matchers::WithinAbs(0.0, 0.1 * potential_tolerance) + ); + CHECK_THAT( + global_maximum_absolute_error, + Catch::Matchers::WithinAbs(0.0, 0.1 * potential_tolerance) + ); + CHECK_THAT( + relative_binding_error, + Catch::Matchers::WithinAbs(0.0, energy_tolerance) + ); + CHECK_THAT( + relative_virial_error, Catch::Matchers::WithinAbs(0.0, energy_tolerance) + ); + CHECK_THAT( + relative_consistency_error, + Catch::Matchers::WithinAbs(0.0, consistency_tolerance) + ); +} + +TEST_CASE( + "New Gravity Potential Matches Legacy Solver On Homogeneous Ellipsoid", + tags::gravity &tags::analytic_comparison &tags::initialization + &tags::integration &tags::legacy_comparison +) { + auto args = test_utils::setup_args(); + args.p.rtol = 1.0e-13; + args.p.max_iters = std::max(args.p.max_iters, 1000); + + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + const double radius = utils::RADIUS; + const double mass = utils::MASS; + + constexpr double x_scale = 1.15; + constexpr double y_scale = 0.95; + constexpr double z_scale = 1.0 / (x_scale * y_scale); + + REQUIRE_THAT( + x_scale * y_scale * z_scale, Catch::Matchers::WithinAbs(1.0, 1.0e-14) + ); + + const double semi_axis_x = x_scale * radius; + const double semi_axis_y = y_scale * radius; + const double semi_axis_z = z_scale * radius; + + auto affine_displacement = [](const mfem::Vector &position, + mfem::Vector &value) { + value.SetSize(3); + value(0) = (x_scale - 1.0) * position(0); + value(1) = (y_scale - 1.0) * position(1); + value(2) = (z_scale - 1.0) * position(2); + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + 3, affine_displacement + ); + mfem::ParGridFunction displacement(f.displacementFes.get()); + displacement.ProjectCoefficient(displacement_coefficient); + + f.mapping->SetDisplacement(displacement); + physics::update_stiffness_matrix(f); + + REQUIRE(f.gravityContext.block_A != nullptr); + REQUIRE(f.gravityContext.source_form != nullptr); + REQUIRE(f.domainMapperStateless != nullptr); + + const double analytic_volume = + (4.0 / 3.0) * M_PI * semi_axis_x * semi_axis_y * semi_axis_z; + const double density = mass / analytic_volume; + + mfem::GridFunction rho_grid(f.densityFes.get()); + rho_grid = density; + zero_vacuum_density(f, rho_grid); + + const double projected_mass = analysis::domain_integrate_grid_function( + f, rho_grid, utils::DOMAINS::STELLAR + ); + const double numerical_density = density * mass / projected_mass; + analysis::conserve_mass(f, rho_grid, mass); + + f.com = analysis::get_com(f, rho_grid); + f.Q = physics::compute_quadrupole_moment_tensor(f, rho_grid, f.com); + + const physics::GravitySolution legacy_solution = + physics::grav_potential(f, args, rho_grid); + const physics::GravitySolution new_solution = + physics::grav_potential_new(f, args, rho_grid, displacement); + + using gravity_form = utils::blocks::gravity_field_form; + + constexpr auto gravity_gradient_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.gradient_term + ); + + constexpr auto gravity_poisson_residual_block = + utils::blocks::get_residual_block( + utils::blocks::gravity_field.poisson_term + ); + + const std::array value_sizes{ + f.densityFes->GetTrueVSize(), f.displacementFes->GetTrueVSize(), + f.gravityFluxFes->GetTrueVSize(), f.gravityPotentialFes->GetTrueVSize() + }; + + const std::array residual_sizes{ + f.gravityFluxFes->GetTrueVSize(), f.gravityPotentialFes->GetTrueVSize() + }; + + const utils::blocks::form_layout gravity_layout( + value_sizes, residual_sizes + ); + const int gravity_system_size = gravity_layout.residual_offsets().Last(); + const int gravity_gradient_size = + gravity_layout.size(gravity_gradient_residual_block); + const int gravity_poisson_size = + gravity_layout.size(gravity_poisson_residual_block); + + mfem::Vector density_true; + mfem::Vector displacement_true; + gravity_test_get_true_dofs(*f.densityFes, rho_grid, density_true); + gravity_test_get_true_dofs( + *f.displacementFes, displacement, displacement_true + ); + + REQUIRE(density_true.Size() == f.densityFes->GetTrueVSize()); + REQUIRE(displacement_true.Size() == f.displacementFes->GetTrueVSize()); + + operators::context::gravity_field::GravityFieldLinearizationContext + residual_linearization_context(f, *f.domainMapperStateless); + + operators::GravityFieldJacobianOperator residual_jacobian( + f, *f.domainMapperStateless, residual_linearization_context, + gravity_layout.value_offsets(), gravity_layout.residual_offsets() + ); + + operators::GravityFieldOperator residual_gravity_operator( + f, *f.domainMapperStateless, residual_linearization_context, + gravity_layout.value_offsets(), residual_jacobian + ); + + operators::context::gravity_field::GravityFieldGeometryContext + residual_geometry_context(f, *f.domainMapperStateless); + + operators::ReducedGravityFieldOperator new_reduced_operator( + residual_gravity_operator, residual_geometry_context, displacement_true + ); + + REQUIRE(new_reduced_operator.Width() == gravity_system_size); + REQUIRE(new_reduced_operator.Height() == gravity_system_size); + + mfem::Vector new_right_hand_side; + new_reduced_operator.BuildRightHandSide(density_true, new_right_hand_side); + + REQUIRE(new_right_hand_side.Size() == gravity_system_size); + + REQUIRE(f.gravityContext.source_form->Width() == density_true.Size()); + REQUIRE(f.gravityContext.source_form->Height() == gravity_poisson_size); + + mfem::Vector legacy_source_action(f.gravityContext.source_form->Height()); + legacy_source_action = 0.0; + + f.gravityContext.source_form->Mult(density_true, legacy_source_action); + + REQUIRE(legacy_source_action.Size() == gravity_poisson_size); + + mfem::BlockVector legacy_right_hand_side(gravity_layout.residual_offsets()); + legacy_right_hand_side = 0.0; + legacy_right_hand_side.GetBlock(gravity_poisson_residual_block) = + legacy_source_action; + + REQUIRE(legacy_right_hand_side.Size() == gravity_system_size); + + MPI_Comm communicator = f.densityFes->GetComm(); + + const double new_right_hand_side_norm = + gravity_test_global_norm(new_right_hand_side, communicator); + const double legacy_right_hand_side_norm = + gravity_test_global_norm(legacy_right_hand_side, communicator); + + REQUIRE(new_right_hand_side_norm > 0.0); + REQUIRE(legacy_right_hand_side_norm > 0.0); + + mfem::Vector right_hand_side_difference(new_right_hand_side); + right_hand_side_difference -= legacy_right_hand_side; + + const double right_hand_side_scale = std::max( + 0.5 * (new_right_hand_side_norm + legacy_right_hand_side_norm), + std::numeric_limits::min() + ); + + const double relative_right_hand_side_difference = + gravity_test_global_norm(right_hand_side_difference, communicator) / + right_hand_side_scale; + + mfem::BlockVector legacy_gravity_state(gravity_layout.residual_offsets()); + mfem::BlockVector new_gravity_state(gravity_layout.residual_offsets()); + + legacy_gravity_state = 0.0; + new_gravity_state = 0.0; + + { + mfem::Vector gradient_true; + mfem::Vector potential_true; + + legacy_solution.gradPhi.GetTrueDofs(gradient_true); + legacy_solution.phi.GetTrueDofs(potential_true); + + REQUIRE(gradient_true.Size() == gravity_gradient_size); + REQUIRE(potential_true.Size() == gravity_poisson_size); + + legacy_gravity_state.GetBlock(gravity_gradient_residual_block) = + gradient_true; + legacy_gravity_state.GetBlock(gravity_poisson_residual_block) = + potential_true; + + new_solution.gradPhi.GetTrueDofs(gradient_true); + new_solution.phi.GetTrueDofs(potential_true); + + REQUIRE(gradient_true.Size() == gravity_gradient_size); + REQUIRE(potential_true.Size() == gravity_poisson_size); + + new_gravity_state.GetBlock(gravity_gradient_residual_block) = + gradient_true; + new_gravity_state.GetBlock(gravity_poisson_residual_block) = + potential_true; + } + + REQUIRE(legacy_gravity_state.Size() == gravity_system_size); + REQUIRE(new_gravity_state.Size() == gravity_system_size); + + REQUIRE(f.gravityContext.block_A->Width() == gravity_system_size); + REQUIRE(f.gravityContext.block_A->Height() == gravity_system_size); + + mfem::Vector legacy_action_at_legacy_solution(gravity_system_size); + mfem::Vector legacy_action_at_new_solution(gravity_system_size); + mfem::Vector new_action_at_legacy_solution(gravity_system_size); + mfem::Vector new_action_at_new_solution(gravity_system_size); + + legacy_action_at_legacy_solution = 0.0; + legacy_action_at_new_solution = 0.0; + new_action_at_legacy_solution = 0.0; + new_action_at_new_solution = 0.0; + + f.gravityContext.block_A->Mult( + legacy_gravity_state, legacy_action_at_legacy_solution + ); + + f.gravityContext.block_A->Mult( + new_gravity_state, legacy_action_at_new_solution + ); + + new_reduced_operator.Mult( + legacy_gravity_state, new_action_at_legacy_solution + ); + + new_reduced_operator.Mult(new_gravity_state, new_action_at_new_solution); + + REQUIRE(legacy_action_at_legacy_solution.Size() == gravity_system_size); + REQUIRE(legacy_action_at_new_solution.Size() == gravity_system_size); + REQUIRE(new_action_at_legacy_solution.Size() == gravity_system_size); + REQUIRE(new_action_at_new_solution.Size() == gravity_system_size); + + mfem::Vector legacy_residual_at_legacy_solution( + legacy_action_at_legacy_solution + ); + mfem::Vector legacy_residual_at_new_solution(legacy_action_at_new_solution); + mfem::Vector new_residual_at_legacy_solution(new_action_at_legacy_solution); + mfem::Vector new_residual_at_new_solution(new_action_at_new_solution); + + legacy_residual_at_legacy_solution -= legacy_right_hand_side; + legacy_residual_at_new_solution -= legacy_right_hand_side; + new_residual_at_legacy_solution -= new_right_hand_side; + new_residual_at_new_solution -= new_right_hand_side; + + const GravityResidualMetrics legacy_at_legacy = measure_gravity_residual( + legacy_residual_at_legacy_solution, gravity_layout.residual_offsets(), + legacy_right_hand_side_norm, communicator + ); + + const GravityResidualMetrics legacy_at_new = measure_gravity_residual( + legacy_residual_at_new_solution, gravity_layout.residual_offsets(), + legacy_right_hand_side_norm, communicator + ); + + const GravityResidualMetrics new_at_legacy = measure_gravity_residual( + new_residual_at_legacy_solution, gravity_layout.residual_offsets(), + new_right_hand_side_norm, communicator + ); + + const GravityResidualMetrics new_at_new = measure_gravity_residual( + new_residual_at_new_solution, gravity_layout.residual_offsets(), + new_right_hand_side_norm, communicator + ); + + mfem::Vector operator_gap_at_legacy_solution( + new_residual_at_legacy_solution + ); + operator_gap_at_legacy_solution -= legacy_residual_at_legacy_solution; + + mfem::Vector operator_gap_at_new_solution(new_residual_at_new_solution); + operator_gap_at_new_solution -= legacy_residual_at_new_solution; + + const GravityResidualMetrics gap_at_legacy = measure_gravity_residual( + operator_gap_at_legacy_solution, gravity_layout.residual_offsets(), + right_hand_side_scale, communicator + ); + + const GravityResidualMetrics gap_at_new = measure_gravity_residual( + operator_gap_at_new_solution, gravity_layout.residual_offsets(), + right_hand_side_scale, communicator + ); + + INFO( + "New/legacy right-hand-side difference = " + << relative_right_hand_side_difference + ); + INFO( + "Legacy operator at legacy solution: total = " + << legacy_at_legacy.relative_total + << ", gradient = " << legacy_at_legacy.relative_gradient + << ", Poisson = " << legacy_at_legacy.relative_poisson + ); + INFO( + "Legacy operator at new solution: total = " + << legacy_at_new.relative_total + << ", gradient = " << legacy_at_new.relative_gradient + << ", Poisson = " << legacy_at_new.relative_poisson + ); + INFO( + "New operator at legacy solution: total = " + << new_at_legacy.relative_total + << ", gradient = " << new_at_legacy.relative_gradient + << ", Poisson = " << new_at_legacy.relative_poisson + ); + INFO( + "New operator at new solution: total = " + << new_at_new.relative_total + << ", gradient = " << new_at_new.relative_gradient + << ", Poisson = " << new_at_new.relative_poisson + ); + INFO( + "Operator gap at legacy solution: total = " + << gap_at_legacy.relative_total + << ", gradient = " << gap_at_legacy.relative_gradient + << ", Poisson = " << gap_at_legacy.relative_poisson + ); + INFO( + "Operator gap at new solution: total = " + << gap_at_new.relative_total + << ", gradient = " << gap_at_new.relative_gradient + << ", Poisson = " << gap_at_new.relative_poisson + ); + + REQUIRE(std::isfinite(legacy_at_legacy.relative_total)); + REQUIRE(std::isfinite(legacy_at_new.relative_total)); + REQUIRE(std::isfinite(new_at_legacy.relative_total)); + REQUIRE(std::isfinite(new_at_new.relative_total)); + REQUIRE(std::isfinite(gap_at_legacy.relative_total)); + REQUIRE(std::isfinite(gap_at_new.relative_total)); + + constexpr double source_parity_tolerance = 1.0e-12; + constexpr double diagonal_residual_tolerance = 1.0e-8; + constexpr double poisson_gap_tolerance = 1.0e-11; + + CHECK_THAT( + relative_right_hand_side_difference, + Catch::Matchers::WithinAbs(0.0, source_parity_tolerance) + ); + + CHECK_THAT( + legacy_at_legacy.relative_total, + Catch::Matchers::WithinAbs(0.0, diagonal_residual_tolerance) + ); + + CHECK_THAT( + new_at_new.relative_total, + Catch::Matchers::WithinAbs(0.0, diagonal_residual_tolerance) + ); + + CHECK_THAT( + gap_at_legacy.relative_poisson, + Catch::Matchers::WithinAbs(0.0, poisson_gap_tolerance) + ); + + CHECK_THAT( + gap_at_new.relative_poisson, + Catch::Matchers::WithinAbs(0.0, poisson_gap_tolerance) + ); + + const int quadrature_order = get_gravity_quadrature_order(f); + + const GravitySolutionComparison comparison = compare_gravity_solutions( + f, legacy_solution, new_solution, quadrature_order + ); + + const GravitationalEnergies legacy_energies = + compute_gravitational_energies( + f, rho_grid, legacy_solution, quadrature_order + ); + + const GravitationalEnergies new_energies = compute_gravitational_energies( + f, rho_grid, new_solution, quadrature_order + ); + + const HomogeneousEllipsoidAnalytic analytic = + compute_homogeneous_ellipsoid_analytic( + semi_axis_x, semi_axis_y, semi_axis_z + ); + + const double analytic_binding_energy = + -(3.0 / 10.0) * utils::G * mass * mass * analytic.energy_kernel; + + const double new_binding_analytic_error = + std::abs(new_energies.binding - analytic_binding_energy) / + std::abs(analytic_binding_energy); + + const double new_virial_analytic_error = + std::abs(new_energies.virial - analytic_binding_energy) / + std::abs(analytic_binding_energy); + + const double new_virial_consistency_error = + std::abs(new_energies.binding - new_energies.virial) / + std::abs(new_energies.binding); + + const double relative_binding_difference = + std::abs(new_energies.binding - legacy_energies.binding) / + std::max( + 0.5 * (std::abs(new_energies.binding) + + std::abs(legacy_energies.binding)), + std::numeric_limits::min() + ); + + const double relative_virial_difference = + std::abs(new_energies.virial - legacy_energies.virial) / + std::max( + 0.5 * (std::abs(new_energies.virial) + + std::abs(legacy_energies.virial)), + std::numeric_limits::min() + ); + + INFO("Numerical density = " << numerical_density); + INFO("Analytic binding energy = " << analytic_binding_energy); + INFO("Legacy binding energy = " << legacy_energies.binding); + INFO("New binding energy = " << new_energies.binding); + INFO("Legacy virial energy = " << legacy_energies.virial); + INFO("New virial energy = " << new_energies.virial); + INFO("New binding analytic error = " << new_binding_analytic_error); + INFO("New virial analytic error = " << new_virial_analytic_error); + INFO("New virial consistency error = " << new_virial_consistency_error); + INFO( + "New/legacy physical gradient difference = " + << comparison.relative_gradient_difference + ); + INFO( + "New/legacy physical potential difference = " + << comparison.relative_potential_difference + ); + INFO( + "New/legacy binding-energy difference = " << relative_binding_difference + ); + INFO( + "New/legacy virial-energy difference = " << relative_virial_difference + ); + + REQUIRE(legacy_energies.binding < 0.0); + REQUIRE(legacy_energies.virial < 0.0); + REQUIRE(new_energies.binding < 0.0); + REQUIRE(new_energies.virial < 0.0); + + REQUIRE(std::isfinite(comparison.relative_gradient_difference)); + REQUIRE(std::isfinite(comparison.relative_potential_difference)); + + constexpr double gradient_parity_tolerance = 5.0e-4; + constexpr double potential_parity_tolerance = 1.0e-4; + constexpr double energy_parity_tolerance = 1.0e-5; + constexpr double analytic_energy_tolerance = 1.0e-5; + constexpr double consistency_tolerance = 1.0e-5; + + CHECK_THAT( + comparison.relative_gradient_difference, + Catch::Matchers::WithinAbs(0.0, gradient_parity_tolerance) + ); + + CHECK_THAT( + comparison.relative_potential_difference, + Catch::Matchers::WithinAbs(0.0, potential_parity_tolerance) + ); + + CHECK_THAT( + relative_binding_difference, + Catch::Matchers::WithinAbs(0.0, energy_parity_tolerance) + ); + + CHECK_THAT( + relative_virial_difference, + Catch::Matchers::WithinAbs(0.0, energy_parity_tolerance) + ); + + CHECK_THAT( + new_binding_analytic_error, + Catch::Matchers::WithinAbs(0.0, analytic_energy_tolerance) + ); + + CHECK_THAT( + new_virial_analytic_error, + Catch::Matchers::WithinAbs(0.0, analytic_energy_tolerance) + ); + + CHECK_THAT( + new_virial_consistency_error, + Catch::Matchers::WithinAbs(0.0, consistency_tolerance) + ); +} + +TEST_CASE( + "New Gravity Potential Deformed Rational Density Virial Self-Consistency", + tags::gravity &tags::self_consistency &tags::initialization + &tags::integration +) { + auto args = test_utils::setup_args(); + args.p.rtol = 1.0e-13; + args.p.max_iters = std::max(args.p.max_iters, 1000); + + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + const double radius = utils::RADIUS; + const double mass = utils::MASS; + + constexpr double x_scale = 1.15; + constexpr double y_scale = 0.95; + constexpr double z_scale = 1.0 / (x_scale * y_scale); + + REQUIRE_THAT( + x_scale * y_scale * z_scale, Catch::Matchers::WithinAbs(1.0, 1.0e-14) + ); + + const double semi_axis_x = x_scale * radius; + const double semi_axis_y = y_scale * radius; + const double semi_axis_z = z_scale * radius; + + auto affine_displacement = [](const mfem::Vector &position, + mfem::Vector &value) { + value.SetSize(3); + value(0) = (x_scale - 1.0) * position(0); + value(1) = (y_scale - 1.0) * position(1); + value(2) = (z_scale - 1.0) * position(2); + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + 3, affine_displacement + ); + + mfem::ParGridFunction displacement(f.displacementFes.get()); + + displacement.ProjectCoefficient(displacement_coefficient); + + f.mapping->SetDisplacement(displacement); + physics::update_stiffness_matrix(f); + + constexpr double concentration = 16.0; + const double density_scale = mass / std::pow(radius, 3.0); + + auto ellipsoidal_density = [semi_axis_x, semi_axis_y, semi_axis_z, + density_scale](const mfem::Vector &position) { + const double ellipsoidal_radius_squared = + position(0) * position(0) / (semi_axis_x * semi_axis_x) + + position(1) * position(1) / (semi_axis_y * semi_axis_y) + + position(2) * position(2) / (semi_axis_z * semi_axis_z); + + if (ellipsoidal_radius_squared >= 1.0) { + return 0.0; + } + + const double denominator = + 1.0 + concentration * ellipsoidal_radius_squared; + + return density_scale * (1.0 - ellipsoidal_radius_squared) / + (denominator * denominator); + }; + + mapping::PhysicalPositionFunctionCoefficient density_coefficient( + *f.mapping, ellipsoidal_density + ); + + mfem::GridFunction density(f.densityFes.get()); + + density.ProjectCoefficient(density_coefficient); + + zero_vacuum_density(f, density); + analysis::conserve_mass(f, density, mass); + + f.com = analysis::get_com(f, density); + f.Q = physics::compute_quadrupole_moment_tensor(f, density, f.com); + + const double normalized_quadrupole = f.Q.FNorm() / (mass * radius * radius); + + INFO("Normalized quadrupole = " << normalized_quadrupole); + + REQUIRE(normalized_quadrupole > 1.0e-3); + + const physics::GravitySolution gravity_solution = + physics::grav_potential_new(f, args, density, displacement); + + const int base_quadrature_order = get_gravity_quadrature_order(f); + + const GravitationalEnergies base_energies = compute_gravitational_energies( + f, density, gravity_solution, base_quadrature_order + ); + + const GravitationalEnergies medium_energies = + compute_gravitational_energies( + f, density, gravity_solution, base_quadrature_order + 4 + ); + + const GravitationalEnergies fine_energies = compute_gravitational_energies( + f, density, gravity_solution, base_quadrature_order + 8 + ); + + REQUIRE(fine_energies.binding < 0.0); + REQUIRE(fine_energies.virial < 0.0); + + const double base_consistency_error = + std::abs(base_energies.binding - base_energies.virial) / + std::abs(base_energies.binding); + + const double medium_consistency_error = + std::abs(medium_energies.binding - medium_energies.virial) / + std::abs(medium_energies.binding); + + const double fine_consistency_error = + std::abs(fine_energies.binding - fine_energies.virial) / + std::abs(fine_energies.binding); + + const double binding_quadrature_change = + std::abs(fine_energies.binding - medium_energies.binding) / + std::abs(fine_energies.binding); + + const double virial_quadrature_change = + std::abs(fine_energies.virial - medium_energies.virial) / + std::abs(fine_energies.virial); + + INFO("Base-order consistency error = " << base_consistency_error); + + INFO("Medium-order consistency error = " << medium_consistency_error); + + INFO("Fine-order consistency error = " << fine_consistency_error); + + INFO( + "Medium-to-fine binding-energy change = " << binding_quadrature_change + ); + + INFO("Medium-to-fine virial-energy change = " << virial_quadrature_change); + + constexpr double virial_tolerance = 1.0e-5; + constexpr double diagnostic_quadrature_tolerance = 1.0e-7; + + CHECK_THAT( + fine_consistency_error, + Catch::Matchers::WithinAbs(0.0, virial_tolerance) + ); + + CHECK_THAT( + binding_quadrature_change, + Catch::Matchers::WithinAbs(0.0, diagnostic_quadrature_tolerance) + ); + + CHECK_THAT( + virial_quadrature_change, + Catch::Matchers::WithinAbs(0.0, diagnostic_quadrature_tolerance) + ); +} + +TEST_CASE( + "New Gravity Potential Resolves Exterior Monopole By Compactification " + "Shell", + tags::gravity &tags::analytic_comparison &tags::initialization + &tags::integration +) { + auto args = test_utils::setup_args(); + args.p.rtol = 1.0e-13; + args.p.max_iters = std::max(args.p.max_iters, 1000); + + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.mapping != nullptr); + REQUIRE(f.domainMapperStateless != nullptr); + REQUIRE(f.compactificationCoordinate != nullptr); + + const double radius = utils::RADIUS; + const double mass = utils::MASS; + const double analytic_volume = + (4.0 / 3.0) * M_PI * radius * radius * radius; + const double density = mass / analytic_volume; + + mfem::ParGridFunction displacement(f.displacementFes.get()); + displacement = 0.0; + + f.mapping->ResetDisplacement(); + physics::update_stiffness_matrix(f); + + mfem::GridFunction rho_uniform(f.densityFes.get()); + rho_uniform = density; + + zero_vacuum_density(f, rho_uniform); + analysis::conserve_mass(f, rho_uniform, mass); + + f.com = analysis::get_com(f, rho_uniform); + f.Q = physics::compute_quadrupole_moment_tensor(f, rho_uniform, f.com); + + const physics::GravitySolution legacy_solution = + physics::grav_potential(f, args, rho_uniform); + + const physics::GravitySolution new_solution = + physics::grav_potential_new(f, args, rho_uniform, displacement); + + const