feat(newton): first newton solver implementation

CMakeLists.txt

@@ -145,7 +145,13 @@ target_sources(mean_field
         libmeanfield/interface/quadrature/policy.cppm
         libmeanfield/interface/quadrature/mfem.cppm
         libmeanfield/interface/solver/fields.cppm
+        libmeanfield/interface/solver/linear_backend.cppm
+        libmeanfield/interface/solver/newton.cppm
         libmeanfield/interface/solver/preconditioning_diagnostics.cppm
+        libmeanfield/interface/solver/stellar_equilibrium_types.cppm
+        libmeanfield/interface/solver/stellar_structure.cppm
+        libmeanfield/interface/solver/stellar_context.cppm
+        libmeanfield/interface/solver/stellar_equilibrium.cppm
         libmeanfield/interface/preconditioning/backend.cppm
         libmeanfield/interface/preconditioning/backend_implementations.cppm
         libmeanfield/interface/preconditioning/gravity_field.cppm
@@ -155,6 +161,7 @@ target_sources(mean_field
         libmeanfield/interface/preconditioning/stellar_structure.cppm
         libmeanfield/interface/preconditioning/specification_border.cppm
         libmeanfield/interface/preconditioning/equilibrium_coordinates.cppm
+        libmeanfield/interface/preconditioning