std::array legacy_metrics = + measure_exterior_monopole_shells( + f, legacy_solution, displacement, ExteriorMonopoleMapping::legacy, + mass + ); + + const std::array new_metrics = + measure_exterior_monopole_shells( + f, new_solution, displacement, ExteriorMonopoleMapping::stateless, + mass + ); + + double maximum_new_potential_error = 0.0; + double maximum_new_radial_field_error = 0.0; + double maximum_new_tangential_field = 0.0; + + for (int shell = 0; shell < 5; ++shell) { + DYNAMIC_SECTION( + "Exterior coordinate in [" + << exterior_shell_boundaries[shell] << ", " + << exterior_shell_boundaries[shell + 1] << ")" + ) { + const ExteriorMonopoleShellMetrics &legacy = legacy_metrics[shell]; + + const ExteriorMonopoleShellMetrics ¤t = new_metrics[shell]; + + maximum_new_potential_error = std::max( + maximum_new_potential_error, current.potential_rms_error + ); + + maximum_new_radial_field_error = std::max( + maximum_new_radial_field_error, current.radial_field_rms_error + ); + + maximum_new_tangential_field = std::max( + maximum_new_tangential_field, current.tangential_field_rms + ); + + INFO("Shell = " << shell); + INFO( + "Exterior-coordinate interval = [" + << exterior_shell_boundaries[shell] << ", " + << exterior_shell_boundaries[shell + 1] << ")" + ); + + INFO( + "Legacy physical-radius range = [" + << legacy.minimum_radius << ", " << legacy.maximum_radius << "]" + ); + + INFO( + "New physical-radius range = [" + << current.minimum_radius << ", " << current.maximum_radius + << "]" + ); + + INFO( + "Legacy scaled-potential RMS error = " + << legacy.potential_rms_error + ); + + INFO( + "New scaled-potential RMS error = " + << current.potential_rms_error + ); + + INFO( + "Legacy scaled-radial-field RMS error = " + << legacy.radial_field_rms_error + ); + + INFO( + "New scaled-radial-field RMS error = " + << current.radial_field_rms_error + ); + + INFO( + "Legacy scaled-tangential-field RMS = " + << legacy.tangential_field_rms + ); + + INFO( + "New scaled-tangential-field RMS = " + << current.tangential_field_rms + ); + + REQUIRE(legacy.quadrature_points > 0); + REQUIRE(current.quadrature_points > 0); + + REQUIRE(std::isfinite(current.minimum_radius)); + REQUIRE(std::isfinite(current.maximum_radius)); + REQUIRE(std::isfinite(current.potential_rms_error)); + REQUIRE(std::isfinite(current.radial_field_rms_error)); + REQUIRE(std::isfinite(current.tangential_field_rms)); + + CHECK(current.minimum_radius > 0.0); + CHECK(current.maximum_radius > current.minimum_radius); + + /* + * These are broad regression bounds, not the virial target. + * The measured values will determine whether a monopole lift + * is warranted. + */ + CHECK(current.potential_rms_error < 1.0e-2); + CHECK(current.radial_field_rms_error < 1.0e-2); + CHECK(current.tangential_field_rms < 1.0e-2); + } + } + + for (int shell = 1; shell < 5; ++shell) { + CHECK( + new_metrics[shell].minimum_radius >= + new_metrics[shell - 1].minimum_radius + ); + + CHECK( + new_metrics[shell].maximum_radius > + new_metrics[shell - 1].maximum_radius + ); + } + + INFO( + "Maximum new scaled-potential shell error = " + << maximum_new_potential_error + ); + + INFO( + "Maximum new scaled-radial-field shell error = " + << maximum_new_radial_field_error + ); + + INFO( + "Maximum new scaled-tangential-field shell amplitude = " + << maximum_new_tangential_field + ); +} + +TEST_CASE( + "New Exterior Monopole Error Is Separated From Finite Element Projection " + "Floor", + tags::gravity &tags::analytic_comparison &tags::initialization + &tags::integration &tags::accuracy +) { + auto args = test_utils::setup_args(); + args.p.rtol = 1.0e-13; + args.p.max_iters = std::max(args.p.max_iters, 1000); + + fem::FEM f = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.mapping != nullptr); + REQUIRE(f.domainMapperStateless != nullptr); + REQUIRE(f.compactificationCoordinate != nullptr); + + const double stellar_radius = utils::RADIUS; + + const double mass = utils::MASS; + + const double analytic_volume = + (4.0 / 3.0) * M_PI * stellar_radius * stellar_radius * stellar_radius; + + const double density = mass / analytic_volume; + + mfem::ParGridFunction displacement(f.displacementFes.get()); + displacement = 0.0; + + f.mapping->ResetDisplacement(); + physics::update_stiffness_matrix(f); + + mfem::GridFunction rho_uniform(f.densityFes.get()); + rho_uniform = density; + + zero_vacuum_density(f, rho_uniform); + + analysis::conserve_mass(f, rho_uniform, mass); + + f.com = analysis::get_com(f, rho_uniform); + + f.Q = physics::compute_quadrupole_moment_tensor(f, rho_uniform, f.com); + + const physics::GravitySolution numerical_solution = + physics::grav_potential_new(f, args, rho_uniform, displacement); + + StatelessMonopolePotentialCoefficient analytic_potential_coefficient( + f, *f.domainMapperStateless, displacement, mass, stellar_radius + ); + + StatelessMonopoleHDivCoefficient analytic_field_coefficient( + f, *f.domainMapperStateless, displacement, mass, stellar_radius + ); + + physics::GravitySolution analytic_projection(f); + analytic_projection.phi = 0.0; + analytic_projection.gradPhi = 0.0; + + analytic_projection.phi.ProjectCoefficient(analytic_potential_coefficient); + + analytic_projection.gradPhi.ProjectCoefficient(analytic_field_coefficient); + + const std::array numerical_metrics = + measure_exterior_monopole_shells( + f, numerical_solution, displacement, + ExteriorMonopoleMapping::stateless, mass + ); + + const std::array projection_metrics = + measure_exterior_monopole_shells( + f, analytic_projection, displacement, + ExteriorMonopoleMapping::stateless, mass + ); + + mfem::Vector numerical_gradient_true; + mfem::Vector numerical_potential_true; + mfem::Vector projected_gradient_true; + mfem::Vector projected_potential_true; + + numerical_solution.gradPhi.GetTrueDofs(numerical_gradient_true); + + numerical_solution.phi.GetTrueDofs(numerical_potential_true); + + analytic_projection.gradPhi.GetTrueDofs(projected_gradient_true); + + analytic_projection.phi.GetTrueDofs(projected_potential_true); + + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + const double gradient_projection_gap = global_relative_vector_error( + numerical_gradient_true, projected_gradient_true, communicator + ); + + const double potential_projection_gap = global_relative_vector_error( + numerical_potential_true, projected_potential_true, communicator + ); + + double maximum_numerical_potential_error = 0.0; + double maximum_projected_potential_error = 0.0; + double maximum_numerical_radial_error = 0.0; + double maximum_projected_radial_error = 0.0; + double maximum_numerical_tangential_field = 0.0; + double maximum_projected_tangential_field = 0.0; + + std::ostringstream report; + + report << "Global numerical/projection gradient DOF gap = " + << gradient_projection_gap << '\n' + << "Global numerical/projection potential DOF gap = " + << potential_projection_gap << '\n'; + + for (int shell = 0; shell < 5; ++shell) { + const ExteriorMonopoleShellMetrics &numerical = + numerical_metrics[shell]; + + const ExteriorMonopoleShellMetrics &projected = + projection_metrics[shell]; + + maximum_numerical_potential_error = std::max( + maximum_numerical_potential_error, numerical.potential_rms_error + ); + + maximum_projected_potential_error = std::max( + maximum_projected_potential_error, projected.potential_rms_error + ); + + maximum_numerical_radial_error = std::max( + maximum_numerical_radial_error, numerical.radial_field_rms_error + ); + + maximum_projected_radial_error = std::max( + maximum_projected_radial_error, projected.radial_field_rms_error + ); + + maximum_numerical_tangential_field = std::max( + maximum_numerical_tangential_field, numerical.tangential_field_rms + ); + + maximum_projected_tangential_field = std::max( + maximum_projected_tangential_field, projected.tangential_field_rms + ); + + report << "Shell " << shell << " xi=[" + << exterior_shell_boundaries[shell] << ", " + << exterior_shell_boundaries[shell + 1] << "):\n" + << " radius range = [" << numerical.minimum_radius << ", " + << numerical.maximum_radius << "]\n" + << " numerical potential error = " + << numerical.potential_rms_error << '\n' + << " projected potential error = " + << projected.potential_rms_error << '\n' + << " numerical radial-field error = " + << numerical.radial_field_rms_error << '\n' + << " projected radial-field error = " + << projected.radial_field_rms_error << '\n' + << " numerical tangential field = " + << numerical.tangential_field_rms << '\n' + << " projected tangential field = " + << projected.tangential_field_rms << '\n'; + } + + INFO(report.str()); + + REQUIRE(std::isfinite(gradient_projection_gap)); + REQUIRE(std::isfinite(potential_projection_gap)); + + REQUIRE(maximum_numerical_potential_error > 0.0); + REQUIRE(maximum_projected_potential_error > 0.0); + REQUIRE(maximum_numerical_radial_error > 0.0); + REQUIRE(maximum_projected_radial_error > 0.0); + + /* + * Broad guards against a broken projection. These are not the final + * physical acceptance thresholds. + */ + CHECK(maximum_projected_potential_error < 5.0e-2); + CHECK(maximum_projected_radial_error < 5.0e-3); + CHECK(maximum_projected_tangential_field < 5.0e-3); + + CHECK(maximum_numerical_potential_error < 5.0e-2); + CHECK(maximum_numerical_radial_error < 5.0e-3); + CHECK(maximum_numerical_tangential_field < 5.0e-3); + + /* + * These are the decisive comparisons. If either fails, the solved + * field is farther from the direct FE representation than it is from + * the continuum monopole, indicating an operator-consistency issue + * rather than a simple approximation floor. + */ + CHECK(gradient_projection_gap < maximum_numerical_radial_error); + + CHECK(potential_projection_gap < maximum_numerical_potential_error); +} + +TEST_CASE( + "New Gravity Potential Matches Analytic Interior Potential For A Deformed " + "Homogeneous Star", + tags::gravity &tags::analytic_comparison &tags::initialization + &tags::integration &tags::accuracy +) { + auto args = test_utils::setup_args(); + args.p.rtol = 1.0e-13; + args.p.atol = 1.0e-14; + args.p.max_iters = std::max(args.p.max_iters, 2000); + + fem::FEM fem = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(fem.mapping != nullptr); + REQUIRE(fem.domainMapperStateless != nullptr); + + const double radius = utils::RADIUS; + const double mass = utils::MASS; + + constexpr double x_scale = 1.15; + constexpr double y_scale = 0.95; + constexpr double z_scale = 1.0 / (x_scale * y_scale); + + const double semi_axis_x = x_scale * radius; + const double semi_axis_y = y_scale * radius; + const double semi_axis_z = z_scale * radius; + + REQUIRE_THAT( + x_scale * y_scale * z_scale, Catch::Matchers::WithinAbs(1.0, 1.0e-14) + ); + + auto displacement_function = [](const mfem::Vector &position, + mfem::Vector &value) { + value.SetSize(3); + value(0) = (x_scale - 1.0) * position(0); + value(1) = (y_scale - 1.0) * position(1); + value(2) = (z_scale - 1.0) * position(2); + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + 3, displacement_function + ); + mfem::ParGridFunction displacement(fem.displacementFes.get()); + displacement.ProjectCoefficient(displacement_coefficient); + + fem.mapping->SetDisplacement(displacement); + physics::update_stiffness_matrix(fem); + + const double analytic_volume = + (4.0 / 3.0) * M_PI * semi_axis_x * semi_axis_y * semi_axis_z; + const double density_value = mass / analytic_volume; + + mfem::GridFunction density(fem.densityFes.get()); + density = density_value; + zero_vacuum_density(fem, density); + + const double projected_mass = analysis::domain_integrate_grid_function( + fem, density, utils::DOMAINS::STELLAR + ); + const double numerical_density = density_value * mass / projected_mass; + analysis::conserve_mass(fem, density, mass); + + fem.com = analysis::get_com(fem, density); + fem.Q = physics::compute_quadrupole_moment_tensor(fem, density, fem.com); + + const HomogeneousEllipsoidAnalytic analytic = + compute_homogeneous_ellipsoid_analytic( + semi_axis_x, semi_axis_y, semi_axis_z + ); + + auto analytic_potential = [numerical_density, semi_axis_x, semi_axis_y, + semi_axis_z, + analytic](const mfem::Vector &position) { + const double potential_kernel = + semi_axis_x * semi_axis_y * semi_axis_z * analytic.energy_kernel - + analytic.coefficient_x * position(0) * position(0) - + analytic.coefficient_y * position(1) * position(1) - + analytic.coefficient_z * position(2) * position(2); + + return -M_PI * utils::G * numerical_density * potential_kernel; + }; + + mapping::PhysicalPositionFunctionCoefficient analytic_potential_coefficient( + *fem.mapping, analytic_potential + ); + const int vacuum_attribute = + fem.domainMapperStateless->GetVacuumElementAttribute(); + mfem::ParGridFunction projected_potential(fem.gravityPotentialFes.get()); + projected_potential.ProjectCoefficient(analytic_potential_coefficient); + const physics::GravitySolution solution = + physics::grav_potential_new(fem, args, density, displacement); + + const int quadrature_order = get_gravity_quadrature_order(fem); + double local_solution_error_squared = 0.0; + double local_projection_error_squared = 0.0; + double local_solution_projection_gap_squared = 0.0; + double local_analytic_norm_squared = 0.0; + double local_projected_norm_squared = 0.0; + double local_maximum_relative_error = 0.0; + + mfem::Vector physical_position(3); + mfem::DenseMatrix mapping_jacobian(3); + + for (int element_id = 0; element_id < fem.mesh->GetNE(); ++element_id) { + mfem::ElementTransformation *transformation = + fem.mesh->GetElementTransformation(element_id); + if (transformation->Attribute == vacuum_attribute) { + continue; + } + + const mfem::IntegrationRule &rule = mfem::IntRules.Get( + transformation->GetGeometryType(), quadrature_order + ); + + for (int quadrature_point_id = 0; + quadrature_point_id < rule.GetNPoints(); ++quadrature_point_id) { + const mfem::IntegrationPoint &point = + rule.IntPoint(quadrature_point_id); + transformation->SetIntPoint(&point); + + fem.mapping->GetPhysicalPoint( + *transformation, point, physical_position + ); + fem.mapping->ComputeJacobian(*transformation, mapping_jacobian); + const double mapping_determinant = mapping_jacobian.Det(); + MFEM_VERIFY( + mapping_determinant > 0.0, + "Deformed potential test encountered a " + "non-positive mapping determinant." + ); + + const double expected_potential = + analytic_potential(physical_position); + const double computed_potential = + solution.phi.GetValue(element_id, point); + const double projected_potential_value = + projected_potential.GetValue(element_id, point); + const double weight = + point.weight * transformation->Weight() * mapping_determinant; + + local_solution_error_squared += + weight * (computed_potential - expected_potential) * + (computed_potential - expected_potential); + local_projection_error_squared += + weight * (projected_potential_value - expected_potential) * + (projected_potential_value - expected_potential); + local_solution_projection_gap_squared += + weight * (computed_potential - projected_potential_value) * + (computed_potential - projected_potential_value); + local_analytic_norm_squared += + weight * expected_potential * expected_potential; + local_projected_norm_squared += + weight * projected_potential_value * projected_potential_value; + local_maximum_relative_error = std::max( + local_maximum_relative_error, + std::abs(computed_potential - expected_potential) / + std::max( + std::abs(expected_potential), + std::numeric_limits::epsilon() + ) + ); + } + } + + const std::array local_values{ + local_solution_error_squared, local_projection_error_squared, + local_solution_projection_gap_squared, local_analytic_norm_squared, + local_projected_norm_squared + }; + std::array global_values{}; + MPI_Allreduce( + local_values.data(), global_values.data(), + static_cast(local_values.size()), MPI_DOUBLE, MPI_SUM, + fem.densityFes->GetComm() + ); + + double maximum_relative_error = 0.0; + MPI_Allreduce( + &local_maximum_relative_error, &maximum_relative_error, 1, MPI_DOUBLE, + MPI_MAX, fem.densityFes->GetComm() + ); + + const double solution_relative_error = + std::sqrt(global_values[0] / global_values[3]); + const double projection_relative_error = + std::sqrt(global_values[1] / global_values[3]); + const double solution_projection_gap = + std::sqrt(global_values[2] / global_values[4]); + + INFO( + "Ellipsoid coefficients = (" << analytic.coefficient_x << ", " + << analytic.coefficient_y << ", " + << analytic.coefficient_z << ")" + ); + INFO( + "Analytic interior-potential L2 relative error = " + << solution_relative_error + ); + INFO( + "Analytic-potential FE projection L2 relative error = " + << projection_relative_error + ); + INFO( + "New-solver / analytic-potential projection relative gap = " + << solution_projection_gap + ); + INFO( + "Maximum interior pointwise relative potential error = " + << maximum_relative_error + ); + + REQUIRE(std::isfinite(solution_relative_error)); + REQUIRE(std::isfinite(projection_relative_error)); + REQUIRE(std::isfinite(solution_projection_gap)); + REQUIRE(std::isfinite(maximum_relative_error)); + + /* + * The field test establishes an O(1e-3) representation floor on this + * mesh. These are intentionally accuracy-regression guards, not claims + * of analytic convergence of the unrefined RT/L2 representation. + */ + CHECK(solution_relative_error < 1.0e-5); + CHECK(projection_relative_error < 1.0e-5); + CHECK(solution_projection_gap < 1.0e-5); + CHECK(maximum_relative_error < 1.0e-5); +} + +struct FerrersN1Analytic { + double potential_constant; + std::array first_coefficients; + std::array, 3> second_coefficients; +}; + +class FerrersVacuumMaskedCoefficient final : public mfem::Coefficient { +public: + FerrersVacuumMaskedCoefficient( + Coefficient &coefficient, + const int vacuum_attribute + ) + : m_coefficient(coefficient), + m_vacuum_attribute(vacuum_attribute) { + } + + double Eval( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point + ) override { + if (transformation.Attribute == m_vacuum_attribute) { + return 0.0; + } + + return m_coefficient.Eval(transformation, integration_point); + } + +private: + Coefficient &m_coefficient; + int m_vacuum_attribute; +}; + +static double compute_ferrers_n1_coefficient( + const std::array< + double, + 3> &semi_axes, + const int first_denominator_axis, + const int second_denominator_axis +) { + const double axis_product = semi_axes[0] * semi_axes[1] * semi_axes[2]; + + const double length_scale = std::cbrt(axis_product); + + auto integrand = [semi_axes, axis_product, length_scale, + first_denominator_axis, + second_denominator_axis](const double t) { + if (t <= 0.0 || t >= 1.0) { + return 0.0; + } + + /* + * Map u in [0, infinity) to t in [0, 1]: + * + * u = L^2 [t / (1 - t)]^2. + */ + const double one_minus_t = 1.0 - t; + const double s = t / one_minus_t; + + const double u = length_scale * length_scale * s * s; + + const double du_dt = + length_scale * length_scale * 2.0 * s / (one_minus_t * one_minus_t); + + const double delta = std::sqrt( + (semi_axes[0] * semi_axes[0] + u) * + (semi_axes[1] * semi_axes[1] + u) * + (semi_axes[2] * semi_axes[2] + u) + ); + + double value = axis_product * du_dt / delta; + + if (first_denominator_axis >= 0) { + value /= semi_axes[first_denominator_axis] * + semi_axes[first_denominator_axis] + + u; + } + + if (second_denominator_axis >= 0) { + value /= semi_axes[second_denominator_axis] * + semi_axes[second_denominator_axis] + + u; + } + + return value; + }; + + double integration_error = 0.0; + + return boost::math::quadrature::gauss_kronrod::integrate( + integrand, 0.0, 1.0, 15, 1.0e-13, &integration_error + ); +} + +static FerrersN1Analytic compute_ferrers_n1_analytic( + const double semi_axis_x, + const double semi_axis_y, + const double semi_axis_z +) { + const std::array semi_axes{ + semi_axis_x, semi_axis_y, semi_axis_z + }; + + FerrersN1Analytic analytic{ + .potential_constant = compute_ferrers_n1_coefficient(semi_axes, -1, -1), + .first_coefficients = {}, + .second_coefficients = {} + }; + + for (int axis = 0; axis < 3; ++axis) { + analytic.first_coefficients[axis] = + compute_ferrers_n1_coefficient(semi_axes, axis, -1); + } + + for (int first_axis = 0; first_axis < 3; ++first_axis) { + for (int second_axis = first_axis; second_axis < 3; ++second_axis) { + const double coefficient = compute_ferrers_n1_coefficient( + semi_axes, first_axis, second_axis + ); + + analytic.second_coefficients[first_axis][second_axis] = coefficient; + + analytic.second_coefficients[second_axis][first_axis] = coefficient; + } + } + + return analytic; +} + +static double evaluate_ferrers_n1_potential( + const mfem::Vector &position, + const double central_density, + const FerrersN1Analytic &analytic +) { + const std::array coordinate_squared{ + position(0) * position(0), position(1) * position(1), + position(2) * position(2) + }; + + /* + * Expansion of + * + * -pi G rho_c abc / 2 + * integral [(1 - m^2(u))^2 / Delta(u)] du. + */ + double potential_kernel = analytic.potential_constant; + + for (int first_axis = 0; first_axis < 3; ++first_axis) { + potential_kernel -= 2.0 * analytic.first_coefficients[first_axis] * + coordinate_squared[first_axis]; + + for (int second_axis = 0; second_axis < 3; ++second_axis) { + potential_kernel += + analytic.second_coefficients[first_axis][second_axis] * + coordinate_squared[first_axis] * + coordinate_squared[second_axis]; + } + } + + return -0.5 * M_PI * utils::G * central_density * potential_kernel; +} + +static void evaluate_ferrers_n1_gradient( + const mfem::Vector &position, + const double central_density, + const FerrersN1Analytic &analytic, + mfem::Vector &gradient +) { + gradient.SetSize(3); + + const std::array coordinate_squared{ + position(0) * position(0), position(1) * position(1), + position(2) * position(2) + }; + + for (int axis = 0; axis < 3; ++axis) { + double coefficient = analytic.first_coefficients[axis]; + + for (int other_axis = 0; other_axis < 3; ++other_axis) { + coefficient -= analytic.second_coefficients[axis][other_axis] * + coordinate_squared[other_axis]; + } + + /* + * The solver stores grad(Phi), which points outward for a + * negative gravitational potential. + */ + gradient(axis) = 2.0 * M_PI * utils::G * central_density * + position(axis) * coefficient; + } +} + +TEST_CASE( + "New Gravity Potential Matches Analytic Ferrers Ellipsoid", + tags::gravity &tags::analytic_comparison &tags::initialization + &tags::integration &tags::accuracy +) { + auto args = test_utils::setup_args(); + + args.p.rtol = 1.0e-13; + args.p.atol = 1.0e-14; + args.p.max_iters = std::max(args.p.max_iters, 2000); + + fem::FEM fem = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(fem.mapping != nullptr); + REQUIRE(fem.domainMapperStateless != nullptr); + + const double radius = utils::RADIUS; + + const double mass = utils::MASS; + + constexpr double x_scale = 1.0; + constexpr double y_scale = 1.0; + constexpr double z_scale = 1.0 / (x_scale * y_scale); + + const double semi_axis_x = x_scale * radius; + const double semi_axis_y = y_scale * radius; + const double semi_axis_z = z_scale * radius; + + REQUIRE_THAT( + x_scale * y_scale * z_scale, Catch::Matchers::WithinAbs(1.0, 1.0e-14) + ); + + auto displacement_function = [](const mfem::Vector &position, + mfem::Vector &value) { + value.SetSize(3); + + value(0) = (x_scale - 1.0) * position(0); + value(1) = (y_scale - 1.0) * position(1); + value(2) = (z_scale - 1.0) * position(2); + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + 3, displacement_function + ); + + mfem::ParGridFunction displacement(fem.displacementFes.get()); + + displacement.ProjectCoefficient(displacement_coefficient); + + fem.mapping->SetDisplacement(displacement); + + physics::update_stiffness_matrix(fem); + + const int vacuum_attribute = + fem.domainMapperStateless->GetVacuumElementAttribute(); + + /* + * For rho = rho_c (1 - m^2), the exact mass is + * + * M = 8 pi a b c rho_c / 15. + */ + const double central_density = + 15.0 * mass / (8.0 * M_PI * semi_axis_x * semi_axis_y * semi_axis_z); + + auto density_function = [central_density, semi_axis_x, semi_axis_y, + semi_axis_z](const mfem::Vector &position) { + const double ellipsoidal_radius_squared = + position(0) * position(0) / (semi_axis_x * semi_axis_x) + + position(1) * position(1) / (semi_axis_y * semi_axis_y) + + position(2) * position(2) / (semi_axis_z * semi_axis_z); + + return central_density * + std::max(0.0, 1.0 - ellipsoidal_radius_squared); + }; + + mapping::PhysicalPositionFunctionCoefficient physical_density_coefficient( + *fem.mapping, density_function + ); + + FerrersVacuumMaskedCoefficient stellar_density_coefficient( + physical_density_coefficient, vacuum_attribute + ); + + mfem::GridFunction density(fem.densityFes.get()); + + density = 0.0; + + density.ProjectCoefficient(stellar_density_coefficient); + + const double projected_mass = analysis::domain_integrate_grid_function( + fem, density, utils::DOMAINS::STELLAR + ); + + REQUIRE(std::isfinite(projected_mass)); + REQUIRE(projected_mass > 0.0); + + /* + * Keep the projected source at exactly the requested mass. Because + * projection and scaling are linear, this also gives the central + * density appropriate to the represented source. + */ + const double density_scale = mass / projected_mass; + + density *= density_scale; + + const double represented_central_density = central_density * density_scale; + + fem.com = analysis::get_com(fem, density); + + fem.Q = physics::compute_quadrupole_moment_tensor(fem, density, fem.com); + + const double normalized_quadrupole = + fem.Q.FNorm() / (mass * radius * radius); + + // REQUIRE(normalized_quadrupole > 1.0e-3); + + const FerrersN1Analytic analytic = + compute_ferrers_n1_analytic(semi_axis_x, semi_axis_y, semi_axis_z); + + /* + * Independent analytic consistency checks. + * + * Sum(A_i) = 2 supplies the constant part of Poisson's + * equation. The B_ij identities supply the -m^2 part. + */ + const double first_coefficient_sum = analytic.first_coefficients[0] + + analytic.first_coefficients[1] + + analytic.first_coefficients[2]; + + REQUIRE_THAT( + first_coefficient_sum, Catch::Matchers::WithinAbs(2.0, 1.0e-11) + ); + + const std::array semi_axes_squared{ + semi_axis_x * semi_axis_x, semi_axis_y * semi_axis_y, + semi_axis_z * semi_axis_z + }; + + for (int axis = 0; axis < 3; ++axis) { + double poisson_coefficient = + 3.0 * analytic.second_coefficients[axis][axis]; + + for (int other_axis = 0; other_axis < 3; ++other_axis) { + if (other_axis != axis) { + poisson_coefficient += + analytic.second_coefficients[axis][other_axis]; + } + } + + REQUIRE_THAT( + poisson_coefficient, + Catch::Matchers::WithinRel(2.0 / semi_axes_squared[axis], 1.0e-10) + ); + } + + const physics::GravitySolution solution = + physics::grav_potential_new(fem, args, density, displacement); + + auto analytic_potential_function = + [represented_central_density, analytic](const mfem::Vector &position) { + return evaluate_ferrers_n1_potential( + position, represented_central_density, analytic + ); + }; + + mapping::PhysicalPositionFunctionCoefficient physical_potential_coefficient( + *fem.mapping, analytic_potential_function + ); + + /* + * This wrapper is required because scalar ProjectCoefficient has no + * attribute overload. It also prevents evaluation of the quartic + * interior formula in the compactified vacuum. + */ + FerrersVacuumMaskedCoefficient stellar_potential_coefficient( + physical_potential_coefficient, vacuum_attribute + ); + + mfem::ParGridFunction projected_potential(fem.gravityPotentialFes.get()); + + projected_potential = 0.0; + + projected_potential.ProjectCoefficient(stellar_potential_coefficient); + + const int quadrature_order = get_gravity_quadrature_order(fem) + 4; + + double local_potential_error_squared = 0.0; + double local_projection_error_squared = 0.0; + double local_solution_projection_gap_squared = 0.0; + double local_potential_norm_squared = 0.0; + double local_projection_norm_squared = 0.0; + double local_field_error_squared = 0.0; + double local_field_norm_squared = 0.0; + double local_maximum_potential_error = 0.0; + + mfem::Vector physical_position(3); + mfem::Vector reference_field(3); + mfem::Vector physical_field(3); + mfem::Vector analytic_field(3); + mfem::Vector field_difference(3); + + mfem::DenseMatrix mapping_jacobian(3, 3); + + for (int element_id = 0; element_id < fem.mesh->GetNE(); ++element_id) { + mfem::ElementTransformation *transformation = + fem.mesh->GetElementTransformation(element_id); + + if (transformation->Attribute == vacuum_attribute) { + continue; + } + + const mfem::IntegrationRule &rule = mfem::IntRules.Get( + transformation->GetGeometryType(), quadrature_order + ); + + for (int quadrature_point_id = 0; + quadrature_point_id < rule.GetNPoints(); ++quadrature_point_id) { + const mfem::IntegrationPoint &point = + rule.IntPoint(quadrature_point_id); + + transformation->SetIntPoint(&point); + + fem.mapping->GetPhysicalPoint( + *transformation, point, physical_position + ); + + fem.mapping->ComputeJacobian(*transformation, mapping_jacobian); + + const double mapping_determinant = mapping_jacobian.Det(); + + MFEM_VERIFY( + std::isfinite(mapping_determinant) && mapping_determinant > 0.0, + "Ferrers test encountered an invalid mapping determinant." + ); + + const double expected_potential = evaluate_ferrers_n1_potential( + physical_position, represented_central_density, analytic + ); + + evaluate_ferrers_n1_gradient( + physical_position, represented_central_density, analytic, + analytic_field + ); + + const double computed_potential = + solution.phi.GetValue(element_id, point); + + const double projected_potential_value = + projected_potential.GetValue(element_id, point); + + solution.gradPhi.GetVectorValue(element_id, point, reference_field); + + mapping_jacobian.Mult(reference_field, physical_field); + + physical_field /= mapping_determinant; + + field_difference = physical_field; + + field_difference -= analytic_field; + + const double weight = + point.weight * transformation->Weight() * mapping_determinant; + + const double potential_error = + computed_potential - expected_potential; + + const double projection_error = + projected_potential_value - expected_potential; + + const double solution_projection_difference = + computed_potential - projected_potential_value; + + local_potential_error_squared += + weight * potential_error * potential_error; + + local_projection_error_squared += + weight * projection_error * projection_error; + + local_solution_projection_gap_squared += + weight * solution_projection_difference * + solution_projection_difference; + + local_potential_norm_squared += + weight * expected_potential * expected_potential; + + local_projection_norm_squared += + weight * projected_potential_value * projected_potential_value; + + local_field_error_squared += + weight * (field_difference * field_difference); + + local_field_norm_squared += + weight * (analytic_field * analytic_field); + + local_maximum_potential_error = std::max( + local_maximum_potential_error, + std::abs(potential_error) / + std::max( + std::abs(expected_potential), + std::numeric_limits::epsilon() + ) + ); + } + } + + const std::array local_values{ + local_potential_error_squared, + local_projection_error_squared, + local_solution_projection_gap_squared, + local_potential_norm_squared, + local_projection_norm_squared, + local_field_error_squared, + local_field_norm_squared + }; + + std::array global_values{}; + + MPI_Allreduce( + local_values.data(), global_values.data(), + static_cast(local_values.size()), MPI_DOUBLE, MPI_SUM, + fem.densityFes->GetComm() + ); + + double maximum_potential_error = 0.0; + + MPI_Allreduce( + &local_maximum_potential_error, &maximum_potential_error, 1, MPI_DOUBLE, + MPI_MAX, fem.densityFes->GetComm() + ); + + REQUIRE(global_values[3] > 0.0); + REQUIRE(global_values[4] > 0.0); + REQUIRE(global_values[6] > 0.0); + + const double potential_relative_error = + std::sqrt(global_values[0] / global_values[3]); + + const double projection_relative_error = + std::sqrt(global_values[1] / global_values[3]); + + const double solution_projection_gap = + std::sqrt(global_values[2] / global_values[4]); + + const double field_relative_error = + std::sqrt(global_values[5] / global_values[6]); + + INFO("Projected mass before normalization = " << projected_mass); + + INFO("Density normalization factor = " << density_scale); + + INFO("Normalized quadrupole = " << normalized_quadrupole); + + INFO("Ferrers potential L2 relative error = " << potential_relative_error); + + INFO( + "Ferrers potential FE-projection relative error = " + << projection_relative_error + ); + + INFO( + "New-solver / Ferrers-potential projection gap = " + << solution_projection_gap + ); + + INFO("Ferrers field L2 relative error = " << field_relative_error); + + INFO( + "Maximum interior pointwise potential relative error = " + << maximum_potential_error + ); + + REQUIRE(std::isfinite(potential_relative_error)); + REQUIRE(std::isfinite(projection_relative_error)); + REQUIRE(std::isfinite(solution_projection_gap)); + REQUIRE(std::isfinite(field_relative_error)); + REQUIRE(std::isfinite(maximum_potential_error)); + + /* + * Initial characterization guards. Unlike the homogeneous case, + * this exact potential is quartic, so the FE representation floor + * will generally be higher. Record the values before deciding + * whether tighter regression thresholds are appropriate. + */ + CHECK(potential_relative_error < 1.0e-5); + CHECK(projection_relative_error < 1.0e-5); + CHECK(solution_projection_gap < 1.0e-5); + CHECK(field_relative_error < 1.0e-5); + CHECK(maximum_potential_error < 1.0e-5); +} diff --git a/tests/physics/gravity_monopole_accuracy.cpp b/tests/physics/gravity_monopole_accuracy.cpp new file mode 100644 index 0000000..2e41d4a --- /dev/null +++ b/tests/physics/gravity_monopole_accuracy.cpp @@ -0,0 +1,1502 @@ +#include +#include + +#include +#include +#include +#include +#include + +#include +#include + +import mean_field; +import test_helpers; + +namespace { + constexpr std::array shell_boundaries{0.0, 0.25, 0.50, + 0.75, 0.90, 1.0}; + constexpr int shell_count = static_cast(shell_boundaries.size()) - 1; + + enum class MappingPath { legacy, stateless }; + + struct ShellAccumulator { + long long points{0}; + double weight{0.0}; + double minimum_radius{std::numeric_limits::infinity()}; + double maximum_radius{0.0}; + double potential_error_squared{0.0}; + double radial_error_squared{0.0}; + double tangential_squared{0.0}; + }; + + struct ShellMetrics { + long long points{0}; + double minimum_radius{0.0}; + double maximum_radius{0.0}; + double potential_rms_error{0.0}; + double radial_rms_error{0.0}; + double tangential_rms{0.0}; + }; + + struct ShellMeasurement { + std::array shells{}; + long long invalid_points{0}; + }; + + constexpr int mapping_status_count = 8; + + struct GravitationalEnergies { + double binding{0.0}; + double virial{0.0}; + double minimum_mapping_determinant{ + std::numeric_limits::infinity() + }; + double maximum_mapping_determinant{ + -std::numeric_limits::infinity() + }; + long long invalid_points{0}; + std::array mapping_status_counts{}; + int first_invalid_element{-1}; + int first_invalid_attribute{-1}; + int first_invalid_quadrature_point{-1}; + double first_invalid_determinant{ + std::numeric_limits::quiet_NaN() + }; + }; + + constexpr int + mapping_status_index(const mean_field::mapping::MappingStatus status) { + return static_cast(status); + } + + void zero_vacuum_density( + const mean_field::fem::FEM &f, + mfem::GridFunction &density + ) { + for (int i = 0; i < f.vacuumDensityTdofs.Size(); ++i) { + density(f.vacuumDensityTdofs[i]) = 0.0; + } + } + + double global_norm( + const mfem::Vector &vector, + MPI_Comm communicator + ) { + const double local_norm_squared = vector * vector; + double global_norm_squared = 0.0; + MPI_Allreduce( + &local_norm_squared, &global_norm_squared, 1, MPI_DOUBLE, MPI_SUM, + communicator + ); + return std::sqrt(global_norm_squared); + } + + double global_dot( + const mfem::Vector &lhs, + const mfem::Vector &rhs, + MPI_Comm communicator + ) { + const double local_dot = lhs * rhs; + double result = 0.0; + MPI_Allreduce( + &local_dot, &result, 1, MPI_DOUBLE, MPI_SUM, communicator + ); + return result; + } + + double global_relative_error( + const mfem::Vector &computed, + const mfem::Vector &reference, + MPI_Comm communicator + ) { + REQUIRE(computed.Size() == reference.Size()); + + mfem::Vector difference(computed); + difference -= reference; + + return global_norm(difference, communicator) / + std::max( + global_norm(reference, communicator), + std::numeric_limits::epsilon() + ); + } + + int get_shell(const double coordinate) { + const double clamped = + std::clamp(coordinate, 0.0, std::nextafter(1.0, 0.0)); + + for (int shell = 0; shell < shell_count; ++shell) { + if (clamped < shell_boundaries[shell + 1]) { + return shell; + } + } + + return shell_count - 1; + } + + bool + retryable_infinity_status(const mean_field::mapping::MappingStatus status) { + return status == mean_field::mapping::MappingStatus:: + at_compactified_infinity || + status == mean_field::mapping::MappingStatus:: + outside_reference_domain || + status == + mean_field::mapping::MappingStatus::non_finite_result || + status == + mean_field::mapping::MappingStatus::non_positive_determinant; + } + + class ProjectionGeometry { + public: + ProjectionGeometry( + const mean_field::fem::FEM &f, + const mean_field::mapping::DomainMapperStateless &mapper, + const mfem::GridFunction &displacement + ) + : m_fem(f), + m_mapper(mapper), + m_displacement(displacement), + m_workspace(f.mesh->Dimension()) { + } + + mean_field::mapping::MappingStatus Evaluate( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point, + mean_field::mapping::MappingPointContext &context, + const bool permit_infinity_limit + ) { + m_used_infinity_limit = false; + + const int element_id = transformation.ElementNo; + MFEM_VERIFY( + element_id >= 0, + "Projection coefficient received an invalid element number." + ); + + const mfem::FiniteElement &displacement_element = + *m_fem.displacementFes->GetFE(element_id); + const mfem::FiniteElement &compactification_element = + *m_fem.compactificationFes->GetFE(element_id); + + mfem::Array displacement_dofs; + mfem::Array compactification_dofs; + + mfem::DofTransformation *displacement_transform = + m_fem.displacementFes->GetElementVDofs( + element_id, displacement_dofs + ); + + mfem::DofTransformation *compactification_transform = + m_fem.compactificationFes->GetElementDofs( + element_id, compactification_dofs + ); + + mfem::Vector element_displacement; + mfem::Vector element_compactification; + + m_displacement.GetSubVector( + displacement_dofs, element_displacement + ); + m_fem.compactificationCoordinate->GetSubVector( + compactification_dofs, element_compactification + ); + + if (displacement_transform != nullptr) { + displacement_transform->InvTransformPrimal( + element_displacement + ); + } + + if (compactification_transform != nullptr) { + compactification_transform->InvTransformPrimal( + element_compactification + ); + } + + const mean_field::mapping::ElementDisplacementData + displacement_data = mean_field::mapping:: + ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement + ); + + const mean_field::mapping::ElementCompactificationData + compactification_data( + compactification_element, element_compactification + ); + + const mean_field::mapping::ElementMappingData mapping_data{ + .displacement = displacement_data, + .compactification = compactification_data + }; + + mfem::Vector compactification_shape( + compactification_element.GetDof() + ); + compactification_element.CalcShape( + integration_point, compactification_shape + ); + + const double coordinate = + element_compactification * compactification_shape; + + mean_field::mapping::MappingStatus status = m_mapper.EvaluatePoint( + mapping_data, transformation, integration_point, m_workspace, + context + ); + + if (status == mean_field::mapping::MappingStatus::valid) { + transformation.SetIntPoint(&integration_point); + return status; + } + + const bool infinity_request = + m_mapper.IsCompactifiedElement(transformation) && + coordinate >= 1.0 - 1.0e-10; + + if (!permit_infinity_limit || !infinity_request || + !retryable_infinity_status(status)) { + transformation.SetIntPoint(&integration_point); + return status; + } + + const mfem::IntegrationPoint ¢er = + mfem::Geometries.GetCenter(transformation.GetGeometryType()); + + constexpr std::array inward_fractions{ + 1.0e-12, 1.0e-11, 1.0e-10, 1.0e-9, 1.0e-8, 1.0e-7, + 1.0e-6, 1.0e-5, 1.0e-4, 1.0e-3, 1.0e-2 + }; + + for (const double fraction : inward_fractions) { + mfem::IntegrationPoint inward; + inward.x = (1.0 - fraction) * integration_point.x + + fraction * center.x; + inward.y = (1.0 - fraction) * integration_point.y + + fraction * center.y; + inward.z = (1.0 - fraction) * integration_point.z + + fraction * center.z; + inward.weight = integration_point.weight; + + status = m_mapper.EvaluatePoint( + mapping_data, transformation, inward, m_workspace, context + ); + + if (status == mean_field::mapping::MappingStatus::valid) { + m_used_infinity_limit = true; + transformation.SetIntPoint(&integration_point); + return status; + } + + if (!retryable_infinity_status(status)) { + break; + } + } + + transformation.SetIntPoint(&integration_point); + return status; + } + + [[nodiscard]] bool UsedInfinityLimit() const noexcept { + return m_used_infinity_limit; + } + + private: + const mean_field::fem::FEM &m_fem; + const mean_field::mapping::DomainMapperStateless &m_mapper; + const mfem::GridFunction &m_displacement; + mean_field::mapping::DomainMapperStateless::Workspace m_workspace; + bool m_used_infinity_limit{false}; + }; + + class MonopolePotentialCoefficient final : public mfem::Coefficient { + public: + MonopolePotentialCoefficient( + const mean_field::fem::FEM &f, + const mean_field::mapping::DomainMapperStateless &mapper, + const mfem::GridFunction &displacement, + const double mass, + const double radius + ) + : m_geometry( + f, + mapper, + displacement + ), + m_vacuum_attribute(mapper.GetVacuumElementAttribute()), + m_mass(mass), + m_radius(radius) { + } + + double Eval( + mfem::ElementTransformation &transformation, + const mfem::IntegrationPoint &integration_point + ) override { + mean_field::mapping::MappingPointContext context; + + const mean_field::mapping::MappingStatus status = + m_geometry.Evaluate( + transformation, integration_point, context, true + ); + + MFEM_VERIFY( + status == mean_field::mapping::MappingStatus::valid, + "Stateless monopole-potential projection failed with status " + << static_cast(status) << " on element " + << transformation.ElementNo << '.' + ); + + if (m_geometry.UsedInfinityLimit()) { + return 0.0; + } + + const double radius = context.physical_position.Norml2(); + + MFEM_VERIFY( + std::isfinite(radius) && radius > 0.0, + "Invalid monopole projection radius." + ); + + if (transformation.Attribute == m_vacuum_attribute) { + return -mean_field::utils::G * m_mass / radius; + } + + return -mean_field::utils::G * m_mass * + (3.0 * m_radius * m_radius - radius * radius) / + (2.0 * m_radius * m_radius * m_radius); + } + + private: + ProjectionGeometry m_geometry; + int m_vacuum_attribute; + double m_mass; + double m_radius; + }; + + void local_to_true( + const mfem::ParFiniteElementSpace &space, + const mfem::Vector &local, + mfem::Vector &true_vector + ) { + true_vector.SetSize(space.GetTrueVSize()); + true_vector = 0.0; + + const mfem::Operator *prolongation = space.GetProlongationMatrix(); + + if (prolongation != nullptr) { + prolongation->MultTranspose(local, true_vector); + } else { + true_vector = local; + } + } + + mfem::Vector assemble_monopole_projection_rhs( + mean_field::fem::FEM &f, + const mfem::GridFunction &displacement, + const double mass, + const double stellar_radius + ) { + mfem::Vector local_rhs(f.gravityFluxFes->GetVSize()); + local_rhs = 0.0; + + mean_field::mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + const int vacuum_attribute = + f.domainMapperStateless->GetVacuumElementAttribute(); + const int quadrature_order = + 2 * f.gravityFluxFes->GetMaxElementOrder() + 8; + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + const mfem::FiniteElement &gravity_element = + *f.gravityFluxFes->GetFE(element_id); + const mfem::FiniteElement &displacement_element = + *f.displacementFes->GetFE(element_id); + const mfem::FiniteElement &compactification_element = + *f.compactificationFes->GetFE(element_id); + + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + + mfem::Array gravity_dofs; + mfem::Array displacement_dofs; + mfem::Array compactification_dofs; + + mfem::DofTransformation *gravity_transform = + f.gravityFluxFes->GetElementVDofs(element_id, gravity_dofs); + mfem::DofTransformation *displacement_transform = + f.displacementFes->GetElementVDofs( + element_id, displacement_dofs + ); + mfem::DofTransformation *compactification_transform = + f.compactificationFes->GetElementDofs( + element_id, compactification_dofs + ); + + mfem::Vector element_displacement; + mfem::Vector element_compactification; + + displacement.GetSubVector(displacement_dofs, element_displacement); + f.compactificationCoordinate->GetSubVector( + compactification_dofs, element_compactification + ); + + if (displacement_transform != nullptr) { + displacement_transform->InvTransformPrimal( + element_displacement + ); + } + + if (compactification_transform != nullptr) { + compactification_transform->InvTransformPrimal( + element_compactification + ); + } + + const mean_field::mapping::ElementDisplacementData + displacement_data = mean_field::mapping:: + ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement + ); + + const mean_field::mapping::ElementCompactificationData + compactification_data( + compactification_element, element_compactification + ); + + const mean_field::mapping::ElementMappingData mapping_data{ + .displacement = displacement_data, + .compactification = compactification_data + }; + + const int dof_count = gravity_element.GetDof(); + const int dimension = transformation->GetSpaceDim(); + + mfem::Vector element_rhs(dof_count); + mfem::Vector analytic_field(dimension); + mfem::Vector pulled_rhs_field(dimension); + mfem::DenseMatrix vector_shape(dof_count, dimension); + + element_rhs = 0.0; + + const mfem::IntegrationRule &rule = mfem::IntRules.Get( + transformation->GetGeometryType(), quadrature_order + ); + + for (int q = 0; q < rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &point = rule.IntPoint(q); + + mean_field::mapping::VolumeMappingContext context; + + const mean_field::mapping::MappingStatus status = + f.domainMapperStateless->EvaluateVolume( + mapping_data, *transformation, point, workspace, context + ); + + MFEM_VERIFY( + status == mean_field::mapping::MappingStatus::valid, + "Mapped monopole projection RHS failed with status " + << static_cast(status) << " on element " + << element_id << ", quadrature point " << q << '.' + ); + + analytic_field = context.mapping.physical_position; + + const double radius = analytic_field.Norml2(); + + MFEM_VERIFY( + std::isfinite(radius) && radius > 0.0, + "Invalid physical radius in projection RHS." + ); + + if (transformation->Attribute == vacuum_attribute) { + analytic_field *= mean_field::utils::G * mass / + (radius * radius * radius); + } else { + analytic_field *= + mean_field::utils::G * mass / + (stellar_radius * stellar_radius * stellar_radius); + } + + context.mapping.mapping_jacobian.MultTranspose( + analytic_field, pulled_rhs_field + ); + + transformation->SetIntPoint(&point); + gravity_element.CalcVShape(*transformation, vector_shape); + + const double weight = point.weight * transformation->Weight(); + + for (int i = 0; i < dof_count; ++i) { + for (int component = 0; component < dimension; + ++component) { + element_rhs(i) += weight * vector_shape(i, component) * + pulled_rhs_field(component); + } + } + } + + if (gravity_transform != nullptr) { + gravity_transform->TransformDual(element_rhs); + } + + local_rhs.AddElementVector(gravity_dofs, element_rhs); + } + + mfem::Vector true_rhs; + local_to_true(*f.gravityFluxFes, local_rhs, true_rhs); + + return true_rhs; + } + + mfem::Vector project_monopole_gradient( + mean_field::fem::FEM &f, + const mfem::ParGridFunction &displacement, + const double mass, + const double stellar_radius + ) { + mfem::Vector displacement_true; + displacement.GetTrueDofs(displacement_true); + + const mfem::Vector projection_rhs = assemble_monopole_projection_rhs( + f, displacement, mass, stellar_radius + ); + + mean_field::operators::PreparedMappedHDivMassOperator mass_operator( + f, *f.domainMapperStateless + ); + mass_operator.Prepare(displacement_true); + + mfem::Vector projected_gradient(f.gravityFluxFes->GetTrueVSize()); + projected_gradient = 0.0; + + mfem::CGSolver solver(f.gravityFluxFes->GetComm()); + solver.SetOperator(mass_operator); + solver.SetRelTol(1.0e-9); + solver.SetAbsTol(1.0e-12); + solver.SetMaxIter(2000); + solver.SetPrintLevel(0); + solver.Mult(projection_rhs, projected_gradient); + + mfem::Vector projection_residual; + mass_operator.Mult(projected_gradient, projection_residual); + projection_residual -= projection_rhs; + + const double source_norm = + global_norm(projection_rhs, f.gravityFluxFes->GetComm()); + const double residual_norm = + global_norm(projection_residual, f.gravityFluxFes->GetComm()); + const double relative_residual = + residual_norm / + std::max(source_norm, std::numeric_limits::epsilon()); + + INFO("Mapped H(div) projection converged = " << solver.GetConverged()); + INFO( + "Mapped H(div) projection iterations = " + << solver.GetNumIterations() + ); + INFO( + "Mapped H(div) projection reported final norm = " + << solver.GetFinalNorm() + ); + INFO( + "Mapped H(div) projection direct residual norm = " << residual_norm + ); + INFO( + "Mapped H(div) projection direct relative residual = " + << relative_residual + ); + + REQUIRE(std::isfinite(relative_residual)); + REQUIRE(relative_residual < 1.0e-8); + return projected_gradient; + } + + double mapped_hdiv_relative_error( + mean_field::fem::FEM &f, + const mfem::ParGridFunction &displacement, + const mfem::Vector &computed, + const mfem::Vector &reference + ) { + REQUIRE(computed.Size() == reference.Size()); + + mfem::Vector displacement_true; + displacement.GetTrueDofs(displacement_true); + + mean_field::operators::PreparedMappedHDivMassOperator mass_operator( + f, *f.domainMapperStateless + ); + mass_operator.Prepare(displacement_true); + + mfem::Vector difference(computed); + difference -= reference; + + mfem::Vector difference_action; + mfem::Vector reference_action; + + mass_operator.Mult(difference, difference_action); + mass_operator.Mult(reference, reference_action); + + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + const double difference_energy = + global_dot(difference, difference_action, communicator); + const double reference_energy = + global_dot(reference, reference_action, communicator); + + REQUIRE(difference_energy >= -1.0e-12 * std::abs(reference_energy)); + REQUIRE(reference_energy > 0.0); + + return std::sqrt(std::max(0.0, difference_energy) / reference_energy); + } + + ShellMeasurement measure_exterior_shells( + mean_field::fem::FEM &f, + const mean_field::physics::GravitySolution &solution, + const mfem::GridFunction &displacement, + const MappingPath mapping_path, + const double mass + ) { + std::array local{}; + long long local_invalid_points = 0; + + mean_field::mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + const int vacuum_attribute = + f.domainMapperStateless->GetVacuumElementAttribute(); + const int quadrature_order = + 2 * std::max( + f.gravityPotentialFes->GetMaxElementOrder(), + f.gravityFluxFes->GetMaxElementOrder() + ) + + 8; + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + + if (transformation->Attribute != vacuum_attribute) { + continue; + } + + const mfem::FiniteElement &displacement_element = + *f.displacementFes->GetFE(element_id); + const mfem::FiniteElement &compactification_element = + *f.compactificationFes->GetFE(element_id); + + mfem::Array displacement_dofs; + mfem::Array compactification_dofs; + + mfem::DofTransformation *displacement_transform = + f.displacementFes->GetElementVDofs( + element_id, displacement_dofs + ); + mfem::DofTransformation *compactification_transform = + f.compactificationFes->GetElementDofs( + element_id, compactification_dofs + ); + + mfem::Vector element_displacement; + mfem::Vector element_compactification; + + displacement.GetSubVector(displacement_dofs, element_displacement); + f.compactificationCoordinate->GetSubVector( + compactification_dofs, element_compactification + ); + + if (displacement_transform != nullptr) { + displacement_transform->InvTransformPrimal( + element_displacement + ); + } + + if (compactification_transform != nullptr) { + compactification_transform->InvTransformPrimal( + element_compactification + ); + } + + const mean_field::mapping::ElementDisplacementData + displacement_data = mean_field::mapping:: + ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement + ); + + const mean_field::mapping::ElementCompactificationData + compactification_data( + compactification_element, element_compactification + ); + + const mean_field::mapping::ElementMappingData mapping_data{ + .displacement = displacement_data, + .compactification = compactification_data + }; + + mfem::Vector compactification_shape( + compactification_element.GetDof() + ); + + const mfem::IntegrationRule &rule = mfem::IntRules.Get( + transformation->GetGeometryType(), quadrature_order + ); + + for (int q = 0; q < rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &point = rule.IntPoint(q); + + transformation->SetIntPoint(&point); + compactification_element.CalcShape( + point, compactification_shape + ); + + const double coordinate = + element_compactification * compactification_shape; + const int shell = get_shell(coordinate); + + mfem::Vector reference_field(3); + mfem::Vector physical_field(3); + mfem::Vector physical_position(3); + + solution.gradPhi.GetVectorValue( + element_id, point, reference_field + ); + + if (mapping_path == MappingPath::stateless) { + mean_field::mapping::VolumeMappingContext context; + + const mean_field::mapping::MappingStatus status = + f.domainMapperStateless->EvaluateVolume( + mapping_data, *transformation, point, workspace, + context + ); + + if (status != mean_field::mapping::MappingStatus::valid) { + ++local_invalid_points; + continue; + } + + physical_position = context.mapping.physical_position; + mean_field::mapping::MapHDivFluxToPhysical( + context.mapping, reference_field, physical_field + ); + } else { + f.mapping->GetPhysicalPoint( + *transformation, point, physical_position + ); + + mfem::DenseMatrix jacobian(3); + f.mapping->ComputeJacobian(*transformation, jacobian); + + const double determinant = jacobian.Det(); + + if (!std::isfinite(determinant) || determinant <= 0.0) { + ++local_invalid_points; + continue; + } + + jacobian.Mult(reference_field, physical_field); + physical_field /= determinant; + } + + const double radius = physical_position.Norml2(); + + if (!std::isfinite(radius) || radius <= 0.0) { + ++local_invalid_points; + continue; + } + + mfem::Vector radial_unit(physical_position); + radial_unit /= radius; + + const double radial_field = physical_field * radial_unit; + + mfem::Vector tangential_field(physical_field); + tangential_field.Add(-radial_field, radial_unit); + + const double potential = + solution.phi.GetValue(element_id, point); + + const double scaled_potential = + -radius * potential / (mean_field::utils::G * mass); + const double scaled_radial_field = + radius * radius * radial_field / + (mean_field::utils::G * mass); + const double scaled_tangential_field = + radius * radius * tangential_field.Norml2() / + (mean_field::utils::G * mass); + + if (!std::isfinite(scaled_potential) || + !std::isfinite(scaled_radial_field) || + !std::isfinite(scaled_tangential_field)) { + ++local_invalid_points; + continue; + } + + const double weight = point.weight * transformation->Weight(); + + ShellAccumulator &accumulator = local[shell]; + + ++accumulator.points; + accumulator.weight += weight; + + accumulator.minimum_radius = + std::min(accumulator.minimum_radius, radius); + accumulator.maximum_radius = + std::max(accumulator.maximum_radius, radius); + + accumulator.potential_error_squared += + weight * (scaled_potential - 1.0) * + (scaled_potential - 1.0); + accumulator.radial_error_squared += + weight * (scaled_radial_field - 1.0) * + (scaled_radial_field - 1.0); + accumulator.tangential_squared += + weight * scaled_tangential_field * scaled_tangential_field; + } + } + + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + ShellMeasurement measurement; + + MPI_Allreduce( + &local_invalid_points, &measurement.invalid_points, 1, + MPI_LONG_LONG, MPI_SUM, communicator + ); + + for (int shell = 0; shell < shell_count; ++shell) { + long long points = 0; + + MPI_Allreduce( + &local[shell].points, &points, 1, MPI_LONG_LONG, MPI_SUM, + communicator + ); + + const double local_sums[4]{ + local[shell].weight, local[shell].potential_error_squared, + local[shell].radial_error_squared, + local[shell].tangential_squared + }; + + double sums[4]{}; + + MPI_Allreduce( + local_sums, sums, 4, MPI_DOUBLE, MPI_SUM, communicator + ); + + double minimum_radius = 0.0; + double maximum_radius = 0.0; + + MPI_Allreduce( + &local[shell].minimum_radius, &minimum_radius, 1, MPI_DOUBLE, + MPI_MIN, communicator + ); + MPI_Allreduce( + &local[shell].maximum_radius, &maximum_radius, 1, MPI_DOUBLE, + MPI_MAX, communicator + ); + + measurement.shells[shell] = { + .points = points, + .minimum_radius = minimum_radius, + .maximum_radius = maximum_radius, + .potential_rms_error = + sums[0] > 0.0 ? std::sqrt(sums[1] / sums[0]) + : std::numeric_limits::infinity(), + .radial_rms_error = + sums[0] > 0.0 ? std::sqrt(sums[2] / sums[0]) + : std::numeric_limits::infinity(), + .tangential_rms = sums[0] > 0.0 + ? std::sqrt(sums[3] / sums[0]) + : std::numeric_limits::infinity() + }; + } + + return measurement; + } + + GravitationalEnergies compute_stellar_energies( + mean_field::fem::FEM &f, + const mfem::GridFunction &density, + const mean_field::physics::GravitySolution &solution, + const mfem::GridFunction &displacement + ) { + mean_field::mapping::DomainMapperStateless::Workspace workspace( + f.mesh->Dimension() + ); + + double local_binding = 0.0; + double local_virial = 0.0; + long long local_invalid_points = 0; + double local_minimum_determinant = + std::numeric_limits::infinity(); + double local_maximum_determinant = + -std::numeric_limits::infinity(); + + const int vacuum_attribute = + f.domainMapperStateless->GetVacuumElementAttribute(); + + const int order = 2 * std::max( + f.gravityPotentialFes->GetMaxElementOrder(), + f.gravityFluxFes->GetMaxElementOrder() + ) + + 8; + std::array local_status_counts{}; + + for (int element_id = 0; element_id < f.mesh->GetNE(); ++element_id) { + mfem::ElementTransformation *transformation = + f.mesh->GetElementTransformation(element_id); + if (transformation->Attribute == vacuum_attribute) { + continue; + } + + const mfem::FiniteElement &displacement_element = + *f.displacementFes->GetFE(element_id); + const mfem::FiniteElement &compactification_element = + *f.compactificationFes->GetFE(element_id); + + mfem::Array displacement_dofs; + mfem::Array compactification_dofs; + + mfem::DofTransformation *displacement_transform = + f.displacementFes->GetElementVDofs( + element_id, displacement_dofs + ); + mfem::DofTransformation *compactification_transform = + f.compactificationFes->GetElementDofs( + element_id, compactification_dofs + ); + + mfem::Vector element_displacement; + mfem::Vector element_compactification; + + displacement.GetSubVector(displacement_dofs, element_displacement); + f.compactificationCoordinate->GetSubVector( + compactification_dofs, element_compactification + ); + + if (displacement_transform != nullptr) { + displacement_transform->InvTransformPrimal( + element_displacement + ); + } + + if (compactification_transform != nullptr) { + compactification_transform->InvTransformPrimal( + element_compactification + ); + } + + const mean_field::mapping::ElementDisplacementData + displacement_data = mean_field::mapping:: + ElementDisplacementDataFromElementVDofs( + displacement_element, element_displacement + ); + + const mean_field::mapping::ElementCompactificationData + compactification_data( + compactification_element, element_compactification + ); + + const mean_field::mapping::ElementMappingData mapping_data{ + .displacement = displacement_data, + .compactification = compactification_data + }; + + const mfem::IntegrationRule &rule = + mfem::IntRules.Get(transformation->GetGeometryType(), order); + + for (int q = 0; q < rule.GetNPoints(); ++q) { + const mfem::IntegrationPoint &point = rule.IntPoint(q); + + mean_field::mapping::VolumeMappingContext context; + + const mean_field::mapping::MappingStatus status = + f.domainMapperStateless->EvaluateVolume( + mapping_data, *transformation, point, workspace, context + ); + + const double mapping_determinant = + context.mapping.mapping_determinant; + if (std::isfinite(mapping_determinant)) { + local_minimum_determinant = std::min( + local_minimum_determinant, mapping_determinant + ); + local_maximum_determinant = std::max( + local_maximum_determinant, mapping_determinant + ); + } + + const int status_index = mapping_status_index(status); + MFEM_VERIFY( + status_index >= 0 && status_index < mapping_status_count, + "Unexpected mapping status." + ); + ++local_status_counts[status_index]; + + if (status != mean_field::mapping::MappingStatus::valid) { + ++local_invalid_points; + continue; + } + + if (status != mean_field::mapping::MappingStatus::valid) { + ++local_invalid_points; + continue; + } + + mfem::Vector reference_field(3); + mfem::Vector physical_field(3); + + solution.gradPhi.GetVectorValue( + element_id, point, reference_field + ); + + mean_field::mapping::MapHDivFluxToPhysical( + context.mapping, reference_field, physical_field + ); + + const double rho = density.GetValue(element_id, point); + const double phi = solution.phi.GetValue(element_id, point); + + local_binding += 0.5 * rho * phi * context.quadrature.weight; + local_virial -= + rho * (context.mapping.physical_position * physical_field) * + context.quadrature.weight; + } + } + + GravitationalEnergies energies; + + MPI_Comm communicator = f.densityFes->GetComm(); + + MPI_Allreduce( + &local_binding, &energies.binding, 1, MPI_DOUBLE, MPI_SUM, + communicator + ); + MPI_Allreduce( + &local_virial, &energies.virial, 1, MPI_DOUBLE, MPI_SUM, + communicator + ); + MPI_Allreduce( + &local_invalid_points, &energies.invalid_points, 1, MPI_LONG_LONG, + MPI_SUM, communicator + ); + MPI_Allreduce( + local_status_counts.data(), energies.mapping_status_counts.data(), + mapping_status_count, MPI_LONG_LONG, MPI_SUM, communicator + ); + MPI_Allreduce( + &local_minimum_determinant, &energies.minimum_mapping_determinant, + 1, MPI_DOUBLE, MPI_MIN, communicator + ); + MPI_Allreduce( + &local_maximum_determinant, &energies.maximum_mapping_determinant, + 1, MPI_DOUBLE, MPI_MAX, communicator + ); + + return energies; + } +} // namespace + +TEST_CASE( + "New Gravity Monopole Accuracy And Projection Floor", + tags::gravity &tags::analytic_comparison &tags::initialization + &tags::integration &tags::accuracy +) { + auto args = test_utils::setup_args(); + args.p.rtol = 1.0e-13; + args.p.max_iters = std::max(args.p.max_iters, 1000); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.mapping != nullptr); + REQUIRE(f.domainMapperStateless != nullptr); + REQUIRE(f.compactificationCoordinate != nullptr); + + const double radius = mean_field::utils::RADIUS; + const double mass = mean_field::utils::MASS; + + const double density_value = + mass / ((4.0 / 3.0) * M_PI * radius * radius * radius); + + mfem::ParGridFunction displacement(f.displacementFes.get()); + displacement = 0.0; + + f.mapping->ResetDisplacement(); + mean_field::physics::update_stiffness_matrix(f); + + mfem::GridFunction density(f.densityFes.get()); + density = density_value; + + zero_vacuum_density(f, density); + + mean_field::analysis::conserve_mass(f, density, mass); + + f.com = mean_field::analysis::get_com(f, density); + f.Q = mean_field::physics::compute_quadrupole_moment_tensor( + f, density, f.com + ); + + const mean_field::physics::GravitySolution legacy_solution = + mean_field::physics::grav_potential(f, args, density); + + const mean_field::physics::GravitySolution numerical_solution = + mean_field::physics::grav_potential_new(f, args, density, displacement); + + MonopolePotentialCoefficient potential_coefficient( + f, *f.domainMapperStateless, displacement, mass, radius + ); + + mean_field::physics::GravitySolution projected_solution(f); + projected_solution.phi = 0.0; + projected_solution.gradPhi = 0.0; + + projected_solution.phi.ProjectCoefficient(potential_coefficient); + + const mfem::Vector projected_gradient_true = + project_monopole_gradient(f, displacement, mass, radius); + + projected_solution.gradPhi.SetFromTrueDofs(projected_gradient_true); + + const ShellMeasurement legacy = measure_exterior_shells( + f, legacy_solution, displacement, MappingPath::legacy, mass + ); + + const ShellMeasurement numerical = measure_exterior_shells( + f, numerical_solution, displacement, MappingPath::stateless, mass + ); + + const ShellMeasurement projected = measure_exterior_shells( + f, projected_solution, displacement, MappingPath::stateless, mass + ); + + const GravitationalEnergies energies = + compute_stellar_energies(f, density, numerical_solution, displacement); + + mfem::Vector numerical_gradient; + mfem::Vector numerical_potential; + mfem::Vector projected_gradient; + mfem::Vector projected_potential; + + numerical_solution.gradPhi.GetTrueDofs(numerical_gradient); + numerical_solution.phi.GetTrueDofs(numerical_potential); + + projected_solution.gradPhi.GetTrueDofs(projected_gradient); + projected_solution.phi.GetTrueDofs(projected_potential); + + MPI_Comm communicator = f.gravityFluxFes->GetComm(); + + const double gradient_projection_gap = mapped_hdiv_relative_error( + f, displacement, numerical_gradient, projected_gradient + ); + + const double potential_projection_gap = global_relative_error( + numerical_potential, projected_potential, communicator + ); + + double maximum_numerical_potential_error = 0.0; + double maximum_projected_potential_error = 0.0; + double maximum_numerical_radial_error = 0.0; + double maximum_projected_radial_error = 0.0; + double maximum_numerical_tangential = 0.0; + double maximum_projected_tangential = 0.0; + + std::ostringstream report; + + for (int shell = 0; shell < shell_count; ++shell) { + const ShellMetrics &old_shell = legacy.shells[shell]; + const ShellMetrics &numerical_shell = numerical.shells[shell]; + const ShellMetrics &projected_shell = projected.shells[shell]; + + maximum_numerical_potential_error = std::max( + maximum_numerical_potential_error, + numerical_shell.potential_rms_error + ); + + maximum_projected_potential_error = std::max( + maximum_projected_potential_error, + projected_shell.potential_rms_error + ); + + maximum_numerical_radial_error = std::max( + maximum_numerical_radial_error, numerical_shell.radial_rms_error + ); + + maximum_projected_radial_error = std::max( + maximum_projected_radial_error, projected_shell.radial_rms_error + ); + + maximum_numerical_tangential = std::max( + maximum_numerical_tangential, numerical_shell.tangential_rms + ); + + maximum_projected_tangential = std::max( + maximum_projected_tangential, projected_shell.tangential_rms + ); + + report << "shell " << shell << " xi=[" << shell_boundaries[shell] + << ", " << shell_boundaries[shell + 1] << ")\n" + << " legacy radius=[" << old_shell.minimum_radius << ", " + << old_shell.maximum_radius << "]\n" + << " new radius=[" << numerical_shell.minimum_radius << ", " + << numerical_shell.maximum_radius << "]\n" + << " potential error: legacy=" << old_shell.potential_rms_error + << ", solved=" << numerical_shell.potential_rms_error + << ", projection=" << projected_shell.potential_rms_error << '\n' + << " radial error: legacy=" << old_shell.radial_rms_error + << ", solved=" << numerical_shell.radial_rms_error + << ", projection=" << projected_shell.radial_rms_error << '\n' + << " tangential amplitude: legacy=" << old_shell.tangential_rms + << ", solved=" << numerical_shell.tangential_rms + << ", projection=" << projected_shell.tangential_rms << '\n'; + } + + const double analytic_energy = + -3.0 * mean_field::utils::G * mass * mass / (5.0 * radius); + + const double binding_error = std::abs(energies.binding - analytic_energy) / + std::abs(analytic_energy); + const double virial_error = + std::abs(energies.virial - analytic_energy) / std::abs(analytic_energy); + const double consistency_error = + std::abs(energies.binding - energies.virial) / + std::abs(energies.binding); + + INFO(report.str()); + + INFO( + "Gradient solution/projection mapped H(div) gap = " + << gradient_projection_gap + ); + INFO( + "Potential solution/projection DOF gap = " << potential_projection_gap + ); + INFO("Analytic energy = " << analytic_energy); + INFO("Computed binding energy = " << energies.binding); + INFO("Computed virial energy = " << energies.virial); + INFO("Relative binding error = " << binding_error); + INFO("Relative virial error = " << virial_error); + INFO("Relative virial consistency error = " << consistency_error); + + REQUIRE(legacy.invalid_points == 0); + REQUIRE(numerical.invalid_points == 0); + REQUIRE(projected.invalid_points == 0); + REQUIRE(energies.invalid_points == 0); + + for (int shell = 0; shell < shell_count; ++shell) { + REQUIRE(legacy.shells[shell].points > 0); + REQUIRE(numerical.shells[shell].points > 0); + REQUIRE(projected.shells[shell].points > 0); + } + + CHECK(maximum_numerical_potential_error < 5.0e-2); + CHECK(maximum_projected_potential_error < 5.0e-2); + CHECK(maximum_numerical_radial_error < 5.0e-3); + CHECK(maximum_projected_radial_error < 5.0e-3); + CHECK(maximum_numerical_tangential < 5.0e-3); + CHECK(maximum_projected_tangential < 5.0e-3); + CHECK(gradient_projection_gap < 5.0e-3); + CHECK(potential_projection_gap < maximum_numerical_potential_error); + + constexpr double virial_target = 1.0e-5; + + CHECK(binding_error < virial_target); + CHECK(virial_error < virial_target); + CHECK(consistency_error < virial_target); +} + +TEST_CASE( + "New Gravity Virial Consistency Across Volume Preserving Deformation", + tags::gravity &tags::self_consistency &tags::initialization + &tags::integration &tags::accuracy +) { + auto args = test_utils::setup_args(); + args.p.rtol = 1.0e-13; + args.p.max_iters = std::max(args.p.max_iters, 1000); + + mean_field::fem::FEM f = + mean_field::fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(f.mapping != nullptr); + REQUIRE(f.domainMapperStateless != nullptr); + + const double radius = mean_field::utils::RADIUS; + const double mass = mean_field::utils::MASS; + + const double central_density = + 15.0 * mass / (8.0 * M_PI * radius * radius * radius); + + auto density_function = [central_density, + radius](const mfem::Vector &position) { + const double normalized_radius_squared = + (position * position) / (radius * radius); + return central_density * std::max(0.0, 1.0 - normalized_radius_squared); + }; + + mfem::FunctionCoefficient density_coefficient(density_function); + mfem::GridFunction density(f.densityFes.get()); + density.ProjectCoefficient(density_coefficient); + + zero_vacuum_density(f, density); + + mean_field::analysis::conserve_mass(f, density, mass); + + constexpr std::array amplitudes{0.0, 0.02, 0.05, 0.1, + 0.2, 0.5, 1.0}; + + std::array consistency_errors{}; + std::array normalized_quadrupoles{}; + std::array binding_energies{}; + std::array virial_energies{}; + + std::ostringstream report; + + for (std::size_t index = 0; index < amplitudes.size(); ++index) { + const double amplitude = amplitudes[index]; + + const double x_scale = 1.0 + 0.15 * amplitude; + const double y_scale = 1.0 - 0.05 * amplitude; + const double z_scale = 1.0 / (x_scale * y_scale); + + REQUIRE_THAT( + x_scale * y_scale * z_scale, + Catch::Matchers::WithinAbs(1.0, 1.0e-14) + ); + + auto displacement_function = + [x_scale, y_scale, + z_scale](const mfem::Vector &position, mfem::Vector &value) { + value.SetSize(3); + + value(0) = (x_scale - 1.0) * position(0); + value(1) = (y_scale - 1.0) * position(1); + value(2) = (z_scale - 1.0) * position(2); + }; + + mfem::VectorFunctionCoefficient displacement_coefficient( + 3, displacement_function + ); + mfem::ParGridFunction displacement(f.displacementFes.get()); + displacement.ProjectCoefficient(displacement_coefficient); + + f.mapping->SetDisplacement(displacement); + mean_field::physics::update_stiffness_matrix(f); + + f.com = mean_field::analysis::get_com(f, density); + f.Q = mean_field::physics::compute_quadrupole_moment_tensor( + f, density, f.com + ); + const mfem::FiniteElementSpace *nodal_space = f.mesh->GetNodalFESpace(); + + const mean_field::physics::GravitySolution solution = + mean_field::physics::grav_potential_new( + f, args, density, displacement + ); + const GravitationalEnergies energies = + compute_stellar_energies(f, density, solution, displacement); + + CAPTURE(amplitude, x_scale, y_scale, z_scale); + INFO( + "Mapping status valid = " + << energies.mapping_status_counts[mapping_status_index( + mean_field::mapping::MappingStatus::valid + )] + ); + INFO( + "Mapping status invalid_dimension = " + << energies.mapping_status_counts[mapping_status_index( + mean_field::mapping::MappingStatus::invalid_dimension + )] + ); + INFO( + "Mapping status non_finite_input = " + << energies.mapping_status_counts[mapping_status_index( + mean_field::mapping::MappingStatus::non_finite_input + )] + ); + INFO( + "Mapping status invalid_reference_radius = " + << energies.mapping_status_counts[mapping_status_index( + mean_field::mapping::MappingStatus::invalid_reference_radius + )] + ); + INFO( + "Mapping status at_compactified_infinity = " + << energies.mapping_status_counts[mapping_status_index( + mean_field::mapping::MappingStatus::at_compactified_infinity + )] + ); + INFO( + "Mapping status outside_reference_domain = " + << energies.mapping_status_counts[mapping_status_index( + mean_field::mapping::MappingStatus::outside_reference_domain + )] + ); + INFO( + "Mapping status non_finite_result = " + << energies.mapping_status_counts[mapping_status_index( + mean_field::mapping::MappingStatus::non_finite_result + )] + ); + INFO( + "Mapping status non_positive_determinant = " + << energies.mapping_status_counts[mapping_status_index( + mean_field::mapping::MappingStatus::non_positive_determinant + )] + ); + INFO("Total invalid mapping points = " << energies.invalid_points); + INFO( + "Mesh nodal order = " + << (nodal_space != nullptr ? nodal_space->GetMaxElementOrder() : -1) + ); + INFO( + "Displacement order = " << f.displacementFes->GetMaxElementOrder() + ); + INFO( + "Minimum discrete mapping determinant = " + << energies.minimum_mapping_determinant + ); + INFO( + "Maximum discrete mapping determinant = " + << energies.maximum_mapping_determinant + ); + + REQUIRE(energies.invalid_points == 0); + REQUIRE(std::isfinite(energies.binding)); + REQUIRE(std::isfinite(energies.virial)); + REQUIRE(energies.binding < 0.0); + REQUIRE(energies.virial < 0.0); + + binding_energies[index] = energies.binding; + virial_energies[index] = energies.virial; + + consistency_errors[index] = + std::abs(energies.binding - energies.virial) / + std::abs(energies.binding); + + normalized_quadrupoles[index] = f.Q.FNorm() / (mass * radius * radius); + + report << "amplitude=" << amplitude << ", scales=(" << x_scale << ", " + << y_scale << ", " << z_scale + << "), normalized quadrupole=" << normalized_quadrupoles[index] + << ", binding=" << binding_energies[index] + << ", virial=" << virial_energies[index] + << ", consistency error=" << consistency_errors[index] << '\n'; + } + + INFO(report.str()); + + for (std::size_t index = 1; index < amplitudes.size(); ++index) { + CHECK( + normalized_quadrupoles[index] > normalized_quadrupoles[index - 1] + ); + } + + CHECK(consistency_errors[0] < 1.0e-5); + for (std::size_t index = 1; index < amplitudes.size(); ++index) { + CHECK(consistency_errors[index] < 5.0e-5); + } +} diff --git a/tests/quadrature/policy.cpp b/tests/quadrature/policy.cpp index e29954b..ae93b04 100644 --- a/tests/quadrature/policy.cpp +++ b/tests/quadrature/policy.cpp @@ -3,8 +3,11 @@ #include #include +#include +#include #include #include +#include #include #include @@ -15,51 +18,104 @@ import test_helpers; using namespace mean_field; namespace { + template + concept HasRuntimeSpaceOrders = requires(T value) { value.space_orders; }; + + static_assert(mean_field::field::FieldTag); + static_assert(mean_field::field::FieldTag); + static_assert(mean_field::field::FieldTag); + static_assert(mean_field::field::FieldTag); + static_assert(mean_field::field::FieldTag); + static_assert(field::Gravity::constraintsAreValid); + static_assert(std::same_as< + field::RelationTargetT, + field::Gravity::Potential>); + static_assert(!HasRuntimeSpaceOrders); + std::string_view get_term_name(const quadrature::Term term) { switch (term) { - case quadrature::Term::gravity_hdiv_mass: return "gravity_hdiv_mass"; - case quadrature::Term::gravity_divergence: return "gravity_divergence"; - case quadrature::Term::gravity_source: return "gravity_source"; - case quadrature::Term::gravity_boundary: return "gravity_boundary"; - case quadrature::Term::density_projection: return "density_projection"; - case quadrature::Term::mass_conservation: return "mass_conservation"; - case quadrature::Term::center_of_mass: return "center_of_mass"; - case quadrature::Term::quadrupole: return "quadrupole"; - case quadrature::Term::gravitational_energy: return "gravitational_energy"; - case quadrature::Term::virial: return "virial"; - case quadrature::Term::error_norm: return "error_norm"; + case quadrature::Term::gravity_hdiv_mass: + return "gravity_hdiv_mass"; + case quadrature::Term::gravity_divergence: + return "gravity_divergence"; + case quadrature::Term::gravity_source: + return "gravity_source"; + case quadrature::Term::gravity_boundary: + return "gravity_boundary"; + case quadrature::Term::centrifugal: + return "centrifugal"; + case quadrature::Term::density_projection: + return "density_projection"; + case quadrature::Term::eos_closure: + return "eos_closure"; + case quadrature::Term::hydrostatic_equilibrium: + return "hydrostatic_equilibrium"; + case quadrature::Term::isobaric_surface: + return "isobaric_surface"; + case quadrature::Term::mesh_extension: + return "mesh_extension"; + case quadrature::Term::mass_conservation: + return "mass_conservation"; + case quadrature::Term::mass_normalization: + return "mass_normalization"; + case quadrature::Term::center_of_mass: + return "center_of_mass"; + case quadrature::Term::quadrupole: + return "quadrupole"; + case quadrature::Term::gravitational_energy: + return "gravitational_energy"; + case quadrature::Term::pressure_integral: + return "pressure_integral"; + case quadrature::Term::virial: + return "virial"; + case quadrature::Term::error_norm: + return "error_norm"; + case quadrature::Term::pressure_force: + return "pressure_force"; } return "unknown"; } - quadrature::Query make_query(const quadrature::Term term, const int base_order) { + quadrature::Query make_query( + const quadrature::Term term, + const int base_order + ) { return {.term = term, .base_order = base_order}; } -} -TEST_CASE("Quadrature Policy Computes Base Orders", tags::unit & tags::quadrature) { - const quadrature::Policy policy(quadrature::make_rule_set(quadrature::Mode::production)); + template + concept CanMakeFec = requires { FieldT::template make_fec(3); }; +} // namespace + +TEST_CASE( + "Quadrature Policy Computes Base Orders", + tags::unit &tags::quadrature +) { + const quadrature::Policy policy( + quadrature::make_rule_set(quadrature::Mode::production) + ); quadrature::Query generic_query = { - .term = quadrature::Term::gravitational_energy, - .trial_order = 3, - .test_order = 4, - .coefficient_order = 2, + .term = quadrature::Term::gravitational_energy, + .trial_order = 3, + .test_order = 4, + .coefficient_order = 2, .geometry_weight_order = 5 }; - const quadrature::Resolution generic_resolution = policy.resolve(generic_query); + const quadrature::Resolution generic_resolution = + policy.resolve(generic_query); CHECK(generic_resolution.base_order == 14); CHECK(generic_resolution.boost == 0); CHECK(generic_resolution.order == 14); CHECK_FALSE(generic_resolution.used_fixed_order); quadrature::Query divergence_query = { - .term = quadrature::Term::gravity_divergence, - .trial_order = 3, - .test_order = 2, - .coefficient_order = 1, + .term = quadrature::Term::gravity_divergence, + .trial_order = 3, + .test_order = 2, + .coefficient_order = 1, .geometry_weight_order = 4 }; @@ -69,147 +125,218 @@ TEST_CASE("Quadrature Policy Computes Base Orders", tags::unit & tags::quadratur CHECK(policy.resolve(divergence_query).base_order == 7); quadrature::Query explicit_query = { - .term = quadrature::Term::gravity_hdiv_mass, - .trial_order = 20, - .test_order = 20, - .coefficient_order = 20, + .term = quadrature::Term::gravity_hdiv_mass, + .trial_order = 20, + .test_order = 20, + .coefficient_order = 20, .geometry_weight_order = 20, - .base_order = 11 + .base_order = 11 }; CHECK(policy.resolve(explicit_query).base_order == 11); CHECK(policy.resolve(explicit_query).order == 11); } -TEST_CASE("Quadrature Policy Composes Global and Term Boosts", tags::unit & tags::quadrature) { - quadrature::RuleSet rule_set = quadrature::make_rule_set(quadrature::Mode::production, 3); +TEST_CASE( + "Quadrature Policy Composes Global and Term Boosts", + tags::unit &tags::quadrature +) { + quadrature::RuleSet rule_set = + quadrature::make_rule_set(quadrature::Mode::production, 3); rule_set.gravity_hdiv_mass.boost = 5; - rule_set.error_norm.boost = 2; + rule_set.error_norm.boost = 2; const quadrature::Policy policy(rule_set); - const quadrature::Resolution mass_resolution = policy.resolve(make_query(quadrature::Term::gravity_hdiv_mass, 7)); + const quadrature::Resolution mass_resolution = + policy.resolve(make_query(quadrature::Term::gravity_hdiv_mass, 7)); CHECK(mass_resolution.base_order == 7); CHECK(mass_resolution.boost == 8); CHECK(mass_resolution.order == 15); CHECK_FALSE(mass_resolution.used_fixed_order); - const quadrature::Resolution error_resolution = policy.resolve(make_query(quadrature::Term::error_norm, 7)); + const quadrature::Resolution error_resolution = + policy.resolve(make_query(quadrature::Term::error_norm, 7)); CHECK(error_resolution.boost == 5); CHECK(error_resolution.order == 12); - const quadrature::Resolution source_resolution = policy.resolve(make_query(quadrature::Term::gravity_source, 7)); + const quadrature::Resolution source_resolution = + policy.resolve(make_query(quadrature::Term::gravity_source, 7)); CHECK(source_resolution.boost == 3); CHECK(source_resolution.order == 10); } -TEST_CASE("Quadrature Fixed Orders Have Defined Precedence", tags::unit & tags::quadrature) { - quadrature::RuleSet rule_set = quadrature::make_rule_set(quadrature::Mode::production, 4); - rule_set.fallback.fixed_order = 17; +TEST_CASE( + "Quadrature Fixed Orders Have Defined Precedence", + tags::unit &tags::quadrature +) { + quadrature::RuleSet rule_set = + quadrature::make_rule_set(quadrature::Mode::production, 4); + rule_set.fallback.fixed_order = 17; rule_set.gravity_hdiv_mass.fixed_order = 23; - rule_set.gravity_hdiv_mass.boost = 100; - rule_set.gravity_source.boost = 100; + rule_set.gravity_hdiv_mass.boost = 100; + rule_set.gravity_source.boost = 100; const quadrature::Policy policy(rule_set); - const quadrature::Resolution term_resolution = policy.resolve(make_query(quadrature::Term::gravity_hdiv_mass, 8)); + const quadrature::Resolution term_resolution = + policy.resolve(make_query(quadrature::Term::gravity_hdiv_mass, 8)); CHECK(term_resolution.base_order == 8); CHECK(term_resolution.boost == 0); CHECK(term_resolution.order == 23); CHECK(term_resolution.used_fixed_order); - const quadrature::Resolution fallback_resolution = policy.resolve(make_query(quadrature::Term::gravity_source, 8)); + const quadrature::Resolution fallback_resolution = + policy.resolve(make_query(quadrature::Term::gravity_source, 8)); CHECK(fallback_resolution.base_order == 8); CHECK(fallback_resolution.boost == 0); CHECK(fallback_resolution.order == 17); CHECK(fallback_resolution.used_fixed_order); } -TEST_CASE("Quadrature Modes Apply Their Expected Baseline Boosts", tags::unit & tags::quadrature) { - constexpr int base_order = 6; +TEST_CASE( + "Quadrature Modes Apply Their Expected Baseline Boosts", + tags::unit &tags::quadrature +) { + constexpr int base_order = 6; constexpr int global_boost = 3; - for (const quadrature::Mode mode : {quadrature::Mode::fast, quadrature::Mode::production, quadrature::Mode::convergence}) { - const quadrature::Policy policy(quadrature::make_rule_set(mode, global_boost)); - const quadrature::Resolution resolution = policy.resolve(make_query(quadrature::Term::error_norm, base_order)); + for (const quadrature::Mode mode : + {quadrature::Mode::fast, quadrature::Mode::production, + quadrature::Mode::convergence}) { + const quadrature::Policy policy( + quadrature::make_rule_set(mode, global_boost) + ); + const quadrature::Resolution resolution = policy.resolve( + make_query(quadrature::Term::error_norm, base_order) + ); CHECK(resolution.boost == global_boost); CHECK(resolution.order == base_order + global_boost); } - const quadrature::Policy reference_policy(quadrature::make_rule_set(quadrature::Mode::reference, global_boost)); - const quadrature::Resolution reference_resolution = reference_policy.resolve(make_query(quadrature::Term::error_norm, base_order)); + const quadrature::Policy reference_policy( + quadrature::make_rule_set(quadrature::Mode::reference, global_boost) + ); + const quadrature::Resolution reference_resolution = + reference_policy.resolve( + make_query(quadrature::Term::error_norm, base_order) + ); CHECK(reference_resolution.boost == global_boost + 8); CHECK(reference_resolution.order == base_order + global_boost + 8); } -TEST_CASE("Quadrature Policy Routes Every Term to Its Control", tags::unit & tags::quadrature) { +TEST_CASE( + "Quadrature Policy Routes Every Term to Its Control", + tags::unit &tags::quadrature +) { quadrature::RuleSet rule_set; - rule_set.gravity_hdiv_mass.boost = 1; - rule_set.gravity_divergence.boost = 2; - rule_set.gravity_source.boost = 3; - rule_set.gravity_boundary.boost = 4; - rule_set.density_projection.boost = 5; - rule_set.mass_conservation.boost = 6; - rule_set.center_of_mass.boost = 7; - rule_set.quadrupole.boost = 8; - rule_set.gravitational_energy.boost = 9; - rule_set.virial.boost = 10; - rule_set.error_norm.boost = 11; + rule_set.gravity_hdiv_mass.boost = 1; + rule_set.gravity_divergence.boost = 2; + rule_set.gravity_source.boost = 3; + rule_set.gravity_boundary.boost = 4; + rule_set.centrifugal.boost = 18; + rule_set.density_projection.boost = 5; + rule_set.eos_closure.boost = 6; + rule_set.hydrostatic_equilibrium.boost = 7; + rule_set.isobaric_surface.boost = 8; + rule_set.mesh_extension.boost = 9; + rule_set.mass_conservation.boost = 10; + rule_set.mass_normalization.boost = 11; + rule_set.center_of_mass.boost = 12; + rule_set.quadrupole.boost = 13; + rule_set.gravitational_energy.boost = 14; + rule_set.pressure_integral.boost = 15; + rule_set.virial.boost = 16; + rule_set.error_norm.boost = 17; const quadrature::Policy policy(rule_set); - const std::array, 11> cases = {{ - {quadrature::Term::gravity_hdiv_mass, 1}, - {quadrature::Term::gravity_divergence, 2}, - {quadrature::Term::gravity_source, 3}, - {quadrature::Term::gravity_boundary, 4}, - {quadrature::Term::density_projection, 5}, - {quadrature::Term::mass_conservation, 6}, - {quadrature::Term::center_of_mass, 7}, - {quadrature::Term::quadrupole, 8}, - {quadrature::Term::gravitational_energy, 9}, - {quadrature::Term::virial, 10}, - {quadrature::Term::error_norm, 11} - }}; + const std::array, 18> cases = { + {{quadrature::Term::gravity_hdiv_mass, 1}, + {quadrature::Term::gravity_divergence, 2}, + {quadrature::Term::gravity_source, 3}, + {quadrature::Term::gravity_boundary, 4}, + {quadrature::Term::centrifugal, 18}, + {quadrature::Term::density_projection, 5}, + {quadrature::Term::eos_closure, 6}, + {quadrature::Term::hydrostatic_equilibrium, 7}, + {quadrature::Term::isobaric_surface, 8}, + {quadrature::Term::mesh_extension, 9}, + {quadrature::Term::mass_conservation, 10}, + {quadrature::Term::mass_normalization, 11}, + {quadrature::Term::center_of_mass, 12}, + {quadrature::Term::quadrupole, 13}, + {quadrature::Term::gravitational_energy, 14}, + {quadrature::Term::pressure_integral, 15}, + {quadrature::Term::virial, 16}, + {quadrature::Term::error_norm, 17}} + }; - for (const auto& [term, expected_boost] : cases) { + for (const auto &[term, expected_boost] : cases) { DYNAMIC_SECTION(get_term_name(term)) { - const quadrature::Resolution resolution = policy.resolve(make_query(term, 20)); + const quadrature::Resolution resolution = + policy.resolve(make_query(term, 20)); CHECK(resolution.boost == expected_boost); CHECK(resolution.order == 20 + expected_boost); } } } -TEST_CASE("Quadrature Policy Rejects Invalid Orders", tags::unit & tags::quadrature) { - const quadrature::Policy policy(quadrature::make_rule_set(quadrature::Mode::production)); +TEST_CASE( + "Quadrature Policy Rejects Invalid Orders", + tags::unit &tags::quadrature +) { + const quadrature::Policy policy( + quadrature::make_rule_set(quadrature::Mode::production) + ); quadrature::Query negative_component_query = { - .term = quadrature::Term::error_norm, - .trial_order = -1 + .term = quadrature::Term::error_norm, .trial_order = -1 }; - REQUIRE_THROWS_AS(policy.resolve(negative_component_query), std::invalid_argument); + REQUIRE_THROWS_AS( + policy.resolve(negative_component_query), std::invalid_argument + ); quadrature::Query negative_base_query = { - .term = quadrature::Term::error_norm, - .base_order = -1 + .term = quadrature::Term::error_norm, .base_order = -1 }; - REQUIRE_THROWS_AS(policy.resolve(negative_base_query), std::invalid_argument); + REQUIRE_THROWS_AS( + policy.resolve(negative_base_query), std::invalid_argument + ); quadrature::RuleSet negative_fixed_rule_set; negative_fixed_rule_set.error_norm.fixed_order = -1; const quadrature::Policy negative_fixed_policy(negative_fixed_rule_set); - REQUIRE_THROWS_AS(negative_fixed_policy.resolve(make_query(quadrature::Term::error_norm, 3)), std::invalid_argument); + REQUIRE_THROWS_AS( + negative_fixed_policy.resolve( + make_query(quadrature::Term::error_norm, 3) + ), + std::invalid_argument + ); quadrature::RuleSet negative_resolved_rule_set; negative_resolved_rule_set.fallback.boost = -4; - const quadrature::Policy negative_resolved_policy(negative_resolved_rule_set); - REQUIRE_THROWS_AS(negative_resolved_policy.resolve(make_query(quadrature::Term::error_norm, 3)), std::invalid_argument); + const quadrature::Policy negative_resolved_policy( + negative_resolved_rule_set + ); + REQUIRE_THROWS_AS( + negative_resolved_policy.resolve( + make_query(quadrature::Term::error_norm, 3) + ), + std::invalid_argument + ); } -TEST_CASE("MFEM Rule Factory Returns the Resolved Rule", tags::unit & tags::quadrature) { - quadrature::RuleSet rule_set = quadrature::make_rule_set(quadrature::Mode::production, 2); +TEST_CASE( + "MFEM Rule Factory Returns the Resolved Rule", + tags::unit &tags::quadrature +) { + quadrature::RuleSet rule_set = + quadrature::make_rule_set(quadrature::Mode::production, 2); rule_set.error_norm.boost = 3; const quadrature::RuleFactory factory{quadrature::Policy(rule_set)}; - const quadrature::MfemRule selected_rule = factory.get(make_query(quadrature::Term::error_norm, 4), mfem::Geometry::CUBE); - const mfem::IntegrationRule& expected_rule = mfem::IntRules.Get(mfem::Geometry::CUBE, 9); + const quadrature::MfemRule selected_rule = factory.get( + make_query(quadrature::Term::error_norm, 4), mfem::Geometry::CUBE + ); + const mfem::IntegrationRule &expected_rule = + mfem::IntRules.Get(mfem::Geometry::CUBE, 9); REQUIRE(selected_rule.integration_rule != nullptr); CHECK(selected_rule.resolution.base_order == 4); @@ -219,47 +346,85 @@ TEST_CASE("MFEM Rule Factory Returns the Resolved Rule", tags::unit & tags::quad CHECK(selected_rule.integration_rule->GetNPoints() > 0); } -TEST_CASE("MFEM Quadrature Rule Integrates Tensor Polynomial Exactly", tags::unit & tags::quadrature) { +TEST_CASE( + "MFEM Quadrature Rule Integrates Tensor Polynomial Exactly", + tags::unit &tags::quadrature +) { constexpr int polynomial_degree = 7; - const quadrature::RuleFactory factory{quadrature::Policy(quadrature::make_rule_set(quadrature::Mode::production))}; - const quadrature::MfemRule selected_rule = factory.get(make_query(quadrature::Term::error_norm, polynomial_degree), mfem::Geometry::CUBE); + const quadrature::RuleFactory factory{quadrature::Policy( + quadrature::make_rule_set(quadrature::Mode::production) + )}; + const quadrature::MfemRule selected_rule = factory.get( + make_query(quadrature::Term::error_norm, polynomial_degree), + mfem::Geometry::CUBE + ); double numerical_integral = 0.0; for (int i = 0; i < selected_rule.integration_rule->GetNPoints(); ++i) { - const mfem::IntegrationPoint& integration_point = selected_rule.integration_rule->IntPoint(i); - numerical_integral += integration_point.weight * std::pow(integration_point.x, polynomial_degree) * std::pow(integration_point.y, polynomial_degree) * std::pow(integration_point.z, polynomial_degree); + const mfem::IntegrationPoint &integration_point = + selected_rule.integration_rule->IntPoint(i); + numerical_integral += integration_point.weight * + std::pow(integration_point.x, polynomial_degree) * + std::pow(integration_point.y, polynomial_degree) * + std::pow(integration_point.z, polynomial_degree); } - const double one_dimensional_integral = 1.0 / static_cast(polynomial_degree + 1); - const double analytic_integral = one_dimensional_integral * one_dimensional_integral * one_dimensional_integral; - CHECK_THAT(numerical_integral, Catch::Matchers::WithinAbs(analytic_integral, 5.0e-14)); + const double one_dimensional_integral = + 1.0 / static_cast(polynomial_degree + 1); + const double analytic_integral = one_dimensional_integral * + one_dimensional_integral * + one_dimensional_integral; + CHECK_THAT( + numerical_integral, + Catch::Matchers::WithinAbs(analytic_integral, 5.0e-14) + ); } -TEST_CASE("Policy Controlled Hdiv Mass Assembly Matches Overintegrated Reference", tags::quadrature & tags::solver & tags::integration) { - mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D(1, 1, 1, mfem::Element::HEXAHEDRON, 1.0, 1.0, 1.0); +TEST_CASE( + "Policy Controlled Hdiv Mass Assembly Matches Overintegrated Reference", + tags::quadrature &tags::solver &tags::integration +) { + mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D( + 1, 1, 1, mfem::Element::HEXAHEDRON, 1.0, 1.0, 1.0 + ); mfem::RT_FECollection rt_collection(2, 3); mfem::FiniteElementSpace rt_space(&mesh, &rt_collection); - const mfem::FiniteElement* rt_element = rt_space.GetTypicalFE(); - mfem::ElementTransformation* transformation = mesh.GetElementTransformation(0); - const int base_order = 2 * rt_element->GetOrder() + transformation->OrderW(); + const mfem::FiniteElement *rt_element = rt_space.GetTypicalFE(); + mfem::ElementTransformation *transformation = + mesh.GetElementTransformation(0); + const int base_order = + 2 * rt_element->GetOrder() + transformation->OrderW(); - const quadrature::RuleFactory production_factory{quadrature::Policy(quadrature::make_rule_set(quadrature::Mode::production))}; - const quadrature::MfemRule production_rule = production_factory.get(make_query(quadrature::Term::gravity_hdiv_mass, base_order), rt_element->GetGeomType()); + const quadrature::RuleFactory production_factory{quadrature::Policy( + quadrature::make_rule_set(quadrature::Mode::production) + )}; + const quadrature::MfemRule production_rule = production_factory.get( + make_query(quadrature::Term::gravity_hdiv_mass, base_order), + rt_element->GetGeomType() + ); - quadrature::RuleSet reference_rule_set = quadrature::make_rule_set(quadrature::Mode::production); + quadrature::RuleSet reference_rule_set = + quadrature::make_rule_set(quadrature::Mode::production); reference_rule_set.gravity_hdiv_mass.boost = 8; - const quadrature::RuleFactory reference_factory{quadrature::Policy(reference_rule_set)}; - const quadrature::MfemRule reference_rule = reference_factory.get(make_query(quadrature::Term::gravity_hdiv_mass, base_order), rt_element->GetGeomType()); + const quadrature::RuleFactory reference_factory{ + quadrature::Policy(reference_rule_set) + }; + const quadrature::MfemRule reference_rule = reference_factory.get( + make_query(quadrature::Term::gravity_hdiv_mass, base_order), + rt_element->GetGeomType() + ); mfem::BilinearForm production_mass(&rt_space); - auto* production_integrator = new mfem::VectorFEMassIntegrator(); - production_integrator->SetIntegrationRule(*production_rule.integration_rule); + auto *production_integrator = new mfem::VectorFEMassIntegrator(); + production_integrator->SetIntegrationRule( + *production_rule.integration_rule + ); production_mass.AddDomainIntegrator(production_integrator); production_mass.Assemble(); production_mass.Finalize(); mfem::BilinearForm reference_mass(&rt_space); - auto* reference_integrator = new mfem::VectorFEMassIntegrator(); + auto *reference_integrator = new mfem::VectorFEMassIntegrator(); reference_integrator->SetIntegrationRule(*reference_rule.integration_rule); reference_mass.AddDomainIntegrator(reference_integrator); reference_mass.Assemble(); @@ -277,55 +442,417 @@ TEST_CASE("Policy Controlled Hdiv Mass Assembly Matches Overintegrated Reference mfem::Vector difference(production_output); difference -= reference_output; - const double relative_difference = difference.Norml2() / reference_output.Norml2(); + const double relative_difference = + difference.Norml2() / reference_output.Norml2(); INFO("Production quadrature order = " << production_rule.resolution.order); INFO("Reference quadrature order = " << reference_rule.resolution.order); INFO("Relative operator difference = " << relative_difference); CHECK_THAT(relative_difference, Catch::Matchers::WithinAbs(0.0, 1.0e-12)); } -TEST_CASE("HDiv Mass Helper Resolves the MFEM Baseline", tags::unit & tags::quadrature & tags::solver) { - mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D(1, 1, 1, mfem::Element::HEXAHEDRON); +TEST_CASE( + "HDiv Mass Helper Resolves the MFEM Baseline", + tags::unit &tags::quadrature &tags::solver +) { + mfem::Mesh mesh = + mfem::Mesh::MakeCartesian3D(1, 1, 1, mfem::Element::HEXAHEDRON); mfem::RT_FECollection rt_collection(2, 3); mfem::FiniteElementSpace rt_space(&mesh, &rt_collection); - quadrature::RuleSet rule_set = quadrature::make_rule_set(quadrature::Mode::production); + quadrature::RuleSet rule_set = + quadrature::make_rule_set(quadrature::Mode::production); rule_set.gravity_hdiv_mass.boost = 3; quadrature::RuleFactory factory{quadrature::Policy(std::move(rule_set))}; - const mfem::FiniteElement& element = *rt_space.GetTypicalFE(); - const mfem::ElementTransformation& transformation = *mesh.GetElementTransformation(0); + const mfem::FiniteElement &element = *rt_space.GetTypicalFE(); + const mfem::ElementTransformation &transformation = + *mesh.GetElementTransformation(0); mfem::VectorFEMassIntegrator integrator; - const quadrature::Resolution resolution = factory.configure_gravity_hdiv_mass(integrator, quadrature::QuadratureRole::discretization, element, transformation); - const int expected_base_order = 2 * element.GetOrder() + transformation.OrderW(); + const quadrature::Resolution resolution = + factory.configure_gravity_hdiv_mass( + integrator, quadrature::QuadratureRole::discretization, element, + transformation + ); + const int expected_base_order = + 2 * element.GetOrder() + transformation.OrderW(); CHECK(resolution.base_order == expected_base_order); CHECK(resolution.boost == 3); CHECK(resolution.order == expected_base_order + 3); } -TEST_CASE("Gravity Divergence Helper Resolves Preconditioner Rule", tags::unit & tags::quadrature & tags::solver) { - mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D(1, 1, 1, mfem::Element::HEXAHEDRON); +TEST_CASE( + "Gravity Divergence Helper Resolves Preconditioner Rule", + tags::unit &tags::quadrature &tags::solver +) { + mfem::Mesh mesh = + mfem::Mesh::MakeCartesian3D(1, 1, 1, mfem::Element::HEXAHEDRON); mfem::RT_FECollection rt_collection(2, 3); mfem::L2_FECollection l2_collection(2, 3); mfem::FiniteElementSpace rt_space(&mesh, &rt_collection); mfem::FiniteElementSpace l2_space(&mesh, &l2_collection); - quadrature::RuleSet rule_set = quadrature::make_rule_set(quadrature::Mode::production); - rule_set.gravity_divergence.boost = 2; + quadrature::RuleSet rule_set = + quadrature::make_rule_set(quadrature::Mode::production); + rule_set.gravity_divergence.boost = 2; rule_set.roles.preconditioner.boost = 3; quadrature::RuleFactory factory{quadrature::Policy(std::move(rule_set))}; - const mfem::FiniteElement& trial_element = *rt_space.GetTypicalFE(); - const mfem::FiniteElement& test_element = *l2_space.GetTypicalFE(); - const mfem::ElementTransformation& transformation = *mesh.GetElementTransformation(0); + const mfem::FiniteElement &trial_element = *rt_space.GetTypicalFE(); + const mfem::FiniteElement &test_element = *l2_space.GetTypicalFE(); + const mfem::ElementTransformation &transformation = + *mesh.GetElementTransformation(0); mfem::VectorFEDivergenceIntegrator integrator; - const quadrature::Resolution resolution = factory.configure_gravity_divergence(integrator, quadrature::QuadratureRole::preconditioner, trial_element, test_element, transformation); - const int expected_base_order = std::max(0, trial_element.GetOrder() - 1) + test_element.GetOrder() + transformation.OrderW(); + const quadrature::Resolution resolution = + factory.configure_gravity_divergence( + integrator, quadrature::QuadratureRole::preconditioner, + trial_element, test_element, transformation + ); + const int expected_base_order = std::max(0, trial_element.GetOrder() - 1) + + test_element.GetOrder() + + transformation.OrderW(); CHECK(resolution.base_order == expected_base_order); CHECK(resolution.boost == 5); CHECK(resolution.order == expected_base_order + 5); +} + +TEST_CASE( + "Field Registry Encodes Spaces Orders And Stable Pair Constraints", + tags::unit &tags::quadrature &tags::initialization +) { + CHECK(mean_field::field::Density::Scalar::familyOrder == 2); + CHECK(mean_field::field::Gravity::Potential::familyOrder == 2); + CHECK(mean_field::field::Gravity::Flux::familyOrder == 2); + CHECK(mean_field::field::Displacement::Vector::familyOrder == 3); + CHECK(mean_field::field::Enthalpy::Scalar::familyOrder == 3); + + CHECK((std::same_as< + mean_field::field::Density::Scalar::Space, mean_field::field::L2>)); + CHECK(( + std::same_as< + mean_field::field::Gravity::Potential::Space, mean_field::field::L2> + )); + CHECK((std::same_as< + mean_field::field::Gravity::Flux::Space, mean_field::field::RT>)); + CHECK((std::same_as< + mean_field::field::Displacement::Vector::Space, + mean_field::field::H1>)); + CHECK((std::same_as< + mean_field::field::Enthalpy::Scalar::Space, mean_field::field::H1>)); + + CHECK(mean_field::field::Density::Scalar::rankValue == 0); + CHECK(mean_field::field::Gravity::Potential::rankValue == 0); + CHECK(mean_field::field::Gravity::Flux::rankValue == 1); + CHECK(mean_field::field::Displacement::Vector::rankValue == 1); + CHECK(mean_field::field::Enthalpy::Scalar::rankValue == 0); + CHECK( + mean_field::field::Gravity::Flux::familyOrder == + mean_field::field::Gravity::Potential::familyOrder + ); + + CHECK( + std::is_empty_v> + ); + CHECK( + std::is_empty_v< + mean_field::field::Field> + ); + CHECK( + std::is_empty_v> + ); + CHECK( + std::is_empty_v> + ); + + STATIC_CHECK(field::RegisteredQuantity); + STATIC_CHECK( + field::GlobalScalarQuantity + ); + STATIC_CHECK_FALSE(field::FieldQuantity); + + STATIC_CHECK( + field::BarotropicConstant::Scalar::storageKind == + field::StorageKind::global_scalar + ); + STATIC_CHECK(field::BarotropicConstant::Scalar::staticBlockSize == 1); + + STATIC_CHECK( + field::Enthalpy::Scalar::storageKind == + field::StorageKind::finite_element + ); + STATIC_CHECK( + field::Enthalpy::Scalar::staticBlockSize == field::dynamicBlockSize + ); + + STATIC_CHECK_FALSE( + CanMakeFec< + field::Field, + field::BarotropicConstant::Scalar> + ); +} + +TEST_CASE( + "Field Forms Produce Typed Quadrature Queries", + tags::unit &tags::quadrature +) { + using GravityField = field::Field; + using DensityField = field::Field; + using EnthalpyField = field::Field; + + constexpr quadrature::Query hdiv_query = + GravityField::make_query( + quadrature::QuadratureRole::discretization, 2, {}, + utils::DOMAINS::ALL, quadrature::MappingKind::general + ); + constexpr quadrature::Query divergence_query = + GravityField::make_query( + quadrature::QuadratureRole::preconditioner, 2 + ); + constexpr quadrature::Query source_query = + GravityField::make_query( + quadrature::QuadratureRole::projection, 2, {}, + utils::DOMAINS::STELLAR + ); + constexpr quadrature::Query center_of_mass_query = + DensityField::make_query( + quadrature::QuadratureRole::diagnostic, 2, std::array{1}, + utils::DOMAINS::STELLAR + ); + constexpr quadrature::Query eos_closure_query = + EnthalpyField::make_query( + quadrature::QuadratureRole::discretization, 2, + std::array{6}, utils::DOMAINS::STELLAR, + quadrature::MappingKind::general + ); + constexpr quadrature::Query equilibrium_gravity_query = + EnthalpyField::make_query( + quadrature::QuadratureRole::discretization, 2, {}, + utils::DOMAINS::STELLAR, quadrature::MappingKind::general + ); + + constexpr quadrature::Query equilibrium_constant_query = + EnthalpyField::make_query( + quadrature::QuadratureRole::discretization, 2, {}, + utils::DOMAINS::STELLAR, quadrature::MappingKind::general + ); + constexpr quadrature::Query rotation_query = + EnthalpyField::make_query( + quadrature::QuadratureRole::discretization, 2, + std::array{2}, utils::DOMAINS::STELLAR, + quadrature::MappingKind::general + ); + constexpr quadrature::Query isobaric_surface_query = + EnthalpyField::make_query( + quadrature::QuadratureRole::discretization, 2, {}, + utils::DOMAINS::STELLAR, quadrature::MappingKind::general + ); + constexpr quadrature::Query mesh_extension_query = + field::Field::make_query< + field::Displacement::Form::MeshExtension>( + quadrature::QuadratureRole::discretization, 2, {}, + utils::DOMAINS::ALL, quadrature::MappingKind::general + ); + constexpr quadrature::Query mass_normalization_query = + DensityField::make_query( + quadrature::QuadratureRole::discretization, 2, {}, + utils::DOMAINS::STELLAR, quadrature::MappingKind::general + ); + constexpr quadrature::Query pressure_integral_query = + EnthalpyField::make_query( + quadrature::QuadratureRole::diagnostic, 2, std::array{9}, + utils::DOMAINS::STELLAR, quadrature::MappingKind::general + ); + + STATIC_CHECK( + mean_field::field::Gravity::Form::SourceProjection::dynamicOrderCount == + 0 + ); + STATIC_CHECK(hdiv_query.base_order.has_value()); + STATIC_CHECK(*hdiv_query.base_order == 8); + STATIC_CHECK(*divergence_query.base_order == 6); + STATIC_CHECK(*source_query.base_order == 6); + STATIC_CHECK(*center_of_mass_query.base_order == 5); + STATIC_CHECK(*eos_closure_query.base_order == 13); + STATIC_CHECK(*equilibrium_gravity_query.base_order == 7); + STATIC_CHECK(*rotation_query.base_order == 7); + STATIC_CHECK(*isobaric_surface_query.base_order == 8); + STATIC_CHECK(*mesh_extension_query.base_order == 6); + STATIC_CHECK(*mass_normalization_query.base_order == 4); + STATIC_CHECK(*pressure_integral_query.base_order == 14); + STATIC_CHECK(*equilibrium_constant_query.base_order == 5); + + CHECK( + equilibrium_constant_query.term == + quadrature::Term::hydrostatic_equilibrium + ); + CHECK(hdiv_query.term == mean_field::quadrature::Term::gravity_hdiv_mass); + CHECK( + hdiv_query.role == + mean_field::quadrature::QuadratureRole::discretization + ); + CHECK(hdiv_query.domain == mean_field::utils::DOMAINS::ALL); + CHECK(hdiv_query.mapping == mean_field::quadrature::MappingKind::general); + CHECK(source_query.term == mean_field::quadrature::Term::gravity_source); + CHECK( + center_of_mass_query.term == + mean_field::quadrature::Term::center_of_mass + ); + CHECK(eos_closure_query.term == mean_field::quadrature::Term::eos_closure); + CHECK( + equilibrium_gravity_query.term == + mean_field::quadrature::Term::hydrostatic_equilibrium + ); + CHECK( + rotation_query.term == + mean_field::quadrature::Term::hydrostatic_equilibrium + ); + CHECK( + isobaric_surface_query.term == + mean_field::quadrature::Term::isobaric_surface + ); + CHECK( + mesh_extension_query.term == + mean_field::quadrature::Term::mesh_extension + ); + CHECK( + mass_normalization_query.term == + mean_field::quadrature::Term::mass_normalization + ); + CHECK( + pressure_integral_query.term == + mean_field::quadrature::Term::pressure_integral + ); + + CHECK_THROWS_AS( + (GravityField::make_query( + mean_field::quadrature::QuadratureRole::discretization, -1 + )), + std::invalid_argument + ); + CHECK_THROWS_AS( + (DensityField::make_query< + mean_field::field::Density::Form::CenterOfMass>( + mean_field::quadrature::QuadratureRole::diagnostic, 2, + std::array{-1} + )), + std::invalid_argument + ); +} + +TEST_CASE( + "Field Factories Construct The Registered MFEM Collections", + tags::unit &tags::quadrature &tags::initialization +) { + using GravityField = field::Field; + using DisplacementField = field::Field; + using DensityField = field::Field; + using EnthalpyField = field::Field; + + std::unique_ptr density_collection = + DensityField::make_fec(3); + std::unique_ptr potential_collection = + GravityField::make_fec(3); + std::unique_ptr flux_collection = + GravityField::make_fec(3); + std::unique_ptr displacement_collection = + DisplacementField::make_fec(3); + std::unique_ptr enthalpy_collection = + EnthalpyField::make_fec(3); + + CHECK( + dynamic_cast(density_collection.get()) != + nullptr + ); + CHECK( + dynamic_cast(potential_collection.get()) != + nullptr + ); + CHECK( + dynamic_cast(flux_collection.get()) != nullptr + ); + CHECK( + dynamic_cast(displacement_collection.get()) != + nullptr + ); + CHECK( + dynamic_cast(enthalpy_collection.get()) != + nullptr + ); + + CHECK_THROWS_AS( + (DensityField::make_fec(0)), + std::invalid_argument + ); +} + +TEST_CASE( + "FEM Setup Realizes Every Registered Field Independently", + tags::integration &tags::initialization &tags::solver +) { + const utils::Args args = test_utils::setup_args(); + const fem::FEM fem = fem::setup_fem(args.mesh_file, args, 0); + + REQUIRE(fem.okay()); + REQUIRE(fem.mesh != nullptr); + REQUIRE(fem.densityFes != nullptr); + REQUIRE(fem.gravityPotentialFes != nullptr); + REQUIRE(fem.gravityFluxFes != nullptr); + REQUIRE(fem.displacementFes != nullptr); + REQUIRE(fem.enthalpyFes != nullptr); + + CHECK(fem.densityFes.get() != fem.gravityPotentialFes.get()); + CHECK(fem.densityFec.get() != fem.gravityPotentialFec.get()); + + CHECK( + fem.densityFes->GetMaxElementOrder() == + mean_field::field::Density::Scalar::familyOrder + ); + CHECK( + fem.gravityPotentialFes->GetMaxElementOrder() == + mean_field::field::Gravity::Potential::familyOrder + ); + CHECK( + fem.gravityFluxFes->GetMaxElementOrder() == + mean_field::field::Gravity::Flux::familyOrder + 1 + ); + CHECK( + fem.displacementFes->GetMaxElementOrder() == + mean_field::field::Displacement::Vector::familyOrder + ); + CHECK( + fem.enthalpyFes->GetMaxElementOrder() == + mean_field::field::Enthalpy::Scalar::familyOrder + ); + + CHECK(fem.densityFes->GetVDim() == 1); + CHECK(fem.gravityPotentialFes->GetVDim() == 1); + CHECK(fem.gravityFluxFes->GetVDim() == 1); + CHECK(fem.displacementFes->GetVDim() == fem.mesh->SpaceDimension()); + CHECK(fem.displacementFes->GetOrdering() == mfem::Ordering::byNODES); + CHECK(fem.enthalpyFes->GetVDim() == 1); + + REQUIRE(fem.blockTrueOffsets.Size() == 3); + CHECK(fem.blockTrueOffsets[0] == 0); + CHECK(fem.blockTrueOffsets[1] == fem.displacementFes->GetTrueVSize()); + CHECK( + fem.blockTrueOffsets[2] == + fem.displacementFes->GetTrueVSize() + fem.densityFes->GetTrueVSize() + ); + + REQUIRE(fem.gravityBlockTrueOffsets.Size() == 3); + CHECK(fem.gravityBlockTrueOffsets[0] == 0); + CHECK(fem.gravityBlockTrueOffsets[1] == fem.gravityFluxFes->GetTrueVSize()); + CHECK( + fem.gravityBlockTrueOffsets[2] == + fem.gravityFluxFes->GetTrueVSize() + + fem.gravityPotentialFes->GetTrueVSize() + ); + + CHECK( + fem.gravityContext.source_form->Height() == + fem.gravityPotentialFes->GetTrueVSize() + ); } \ No newline at end of file diff --git a/tests/test_helpers.cppm b/tests/test_helpers.cppm index 47c8eea..5b79160 100644 --- a/tests/test_helpers.cppm +++ b/tests/test_helpers.cppm @@ -1,23 +1,31 @@ module; -#include -#include #include +#include #include +#include +#include #include #include export module test_helpers; import mean_field; -template -struct Tag { +template struct Tag { std::array chars{}; // ReSharper disable once CppNonExplicitConvertingConstructor - consteval Tag(std::array arr) : chars(arr) {} + consteval Tag( + std::array< + char, + N> arr + ) + : chars(arr) { + } // ReSharper disable once CppNonExplicitConversionOperator - constexpr operator const char*() const { return chars.data(); } + constexpr operator const char *() const { + return chars.data(); + } // ReSharper disable once CppNonExplicitConversionOperator constexpr operator Catch::StringRef() const { @@ -25,7 +33,7 @@ struct Tag { } template - consteval Tag operator&(const Tag& other) const { + consteval Tag operator&(const Tag &other) const { std::array res{}; std::ranges::copy(chars.begin(), chars.end() - 1, res.begin()); std::ranges::copy(other.chars, res.begin() + (N - 1)); @@ -33,18 +41,22 @@ struct Tag { } }; -template -consteval auto make_tag(const char (&str)[N]) { +template consteval auto make_tag(const char (&str)[N]) { std::array res{}; res[0] = '['; std::ranges::copy(str, str + N - 1, res.begin() + 1); - res[N] = ']'; + res[N] = ']'; res[N + 1] = '\0'; return Tag{res}; } -template -consteval auto sub_tag(const Tag& parent, const char (&str)[M]) { +template < + std::size_t N, + std::size_t M> +consteval auto sub_tag( + const Tag &parent, + const char (&str)[M] +) { return parent & make_tag(str); } @@ -54,11 +66,11 @@ namespace test_utils::detail { mean_field::utils::Args make_default_args() { mean_field::utils::Args args; args.mesh_file = "sandbox.smesh"; - args.p.rtol = 1.0e-12; - args.p.atol = 1.0e-12; + args.p.rtol = 1.0e-12; + args.p.atol = 1.0e-12; return args; } -} +} // namespace test_utils::detail export namespace test_utils { void set_args(mean_field::utils::Args args) { @@ -72,26 +84,216 @@ export namespace test_utils { return detail::make_default_args(); } -} +} // namespace test_utils + +export namespace gravity_prepared_test_utils { + inline mfem::Vector make_deterministic_vector( + const int size, + const double phase = 0.0 + ) { + mfem::Vector vector(size); + + for (int i = 0; i < size; ++i) { + const double index = static_cast(i + 1); + vector(i) = std::sin(0.37 * index + phase) + + 0.31 * std::cos(0.19 * index - 0.5 * phase); + } + + return vector; + } + + inline mfem::Vector make_displacement( + const mean_field::fem::FEM &f, + const double scale + ) { + mfem::ParGridFunction displacement(f.displacementFes.get()); + + auto displacement_function = + [scale](const mfem::Vector &position, mfem::Vector &value) { + value.SetSize(3); + value(0) = scale * (0.04 * position(0) + + 0.01 * position(1) * position(2)); + value(1) = scale * (-0.03 * position(1) + + 0.008 * position(0) * position(2)); + value(2) = scale * (0.02 * position(2) - + 0.006 * position(0) * position(1)); + }; + + mfem::VectorFunctionCoefficient coefficient( + f.mesh->Dimension(), displacement_function + ); + displacement.ProjectCoefficient(coefficient); + + mfem::Vector displacement_true; + displacement.GetTrueDofs(displacement_true); + return displacement_true; + } + + inline mfem::Vector make_domain_supported_density( + const mean_field::fem::FEM &f, + const bool stellar + ) { + mfem::Vector attribute_values(f.mesh->attributes.Max()); + attribute_values = 0.0; + + const int vacuum_attribute = + f.domainMapperStateless->GetVacuumElementAttribute(); + + for (int i = 0; i < f.mesh->attributes.Size(); ++i) { + const int attribute = f.mesh->attributes[i]; + const bool is_stellar = attribute != vacuum_attribute; + + if (is_stellar == stellar) { + attribute_values(attribute - 1) = 1.0; + } + } + + mfem::PWConstCoefficient coefficient(attribute_values); + mfem::ParGridFunction density(f.densityFes.get()); + density.ProjectCoefficient(coefficient); + + mfem::Vector density_true; + density.GetTrueDofs(density_true); + return density_true; + } + + inline mfem::Vector linear_combination( + const mfem::Vector &first, + const double first_scale, + const mfem::Vector &second, + const double second_scale + ) { + MFEM_VERIFY( + first.Size() == second.Size(), + "Cannot combine vectors with different sizes." + ); + + mfem::Vector combination(first); + combination *= first_scale; + combination.Add(second_scale, second); + return combination; + } + + inline double global_norm( + const mfem::Vector &vector, + MPI_Comm communicator + ) { + const double local_norm_squared = vector * vector; + double global_norm_squared = 0.0; + MPI_Allreduce( + &local_norm_squared, &global_norm_squared, 1, MPI_DOUBLE, MPI_SUM, + communicator + ); + return std::sqrt(global_norm_squared); + } + + inline double global_dot( + const mfem::Vector &first, + const mfem::Vector &second, + MPI_Comm communicator + ) { + MFEM_VERIFY( + first.Size() == second.Size(), + "Cannot take the dot product of vectors with different sizes." + ); + + const double local_dot = first * second; + double global_dot = 0.0; + MPI_Allreduce( + &local_dot, &global_dot, 1, MPI_DOUBLE, MPI_SUM, communicator + ); + return global_dot; + } + + inline double relative_error( + const mfem::Vector &computed, + const mfem::Vector &reference, + MPI_Comm communicator + ) { + MFEM_VERIFY( + computed.Size() == reference.Size(), + "Cannot compare vectors with different sizes." + ); + + mfem::Vector difference(computed); + difference -= reference; + + return global_norm(difference, communicator) / + std::max( + global_norm(reference, communicator), + std::numeric_limits::epsilon() + ); + } + + inline double relative_scalar_error( + const double computed, + const double reference + ) { + return std::abs(computed - reference) / + std::max( + std::abs(reference), std::numeric_limits::epsilon() + ); + } +} // namespace gravity_prepared_test_utils export namespace tags { - inline constexpr auto geometry = make_tag("geometry"); - inline constexpr auto physics = make_tag("physics"); - inline constexpr auto unit = make_tag("unit"); - inline constexpr auto mesh = make_tag("mesh"); - inline constexpr auto integration = make_tag("integration"); - inline constexpr auto solver = make_tag("solver"); + inline constexpr auto geometry = make_tag("geometry"); + inline constexpr auto physics = make_tag("physics"); + inline constexpr auto unit = make_tag("unit"); + inline constexpr auto mesh = make_tag("mesh"); + inline constexpr auto integration = make_tag("integration"); + inline constexpr auto solver = make_tag("solver"); + inline constexpr auto integrator = make_tag("integrator"); + inline constexpr auto mapping = make_tag("mapping"); + inline constexpr auto utils = make_tag("utils"); + inline constexpr auto mfem_operators = make_tag("operators"); + inline constexpr auto initialization = make_tag("initialization"); + inline constexpr auto accuracy = make_tag("accuracy"); + inline constexpr auto closure = make_tag("closure"); + inline constexpr auto kernels = make_tag("kernels"); - inline constexpr auto gravity = sub_tag(physics, "gravity"); - inline constexpr auto hydro = sub_tag(physics, "hydro"); - inline constexpr auto jacobian = sub_tag(integration & physics , "jacobian"); - inline constexpr auto residuals = sub_tag(integration & physics , "residuals"); - inline constexpr auto h_refinement = sub_tag(mesh & solver , "h_refinement"); - inline constexpr auto volume = sub_tag(mesh & geometry , "volume"); - inline constexpr auto quadrature = sub_tag(mesh & geometry & solver , "quadrature"); + inline constexpr auto legacy_comparison = make_tag("legacy_comparison"); + inline constexpr auto pressure = sub_tag(physics, "pressure"); - inline constexpr auto analytic_comparison = sub_tag(solver & physics & residuals , "analytic_comparison"); - inline constexpr auto self_consistency = sub_tag(solver & physics , "self_consistency"); + inline constexpr auto hydro = sub_tag(physics, "hydro"); + inline constexpr auto jacobian = sub_tag(integration & physics, "jacobian"); + inline constexpr auto residuals = + sub_tag(integration & physics, "residuals"); + inline constexpr auto volume = sub_tag(mesh & geometry, "volume"); + inline constexpr auto quadrature = + sub_tag(mesh & geometry & solver, "quadrature"); + inline constexpr auto convergence = sub_tag(solver, "convergence"); + inline constexpr auto transformations = + sub_tag(mesh & geometry, "transformations"); -} + inline constexpr auto h_refinement = + sub_tag(mesh & convergence, "h_refinement"); + inline constexpr auto p_refinement = + sub_tag(mesh & convergence, "p_refinement"); + inline constexpr auto analytic_comparison = + sub_tag(solver & physics & residuals, "analytic_comparison"); + inline constexpr auto self_consistency = + sub_tag(solver & physics, "self_consistency"); + + inline constexpr auto centrifugal = + sub_tag(solver & physics, "centrifugal"); + inline constexpr auto advection = sub_tag(solver & physics, "advection"); + inline constexpr auto coriolis = sub_tag(solver & physics, "coriolis"); + inline constexpr auto gravity = sub_tag(solver & physics, "gravity"); + inline constexpr auto enthalpy = sub_tag(solver & physics, "enthalpy"); + inline constexpr auto barotrope = sub_tag(physics, "barotrope"); + inline constexpr auto mass_continuity = + sub_tag(solver & physics, "mass_continuity"); + inline constexpr auto pressure_gradient = + sub_tag(solver & physics, "pressure_gradient"); + inline constexpr auto viscosity = sub_tag(solver & physics, "viscosity"); + + inline constexpr auto compactification = + sub_tag(mesh & mapping, "compactification"); + inline constexpr auto kelvin = sub_tag(compactification, "kelvin"); + + inline constexpr auto prepared = sub_tag(solver & physics, "prepared"); + inline constexpr auto contexts = sub_tag(solver, "contexts"); + +} // namespace tags diff --git a/tests/test_main.cpp b/tests/test_main.cpp index 35addf5..775362e 100644 --- a/tests/test_main.cpp +++ b/tests/test_main.cpp @@ -1,127 +1,496 @@ +#include #include -#include -#include #include +#include +#include +#include +#include #include #include -#include -#include -#include -#include +#include #include +#include #include +#include -#include #include +#include import mean_field; import test_helpers; +std::string escapeHtml(const std::string &data) { + std::string buffer; + buffer.reserve(data.size()); + for (size_t pos = 0; pos != data.size(); ++pos) { + switch (data[pos]) { + case '&': + buffer.append("&"); + break; + case '\"': + buffer.append("""); + break; + case '\'': + buffer.append("'"); + break; + case '<': + buffer.append("<"); + break; + case '>': + buffer.append(">"); + break; + default: + buffer.append(&data[pos], 1); + break; + } + } + return buffer; +} + +std::string ansiToHtml(const std::string &text) { + // Convert text to HTML-safe first + std::string htmlEscaped = escapeHtml(text); + + std::ostringstream oss; + size_t i = 0; + size_t len = htmlEscaped.length(); + int openSpans = 0; + + auto closeSpans = [&oss, &openSpans]() { + while (openSpans > 0) { + oss << ""; + --openSpans; + } + }; + + while (i < len) { + // Look for ANSI CSI sequence '\033[' or '\x1b[' + if ((htmlEscaped[i] == '\033' || htmlEscaped[i] == '\x1b') && + i + 1 < len && htmlEscaped[i + 1] == '[') { + size_t seqStart = i + 2; + size_t seqEnd = htmlEscaped.find('m', seqStart); + + if (seqEnd != std::string::npos) { + std::string codeStr = + htmlEscaped.substr(seqStart, seqEnd - seqStart); + i = seqEnd + 1; + + std::istringstream codeStream(codeStr); + std::string codeVal; + + // Defaults if sequence is just \033[m (Reset) + if (codeStr.empty()) { + closeSpans(); + continue; + } + + while (std::getline(codeStream, codeVal, ';')) { + int code = 0; + try { + code = std::stoi(codeVal); + } catch (...) { + continue; + } + + switch (code) { + case 0: // Reset + closeSpans(); + break; + case 1: // Bold + oss << ""; + openSpans++; + break; + case 2: // Dim + oss << ""; + openSpans++; + break; + // Standard Foreground Colors + case 30: + oss << ""; + openSpans++; + break; // Black + case 31: + oss << ""; + openSpans++; + break; // Red + case 32: + oss << ""; + openSpans++; + break; // Green + case 33: + oss << ""; + openSpans++; + break; // Yellow + case 34: + oss << ""; + openSpans++; + break; // Blue + case 35: + oss << ""; + openSpans++; + break; // Magenta + case 36: + oss << ""; + openSpans++; + break; // Cyan + case 37: + oss << ""; + openSpans++; + break; // Light Gray + // Bright Foreground Colors + case 90: + oss << ""; + openSpans++; + break; // Dark Gray + case 91: + oss << ""; + openSpans++; + break; // Bright Red + case 92: + oss << ""; + openSpans++; + break; // Bright Green + case 93: + oss << ""; + openSpans++; + break; // Bright Yellow + case 94: + oss << ""; + openSpans++; + break; // Bright Blue + case 95: + oss << ""; + openSpans++; + break; // Bright Magenta + case 96: + oss << ""; + openSpans++; + break; // Bright Cyan + case 97: + oss << ""; + openSpans++; + break; // White + default: + break; + } + } + continue; + } + } + oss << htmlEscaped[i]; + ++i; + } + + closeSpans(); + return oss.str(); +} + +std::vector wrapText( + const std::string &text, + size_t width +) { + std::vector lines; + std::istringstream words(text); + std::string word, line; + + while (words >> word) { + if (line.length() + word.length() + 1 > width) { + if (!line.empty()) { + lines.push_back(line); + line.clear(); + } + if (word.length() > width) { + lines.push_back(word.substr(0, width - 3) + "..."); + continue; + } + } + if (!line.empty()) + line += " "; + line += word; + } + if (!line.empty()) + lines.push_back(line); + if (lines.empty()) + lines.push_back(""); + + return lines; +} + class CheckReporter : public Catch::StreamingReporterBase { - // Accumulate failure messages for the current test case + struct TestCaseData { + std::string name; + std::string tags; + bool passed; + std::size_t assertionsPassed; + std::size_t assertionsFailed; + std::vector failureMessages; + std::vector infoMessages; + }; + std::vector m_currentFailures; + std::vector m_currentInfos; + std::vector m_testRunData; public: using StreamingReporterBase::StreamingReporterBase; static std::string getDescription() { - return "Fixed-width table reporter with detailed assertion failures."; + return "Console reporter with wrapping, tags, and collapsible HTML " + "export " + "with ANSI color rendering."; } - void testRunStarting(Catch::TestRunInfo const& _testRunInfo) override { + void testRunStarting(Catch::TestRunInfo const &_testRunInfo) override { StreamingReporterBase::testRunStarting(_testRunInfo); std::cout << '\n'; - std::cout << std::left << std::setw(55) << "Test Case Name" - << "Status " - << std::right << std::setw(8) << "Passed" + std::cout << std::left << std::setw(85) << "Test Case Name" + << "Status " << std::right << std::setw(8) << "Passed" << std::setw(8) << "Failed" << '\n'; - std::cout << std::string(81, '-') << '\n'; + std::cout << std::string(121, '-') << '\n'; } - // 1. Hook into every assertion to catch failures - void assertionEnded(Catch::AssertionStats const& assertionStats) override { + void assertionEnded(Catch::AssertionStats const &assertionStats) override { StreamingReporterBase::assertionEnded(assertionStats); - // If the assertion failed, build a detailed message + // Capture INFO messages regardless of pass/fail status + for (auto const &msg : assertionStats.infoMessages) { + m_currentInfos.push_back(msg.message); + } + if (!assertionStats.assertionResult.isOk()) { - auto const& result = assertionStats.assertionResult; + auto const &result = assertionStats.assertionResult; std::ostringstream oss; - // Format: -> FAILED: [file:line] oss << " \033[31m-> FAILED:\033[0m " - << result.getSourceInfo().file << ":" << result.getSourceInfo().line << '\n'; + << result.getSourceInfo().file << ":" + << result.getSourceInfo().line << '\n'; + oss << " " << result.getTestMacroName() << "( " + << result.getExpression() << " )\n"; - // Print the macro used (e.g., REQUIRE, CHECK) and the expression - oss << " " << result.getTestMacroName() << "( " << result.getExpression() << " )\n"; - - // Print what it actually evaluated to (e.g., 1 == 2) if (result.hasExpandedExpression()) { oss << " with expansion:\n" << " " << result.getExpandedExpression() << '\n'; } - // Capture any INFO() messages attached to this assertion - for (auto const& msg : assertionStats.infoMessages) { - oss << " info: " << msg.message << '\n'; + for (auto const &msg : assertionStats.infoMessages) { + oss << " \033[36m[INFO]\033[0m " << msg.message << '\n'; } m_currentFailures.push_back(oss.str()); } } - void testCaseEnded(Catch::TestCaseStats const& stats) override { + void testCaseEnded(Catch::TestCaseStats const &stats) override { StreamingReporterBase::testCaseEnded(stats); - bool passed = stats.totals.assertions.allPassed(); + bool passed = stats.totals.assertions.allPassed(); std::string mark = passed ? "\033[32m✓\033[0m" : "\033[31m✗\033[0m"; std::string name = stats.testInfo->name; - if (name.length() > 53) { - name = name.substr(0, 50) + "..."; + auto wrappedName = wrapText(name, 83); + + std::cout << std::left << std::setw(85) << wrappedName[0] << mark + << " " << std::right << std::setw(8) + << stats.totals.assertions.passed << std::setw(8) + << stats.totals.assertions.failed << '\n'; + + for (size_t i = 1; i < wrappedName.size(); ++i) { + std::cout << " \033[90m↳ \033[0m" // Dim indent arrow + << std::left << std::setw(81) << wrappedName[i] << '\n'; } - // Print the table row - std::cout << std::left << std::setw(55) << name - << mark << " " - << std::right << std::setw(8) << stats.totals.assertions.passed - << std::setw(8) << stats.totals.assertions.failed << '\n'; + std::string tagsStr = stats.testInfo->tagsAsString(); + if (!tagsStr.empty()) { + auto wrappedTags = wrapText("Tags: " + tagsStr, 83); + for (const auto &line : wrappedTags) { + std::cout << " \033[36m" << line << "\033[0m\n"; // Cyan + } + } - // 2. Print all accumulated failures under the row if (!m_currentFailures.empty()) { std::cout << '\n'; - for (auto const& failure : m_currentFailures) { + for (auto const &failure : m_currentFailures) { std::cout << failure << '\n'; } - // Add a separator so multiple failing tests don't blur together - std::cout << std::string(81, '-') << '\n'; - - // Clear the buffer for the next test case - m_currentFailures.clear(); + std::cout << std::string(121, '-') << '\n'; } + + m_testRunData.push_back( + {name, tagsStr, passed, stats.totals.assertions.passed, + stats.totals.assertions.failed, m_currentFailures, m_currentInfos} + ); + + m_currentFailures.clear(); + m_currentInfos.clear(); } - void testRunEnded(Catch::TestRunStats const& _testRunStats) override { + void testRunEnded(Catch::TestRunStats const &_testRunStats) override { StreamingReporterBase::testRunEnded(_testRunStats); - std::cout << std::string(81, '=') << '\n'; + std::cout << std::string(121, '=') << '\n'; - auto const& tc = _testRunStats.totals.testCases; - auto const& as = _testRunStats.totals.assertions; + auto const &tc = _testRunStats.totals.testCases; + auto const &as = _testRunStats.totals.assertions; - std::string tc_passed_str = tc.passed > 0 ? "\033[32m" + std::to_string(tc.passed) + " passed\033[0m" : "0 passed"; - std::string tc_failed_str = tc.failed > 0 ? "\033[31m" + std::to_string(tc.failed) + " failed\033[0m" : "0 failed"; + std::string tc_passed_str = + tc.passed > 0 + ? "\033[32m" + std::to_string(tc.passed) + " passed\033[0m" + : "0 passed"; + std::string tc_failed_str = + tc.failed > 0 + ? "\033[31m" + std::to_string(tc.failed) + " failed\033[0m" + : "0 failed"; - std::string as_passed_str = as.passed > 0 ? "\033[32m" + std::to_string(as.passed) + " passed\033[0m" : "0 passed"; - std::string as_failed_str = as.failed > 0 ? "\033[31m" + std::to_string(as.failed) + " failed\033[0m" : "0 failed"; + std::string as_passed_str = + as.passed > 0 + ? "\033[32m" + std::to_string(as.passed) + " passed\033[0m" + : "0 passed"; + std::string as_failed_str = + as.failed > 0 + ? "\033[31m" + std::to_string(as.failed) + " failed\033[0m" + : "0 failed"; - std::cout << "Test Cases: " << tc_passed_str << ", " << tc_failed_str << ", " << tc.total() << " total\n"; - std::cout << "Assertions: " << as_passed_str << ", " << as_failed_str << ", " << as.total() << " total\n\n"; + std::cout << "Test Cases: " << tc_passed_str << ", " << tc_failed_str + << ", " << tc.total() << " total\n"; + std::cout << "Assertions: " << as_passed_str << ", " << as_failed_str + << ", " << as.total() << " total\n\n"; + + generateHtmlReport(_testRunStats); + } + +private: + void generateHtmlReport(Catch::TestRunStats const &stats) { + std::ofstream html("test_summary.html"); + if (!html) + return; + + html + << "\n\n\n" + << "\n" + << "\n" + << "Test Run Summary\n" + << "\n\n\n"; + + html << "

Test Run Summary

\n"; + + // Summary Cards + html << "
\n"; + html << "

Total Cases

" + << stats.totals.testCases.total() << "

\n"; + html << "

Cases Passed

" + << stats.totals.testCases.passed << "

\n"; + html << "

Cases Failed

" + << stats.totals.testCases.failed << "

\n"; + html << "
\n"; + + for (const auto &test : m_testRunData) { + std::string statusClass = test.passed ? "passed" : "failed"; + html << "
\n"; + html << "
\n"; + html << "
\n"; + html << "

" << escapeHtml(test.name) + << "

\n"; + if (!test.tags.empty()) { + html << "
" << escapeHtml(test.tags) + << "
\n"; + } + html << "
\n"; + html << "
\n"; + html << " ✓ " + << test.assertionsPassed << " | "; + html << " ✗ " + << test.assertionsFailed << "\n"; + html << "
\n"; + html << "
\n"; + + // Collapsible INFO Messages section with ANSI color rendering + if (!test.infoMessages.empty()) { + html << "
\n"; + html << " Info Logs (" << test.infoMessages.size() + << ")\n"; + html << " 
";
+                for (const auto &info : test.infoMessages) {
+                    html << "[INFO] " << ansiToHtml(info) << "\n";
+                }
+                html << "
\n"; + html << "
\n"; + } + + // Collapsible Failures section with ANSI color rendering + if (!test.failureMessages.empty()) { + html << "
\n"; + html << " Failure Details (" + << test.failureMessages.size() << ")\n"; + html << " 
";
+                for (const auto &msg : test.failureMessages) {
+                    html << ansiToHtml(msg) << "\n";
+                }
+                html << "
\n"; + html << "
\n"; + } + + html << "
\n"; + } + + html << "\n\n"; } }; -CATCH_REGISTER_REPORTER("check", CheckReporter) -int main(int argc, char* argv[]) { +CATCH_REGISTER_REPORTER( + "check", + CheckReporter +) + +int main( + int argc, + char *argv[] +) { fourdst::config::Config cfg; CLI::App app{"Mean Field Tests"}; @@ -148,49 +517,56 @@ int main(int argc, char* argv[]) { } } - std::vector config_argv; + std::vector config_argv; config_argv.reserve(config_arguments.size()); - for (const std::string& argument : config_arguments) { + for (const std::string &argument : config_arguments) { config_argv.push_back(argument.c_str()); } try { app.parse(static_cast(config_argv.size()), config_argv.data()); - } catch (const CLI::ParseError& error) { + } catch (const CLI::ParseError &error) { return app.exit(error); } std::vector catch_arguments; catch_arguments.emplace_back(argv[0]); - for (const std::string& argument : app.remaining()) { + for (const std::string &argument : app.remaining()) { catch_arguments.push_back(argument); } - for (const std::string& argument : forced_catch_arguments) { + for (const std::string &argument : forced_catch_arguments) { catch_arguments.push_back(argument); } - const auto is_reporter_option = [](const std::string& argument) { - return argument == "-r" || argument == "--reporter" || argument.starts_with("-r=") || argument.starts_with("--reporter="); + const auto is_reporter_option = [](const std::string &argument) { + return argument == "-r" || argument == "--reporter" || + argument.starts_with("-r=") || + argument.starts_with("--reporter="); }; - if (const bool has_reporter = std::ranges::any_of(catch_arguments, is_reporter_option); !has_reporter) { + if (const bool has_reporter = + std::ranges::any_of(catch_arguments, is_reporter_option); + !has_reporter) { catch_arguments.emplace_back("--reporter"); catch_arguments.emplace_back("check"); } - std::vector catch_argv; + std::vector catch_argv; catch_argv.reserve(catch_arguments.size()); - for (const std::string& argument : catch_arguments) { + for (const std::string &argument : catch_arguments) { catch_argv.push_back(argument.c_str()); } Catch::Session session; - if (const int catch_parse_result = session.applyCommandLine(static_cast(catch_argv.size()), catch_argv.data()); catch_parse_result != 0) { + if (const int catch_parse_result = session.applyCommandLine( + static_cast(catch_argv.size()), catch_argv.data() + ); + catch_parse_result != 0) { return catch_parse_result; } @@ -201,7 +577,8 @@ int main(int argc, char* argv[]) { const int hdiv_max_q1d = mfem::DeviceDofQuadLimits::Get().HDIV_MAX_Q1D; std::cout << "H(div) maximum Q1D = " << hdiv_max_q1d << '\n'; - std::cout << "Approximate maximum safe integration order = " << 2 * hdiv_max_q1d - 1 << '\n'; + std::cout << "Approximate maximum safe integration order = " + << 2 * hdiv_max_q1d - 1 << '\n'; mean_field::utils::Args test_args = cfg.main(); diff --git a/tests/utils/blocks.cpp b/tests/utils/blocks.cpp new file mode 100644 index 0000000..112d89d --- /dev/null +++ b/tests/utils/blocks.cpp @@ -0,0 +1,861 @@ +#include +#include +#include +#include + +import mean_field; +import test_helpers; + +using namespace mean_field; + +namespace { + namespace blocks = utils::blocks; + + template struct contains_type; + + template + struct contains_type> : std::false_type { }; + + template + struct contains_type> + : std::conditional_t< + std::is_same_v, + std::true_type, + contains_type>> { }; + + template + inline constexpr bool contains_type_v = contains_type::value; + + template struct type_at; + + template + struct type_at<0, blocks::type_list> { + using type = Head; + }; + + template + struct type_at> { + static_assert(index > 0); + using type = + typename type_at>::type; + }; + + template + using type_at_t = typename type_at::type; + + template struct block_row_traits; + + template + struct block_row_traits> { + using residual = Residual; + using values = blocks::type_list; + + static constexpr int value_count = sizeof...(Values); + }; + + template + inline constexpr bool row_has_exact_values_v = + block_row_traits::value_count == sizeof...(ExpectedValues) && + (contains_type_v< + ExpectedValues, + typename block_row_traits::values> && + ...); + + struct foreign_value final : blocks::value_block_base { }; + struct foreign_residual final : blocks::residual_block_base { }; +} // namespace + +TEST_CASE( + "Block Types Preserve Their Semantic Hierarchy", + tags::unit &tags::solver &tags::utils +) { + STATIC_REQUIRE( + std::is_base_of_v + ); + STATIC_REQUIRE(std::is_base_of_v); + STATIC_REQUIRE( + std::is_base_of_v< + blocks::residual_block_base, blocks::residual_block<0>> + ); + STATIC_REQUIRE( + std::is_base_of_v> + ); + + STATIC_REQUIRE(std::is_base_of_v); + STATIC_REQUIRE(std::is_base_of_v); + STATIC_REQUIRE(std::is_base_of_v); + STATIC_REQUIRE(std::is_base_of_v); + + STATIC_REQUIRE(std::is_base_of_v); + STATIC_REQUIRE( + std::is_base_of_v + ); + STATIC_REQUIRE(std::is_base_of_v); + STATIC_REQUIRE(std::is_base_of_v); + STATIC_REQUIRE(std::is_base_of_v); + + STATIC_REQUIRE( + std::is_base_of_v< + blocks::value_block_base, blocks::density::mass::value> + ); + STATIC_REQUIRE( + std::is_base_of_v< + blocks::residual_block_base, blocks::density::mass::residual> + ); + STATIC_REQUIRE( + std::is_base_of_v< + blocks::value_block_base, blocks::gravity::gradient::value> + ); + STATIC_REQUIRE( + std::is_base_of_v< + blocks::residual_block_base, blocks::gravity::gradient::residual> + ); + STATIC_REQUIRE( + std::is_base_of_v< + blocks::value_block_base, blocks::gravity::poisson::value> + ); + STATIC_REQUIRE( + std::is_base_of_v< + blocks::residual_block_base, blocks::gravity::poisson::residual> + ); + STATIC_REQUIRE( + std::is_base_of_v< + blocks::value_block_base, blocks::enthalpy::specific::value> + ); + STATIC_REQUIRE( + std::is_base_of_v< + blocks::residual_block_base, blocks::enthalpy::specific::residual> + ); + + STATIC_REQUIRE(std::is_empty_v); + STATIC_REQUIRE(std::is_empty_v); + STATIC_REQUIRE(std::is_empty_v); + STATIC_REQUIRE(std::is_empty_v); + STATIC_REQUIRE(std::is_empty_v); + STATIC_REQUIRE(std::is_empty_v); + STATIC_REQUIRE(std::is_empty_v); + STATIC_REQUIRE(std::is_empty_v); + + STATIC_REQUIRE( + std::is_base_of_v + ); + + STATIC_REQUIRE( + std::is_base_of_v< + blocks::term, blocks::barotropic_constant::mass_normalization> + ); + + STATIC_REQUIRE( + std::is_base_of_v< + blocks::value_block_base, + blocks::barotropic_constant::mass_normalization::value> + ); + + STATIC_REQUIRE( + std::is_base_of_v< + blocks::residual_block_base, + blocks::barotropic_constant::mass_normalization::residual> + ); + + STATIC_REQUIRE( + blocks::barotropic_constant::mass_normalization::value:: + static_block_size == 1 + ); + + STATIC_REQUIRE( + blocks::barotropic_constant::mass_normalization::residual:: + static_block_size == 1 + ); + + STATIC_REQUIRE(std::is_empty_v); + STATIC_REQUIRE( + std::is_empty_v + ); + + CHECK(true); +} + +TEST_CASE( + "Type Lists Resolve Their Types At Compile Time", + tags::unit &tags::solver &tags::utils +) { + using list = blocks::type_list< + blocks::density::mass::value, blocks::displacement::geometry::value, + blocks::gravity::gradient::value, blocks::gravity::poisson::value>; + + STATIC_REQUIRE(list::size == 4); + STATIC_REQUIRE( + blocks::type_index_v == 0 + ); + STATIC_REQUIRE( + blocks::type_index_v == 1 + ); + STATIC_REQUIRE( + blocks::type_index_v == 2 + ); + STATIC_REQUIRE( + blocks::type_index_v == 3 + ); + + STATIC_REQUIRE( + std::is_same_v, blocks::density::mass::value> + ); + STATIC_REQUIRE( + std::is_same_v< + type_at_t<1, list>, blocks::displacement::geometry::value> + ); + STATIC_REQUIRE( + std::is_same_v, blocks::gravity::gradient::value> + ); + STATIC_REQUIRE( + std::is_same_v, blocks::gravity::poisson::value> + ); + + CHECK(true); +} + +TEST_CASE( + "Gravity Field Form Resolves Value And Residual Blocks", + tags::unit &tags::solver &tags::utils +) { + using form = blocks::gravity_field_form; + + constexpr auto density_value = + blocks::get_value_block(blocks::density_field.mass_term); + constexpr auto displacement_value = + blocks::get_value_block(blocks::displacement_field.geometry_term); + constexpr auto gravity_gradient_value = + blocks::get_value_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_potential_value = + blocks::get_value_block(blocks::gravity_field.poisson_term); + constexpr auto gravity_gradient_residual = + blocks::get_residual_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_poisson_residual = + blocks::get_residual_block(blocks::gravity_field.poisson_term); + + STATIC_REQUIRE(form::value_block_count == 4); + STATIC_REQUIRE(form::residual_block_count == 2); + + STATIC_REQUIRE( + std::is_same_v< + std::remove_cv_t, blocks::value_block<0>> + ); + STATIC_REQUIRE( + std::is_same_v< + std::remove_cv_t, + blocks::value_block<1>> + ); + STATIC_REQUIRE( + std::is_same_v< + std::remove_cv_t, + blocks::value_block<2>> + ); + STATIC_REQUIRE( + std::is_same_v< + std::remove_cv_t, + blocks::value_block<3>> + ); + STATIC_REQUIRE( + std::is_same_v< + std::remove_cv_t, + blocks::residual_block<0>> + ); + STATIC_REQUIRE( + std::is_same_v< + std::remove_cv_t, + blocks::residual_block<1>> + ); + + CHECK(static_cast(density_value) == 0); + CHECK(static_cast(displacement_value) == 1); + CHECK(static_cast(gravity_gradient_value) == 2); + CHECK(static_cast(gravity_potential_value) == 3); + CHECK(static_cast(gravity_gradient_residual) == 0); + CHECK(static_cast(gravity_poisson_residual) == 1); +} + +TEST_CASE( + "Resolved Blocks Implicitly Convert For MFEM Interfaces", + tags::unit &tags::solver &tags::utils +) { + using form = blocks::gravity_field_form; + + constexpr auto density_value = + blocks::get_value_block(blocks::density_field.mass_term); + constexpr auto gravity_potential_value = + blocks::get_value_block(blocks::gravity_field.poisson_term); + constexpr auto gravity_gradient_residual = + blocks::get_residual_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_poisson_residual = + blocks::get_residual_block(blocks::gravity_field.poisson_term); + + auto consume_block_index = [](const int block_index) { + return block_index; + }; + + CHECK(consume_block_index(density_value) == 0); + CHECK(consume_block_index(gravity_potential_value) == 3); + CHECK(consume_block_index(gravity_gradient_residual) == 0); + CHECK(consume_block_index(gravity_poisson_residual) == 1); +} + +TEST_CASE( + "Block Indices Belong To Their Form", + tags::unit &tags::solver &tags::utils +) { + using reordered_form = blocks::block_form< + blocks::type_list< + blocks::gravity::poisson::value, blocks::gravity::gradient::value, + blocks::density::mass::value, + blocks::displacement::geometry::value>, + blocks::type_list< + blocks::gravity::poisson::residual, + blocks::gravity::gradient::residual>>; + + constexpr auto gravity_potential_value = + blocks::get_value_block( + blocks::gravity_field.poisson_term + ); + constexpr auto gravity_gradient_value = + blocks::get_value_block( + blocks::gravity_field.gradient_term + ); + constexpr auto density_value = blocks::get_value_block( + blocks::density_field.mass_term + ); + constexpr auto displacement_value = blocks::get_value_block( + blocks::displacement_field.geometry_term + ); + constexpr auto gravity_poisson_residual = + blocks::get_residual_block( + blocks::gravity_field.poisson_term + ); + constexpr auto gravity_gradient_residual = + blocks::get_residual_block( + blocks::gravity_field.gradient_term + ); + + STATIC_REQUIRE(static_cast(gravity_potential_value) == 0); + STATIC_REQUIRE(static_cast(gravity_gradient_value) == 1); + STATIC_REQUIRE(static_cast(density_value) == 2); + STATIC_REQUIRE(static_cast(displacement_value) == 3); + STATIC_REQUIRE(static_cast(gravity_poisson_residual) == 0); + STATIC_REQUIRE(static_cast(gravity_gradient_residual) == 1); + + CHECK(true); +} + +TEST_CASE( + "Form Layout Constructs Runtime Offsets From Block Sizes", + tags::unit &tags::solver &tags::utils +) { + using form = blocks::gravity_field_form; + + const std::array value_sizes{11, 13, 17, 19}; + const std::array residual_sizes{23, 29}; + const blocks::form_layout layout(value_sizes, residual_sizes); + + constexpr auto density_value = + blocks::get_value_block(blocks::density_field.mass_term); + constexpr auto displacement_value = + blocks::get_value_block(blocks::displacement_field.geometry_term); + constexpr auto gravity_gradient_value = + blocks::get_value_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_potential_value = + blocks::get_value_block(blocks::gravity_field.poisson_term); + constexpr auto gravity_gradient_residual = + blocks::get_residual_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_poisson_residual = + blocks::get_residual_block(blocks::gravity_field.poisson_term); + + CHECK(layout.size(density_value) == 11); + CHECK(layout.size(displacement_value) == 13); + CHECK(layout.size(gravity_gradient_value) == 17); + CHECK(layout.size(gravity_potential_value) == 19); + CHECK(layout.size(gravity_gradient_residual) == 23); + CHECK(layout.size(gravity_poisson_residual) == 29); + + CHECK(layout.offset(density_value) == 0); + CHECK(layout.offset(displacement_value) == 11); + CHECK(layout.offset(gravity_gradient_value) == 24); + CHECK(layout.offset(gravity_potential_value) == 41); + CHECK(layout.offset(gravity_gradient_residual) == 0); + CHECK(layout.offset(gravity_poisson_residual) == 23); + + REQUIRE(layout.value_offsets().Size() == 5); + CHECK(layout.value_offsets()[0] == 0); + CHECK(layout.value_offsets()[1] == 11); + CHECK(layout.value_offsets()[2] == 24); + CHECK(layout.value_offsets()[3] == 41); + CHECK(layout.value_offsets()[4] == 60); + + REQUIRE(layout.residual_offsets().Size() == 3); + CHECK(layout.residual_offsets()[0] == 0); + CHECK(layout.residual_offsets()[1] == 23); + CHECK(layout.residual_offsets()[2] == 52); +} + +TEST_CASE( + "Form Layout Supports Empty Runtime Blocks", + tags::unit &tags::solver &tags::utils +) { + using form = blocks::gravity_field_form; + + const std::array value_sizes{3, 0, 5, 0}; + const std::array residual_sizes{0, 7}; + const blocks::form_layout layout(value_sizes, residual_sizes); + + constexpr auto density_value = + blocks::get_value_block(blocks::density_field.mass_term); + constexpr auto displacement_value = + blocks::get_value_block(blocks::displacement_field.geometry_term); + constexpr auto gravity_gradient_value = + blocks::get_value_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_potential_value = + blocks::get_value_block(blocks::gravity_field.poisson_term); + constexpr auto gravity_gradient_residual = + blocks::get_residual_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_poisson_residual = + blocks::get_residual_block(blocks::gravity_field.poisson_term); + + CHECK(layout.size(density_value) == 3); + CHECK(layout.size(displacement_value) == 0); + CHECK(layout.size(gravity_gradient_value) == 5); + CHECK(layout.size(gravity_potential_value) == 0); + CHECK(layout.size(gravity_gradient_residual) == 0); + CHECK(layout.size(gravity_poisson_residual) == 7); + + CHECK(layout.offset(density_value) == 0); + CHECK(layout.offset(displacement_value) == 3); + CHECK(layout.offset(gravity_gradient_value) == 3); + CHECK(layout.offset(gravity_potential_value) == 8); + CHECK(layout.offset(gravity_gradient_residual) == 0); + CHECK(layout.offset(gravity_poisson_residual) == 0); + + CHECK(layout.value_offsets().Last() == 8); + CHECK(layout.residual_offsets().Last() == 7); +} + +TEST_CASE( + "Form Layout Integrates With MFEM Block Vectors", + tags::unit &tags::solver &tags::utils +) { + using form = blocks::gravity_field_form; + + const std::array value_sizes{3, 5, 7, 11}; + const std::array residual_sizes{13, 17}; + const blocks::form_layout layout(value_sizes, residual_sizes); + + constexpr auto density_value = + blocks::get_value_block(blocks::density_field.mass_term); + constexpr auto displacement_value = + blocks::get_value_block(blocks::displacement_field.geometry_term); + constexpr auto gravity_gradient_value = + blocks::get_value_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_potential_value = + blocks::get_value_block(blocks::gravity_field.poisson_term); + constexpr auto gravity_gradient_residual = + blocks::get_residual_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_poisson_residual = + blocks::get_residual_block(blocks::gravity_field.poisson_term); + + mfem::BlockVector values(layout.value_offsets()); + mfem::BlockVector residuals(layout.residual_offsets()); + + values = 0.0; + residuals = 0.0; + + values.GetBlock(density_value) = 1.0; + values.GetBlock(displacement_value) = 2.0; + values.GetBlock(gravity_gradient_value) = 3.0; + values.GetBlock(gravity_potential_value) = 4.0; + + residuals.GetBlock(gravity_gradient_residual) = 5.0; + residuals.GetBlock(gravity_poisson_residual) = 6.0; + + CHECK(values.GetBlock(density_value).Size() == 3); + CHECK(values.GetBlock(displacement_value).Size() == 5); + CHECK(values.GetBlock(gravity_gradient_value).Size() == 7); + CHECK(values.GetBlock(gravity_potential_value).Size() == 11); + CHECK(residuals.GetBlock(gravity_gradient_residual).Size() == 13); + CHECK(residuals.GetBlock(gravity_poisson_residual).Size() == 17); + + CHECK(values.GetBlock(density_value).Min() == 1.0); + CHECK(values.GetBlock(density_value).Max() == 1.0); + CHECK(values.GetBlock(displacement_value).Min() == 2.0); + CHECK(values.GetBlock(displacement_value).Max() == 2.0); + CHECK(values.GetBlock(gravity_gradient_value).Min() == 3.0); + CHECK(values.GetBlock(gravity_gradient_value).Max() == 3.0); + CHECK(values.GetBlock(gravity_potential_value).Min() == 4.0); + CHECK(values.GetBlock(gravity_potential_value).Max() == 4.0); + CHECK(residuals.GetBlock(gravity_gradient_residual).Min() == 5.0); + CHECK(residuals.GetBlock(gravity_gradient_residual).Max() == 5.0); + CHECK(residuals.GetBlock(gravity_poisson_residual).Min() == 6.0); + CHECK(residuals.GetBlock(gravity_poisson_residual).Max() == 6.0); +} + +TEST_CASE( + "Compile Time Blocks Configure An MFEM Block Operator", + tags::unit &tags::solver &tags::utils +) { + using form = blocks::gravity_field_form; + + const std::array value_sizes{3, 5, 7, 11}; + const std::array residual_sizes{13, 17}; + const blocks::form_layout layout(value_sizes, residual_sizes); + + constexpr auto density_value = + blocks::get_value_block(blocks::density_field.mass_term); + constexpr auto gravity_gradient_residual = + blocks::get_residual_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_poisson_residual = + blocks::get_residual_block(blocks::gravity_field.poisson_term); + + mfem::DenseMatrix source_block( + layout.size(gravity_poisson_residual), layout.size(density_value) + ); + source_block = 1.0; + + mfem::BlockOperator block_operator( + layout.residual_offsets(), layout.value_offsets() + ); + block_operator.SetBlock( + gravity_poisson_residual, density_value, &source_block + ); + + mfem::BlockVector values(layout.value_offsets()); + mfem::BlockVector residuals(layout.residual_offsets()); + + values = 0.0; + residuals = 0.0; + values.GetBlock(density_value) = 2.0; + + block_operator.Mult(values, residuals); + + CHECK(residuals.GetBlock(gravity_gradient_residual).Norml2() == 0.0); + + const mfem::Vector &poisson_residual = + residuals.GetBlock(gravity_poisson_residual); + REQUIRE(poisson_residual.Size() == residual_sizes[1]); + + for (int i = 0; i < poisson_residual.Size(); ++i) { + CHECK(poisson_residual(i) == 2.0 * value_sizes[0]); + } +} + +TEST_CASE( + "Gravity Jacobian Form Describes The Expected Couplings", + tags::unit &tags::solver &tags::utils +) { + using gradient_row = type_at_t<0, blocks::gravity_jacobian_form>; + using poisson_row = type_at_t<1, blocks::gravity_jacobian_form>; + + using gradient_traits = block_row_traits; + using poisson_traits = block_row_traits; + + STATIC_REQUIRE(blocks::gravity_jacobian_form::size == 2); + + STATIC_REQUIRE( + std::is_same_v< + typename gradient_traits::residual, + blocks::gravity::gradient::residual> + ); + STATIC_REQUIRE(gradient_traits::value_count == 3); + STATIC_REQUIRE( + contains_type_v< + blocks::gravity::gradient::value, typename gradient_traits::values> + ); + STATIC_REQUIRE( + contains_type_v< + blocks::gravity::poisson::value, typename gradient_traits::values> + ); + STATIC_REQUIRE( + contains_type_v< + blocks::displacement::geometry::value, + typename gradient_traits::values> + ); + STATIC_REQUIRE_FALSE( + contains_type_v< + blocks::density::mass::value, typename gradient_traits::values> + ); + + STATIC_REQUIRE( + std::is_same_v< + typename poisson_traits::residual, + blocks::gravity::poisson::residual> + ); + STATIC_REQUIRE(poisson_traits::value_count == 3); + STATIC_REQUIRE( + contains_type_v< + blocks::gravity::gradient::value, typename poisson_traits::values> + ); + STATIC_REQUIRE( + contains_type_v< + blocks::density::mass::value, typename poisson_traits::values> + ); + STATIC_REQUIRE( + contains_type_v< + blocks::displacement::geometry::value, + typename poisson_traits::values> + ); + STATIC_REQUIRE_FALSE( + contains_type_v< + blocks::gravity::poisson::value, typename poisson_traits::values> + ); + + CHECK(true); +} + +TEST_CASE( + "Barotropic Equilibrium Form Encodes The Agreed Row And Column Layouts", + tags::unit &tags::solver &tags::utils +) { + using form = blocks::barotropic_equilibrium_form; + + constexpr auto density_value = + blocks::get_value_block(blocks::density_field.mass_term); + constexpr auto displacement_value = + blocks::get_value_block(blocks::displacement_field.geometry_term); + constexpr auto gravity_gradient_value = + blocks::get_value_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_potential_value = + blocks::get_value_block(blocks::gravity_field.poisson_term); + constexpr auto enthalpy_value = + blocks::get_value_block(blocks::enthalpy_field.specific_term); + constexpr auto barotropic_constant_value = blocks::get_value_block( + blocks::barotropic_constant_field.mass_normalization_term + ); + + constexpr auto gravity_gradient_residual = + blocks::get_residual_block(blocks::gravity_field.gradient_term); + constexpr auto gravity_poisson_residual = + blocks::get_residual_block(blocks::gravity_field.poisson_term); + constexpr auto density_residual = + blocks::get_residual_block(blocks::density_field.mass_term); + constexpr auto displacement_residual = blocks::get_residual_block( + blocks::displacement_field.geometry_term + ); + constexpr auto enthalpy_residual = + blocks::get_residual_block(blocks::enthalpy_field.specific_term); + constexpr auto mass_residual = blocks::get_residual_block( + blocks::barotropic_constant_field.mass_normalization_term + ); + + STATIC_REQUIRE(form::value_block_count == 6); + STATIC_REQUIRE(form::residual_block_count == 6); + + STATIC_REQUIRE(static_cast(density_value) == 0); + STATIC_REQUIRE(static_cast(displacement_value) == 1); + STATIC_REQUIRE(static_cast(gravity_gradient_value) == 2); + STATIC_REQUIRE(static_cast(gravity_potential_value) == 3); + STATIC_REQUIRE(static_cast(enthalpy_value) == 4); + STATIC_REQUIRE(static_cast(barotropic_constant_value) == 5); + + STATIC_REQUIRE(static_cast(gravity_gradient_residual) == 0); + STATIC_REQUIRE(static_cast(gravity_poisson_residual) == 1); + STATIC_REQUIRE(static_cast(density_residual) == 2); + STATIC_REQUIRE(static_cast(displacement_residual) == 3); + STATIC_REQUIRE(static_cast(enthalpy_residual) == 4); + STATIC_REQUIRE(static_cast(mass_residual) == 5); + + CHECK(true); +} + +TEST_CASE( + "Barotropic Jacobian Form Encodes The Exact Direct Coupling Graph", + tags::unit &tags::solver &tags::utils +) { + using jacobian = blocks::barotropic_equilibrium_jacobian_form; + + using gradient_row = type_at_t<0, jacobian>; + using poisson_row = type_at_t<1, jacobian>; + using density_row = type_at_t<2, jacobian>; + using displacement_row = type_at_t<3, jacobian>; + using enthalpy_row = type_at_t<4, jacobian>; + using mass_row = type_at_t<5, jacobian>; + + STATIC_REQUIRE(jacobian::size == 6); + + STATIC_REQUIRE( + row_has_exact_values_v< + gradient_row, blocks::gravity::gradient::value, + blocks::gravity::poisson::value, + blocks::displacement::geometry::value> + ); + + STATIC_REQUIRE( + row_has_exact_values_v< + poisson_row, blocks::gravity::gradient::value, + blocks::density::mass::value, blocks::displacement::geometry::value> + ); + + STATIC_REQUIRE( + row_has_exact_values_v< + density_row, blocks::density::mass::value, + blocks::enthalpy::specific::value, + blocks::displacement::geometry::value> + ); + + STATIC_REQUIRE( + row_has_exact_values_v< + displacement_row, blocks::displacement::geometry::value, + blocks::enthalpy::specific::value> + ); + + STATIC_REQUIRE( + row_has_exact_values_v< + enthalpy_row, blocks::enthalpy::specific::value, + blocks::gravity::poisson::value, + blocks::displacement::geometry::value, + blocks::barotropic_constant::mass_normalization::value> + ); + + STATIC_REQUIRE( + row_has_exact_values_v< + mass_row, blocks::density::mass::value, + blocks::displacement::geometry::value> + ); + + STATIC_REQUIRE_FALSE( + blocks::has_jacobian_coupling_v< + blocks::displacement::geometry::residual, + blocks::gravity::poisson::value, jacobian> + ); + + STATIC_REQUIRE_FALSE( + blocks::has_jacobian_coupling_v< + blocks::barotropic_constant::mass_normalization::residual, + blocks::barotropic_constant::mass_normalization::value, jacobian> + ); + + STATIC_REQUIRE_FALSE( + blocks::has_jacobian_coupling_v< + blocks::barotropic_constant::mass_normalization::residual, + blocks::enthalpy::specific::value, jacobian> + ); + + CHECK(true); +} + +TEST_CASE( + "Block Validators Reject Structurally Malformed Forms", + tags::unit &tags::solver &tags::utils +) { + using form = blocks::barotropic_equilibrium_form; + using jacobian = blocks::barotropic_equilibrium_jacobian_form; + + using gradient_row = type_at_t<0, jacobian>; + using poisson_row = type_at_t<1, jacobian>; + using density_row = type_at_t<2, jacobian>; + using displacement_row = type_at_t<3, jacobian>; + using enthalpy_row = type_at_t<4, jacobian>; + using mass_row = type_at_t<5, jacobian>; + + using missing_row = blocks::type_list< + gradient_row, poisson_row, density_row, displacement_row, enthalpy_row>; + + using duplicate_row = blocks::type_list< + gradient_row, poisson_row, density_row, displacement_row, enthalpy_row, + enthalpy_row>; + + using reordered_rows = blocks::type_list< + poisson_row, gradient_row, density_row, displacement_row, enthalpy_row, + mass_row>; + + using foreign_value_row = blocks::block_row< + blocks::enthalpy::specific::residual, blocks::enthalpy::specific::value, + blocks::gravity::poisson::value, blocks::displacement::geometry::value, + foreign_value>; + + using foreign_value_jacobian = blocks::type_list< + gradient_row, poisson_row, density_row, displacement_row, + foreign_value_row, mass_row>; + + using duplicate_value_row = blocks::block_row< + blocks::enthalpy::specific::residual, blocks::enthalpy::specific::value, + blocks::gravity::poisson::value, blocks::displacement::geometry::value, + blocks::barotropic_constant::mass_normalization::value, + blocks::barotropic_constant::mass_normalization::value>; + + using duplicate_value_jacobian = blocks::type_list< + gradient_row, poisson_row, density_row, displacement_row, + duplicate_value_row, mass_row>; + + using unknown_residual_row = + blocks::block_row; + + using unknown_residual_jacobian = blocks::type_list< + gradient_row, poisson_row, density_row, displacement_row, enthalpy_row, + unknown_residual_row>; + + using duplicate_value_form = blocks::block_form< + blocks::type_list< + blocks::density::mass::value, blocks::density::mass::value>, + blocks::type_list>; + + STATIC_REQUIRE(blocks::block_form_is_valid_v); + STATIC_REQUIRE((blocks::valid_jacobian_form)); + + STATIC_REQUIRE_FALSE(blocks::block_form_is_valid_v); + + STATIC_REQUIRE_FALSE((blocks::valid_jacobian_form)); + + STATIC_REQUIRE_FALSE((blocks::valid_jacobian_form)); + + STATIC_REQUIRE_FALSE((blocks::valid_jacobian_form)); + + STATIC_REQUIRE_FALSE(( + blocks::valid_jacobian_form + )); + + STATIC_REQUIRE_FALSE(( + blocks::valid_jacobian_form + )); + + STATIC_REQUIRE_FALSE(( + blocks::valid_jacobian_form + )); + + CHECK(true); +} + +TEST_CASE( + "Barotropic Layout Preserves Distinct Row And Column Offsets", + tags::unit &tags::solver &tags::utils +) { + using form = blocks::barotropic_equilibrium_form; + + // Columns: [rho, d, g, Phi, h, C] + const std::array value_sizes{11, 13, 17, + 19, 23, 1}; + + // Rows: [R_g, R_Phi, R_rho, R_d, R_h, R_M] + const std::array residual_sizes{17, 19, 11, + 13, 23, 1}; + + const blocks::form_layout layout(value_sizes, residual_sizes); + + constexpr auto constant_value = blocks::get_value_block( + blocks::barotropic_constant_field.mass_normalization_term + ); + constexpr auto mass_residual = blocks::get_residual_block( + blocks::barotropic_constant_field.mass_normalization_term + ); + + CHECK(layout.size(constant_value) == 1); + CHECK(layout.size(mass_residual) == 1); + + CHECK(layout.offset(constant_value) == 83); + CHECK(layout.offset(mass_residual) == 83); + + CHECK(layout.value_offsets().Last() == 84); + CHECK(layout.residual_offsets().Last() == 84); + + const std::array invalid_value_sizes{11, 13, + 17, 19, + 23, 2}; + + CHECK_THROWS( + blocks::form_layout(invalid_value_sizes, residual_sizes) + ); +} \ No newline at end of file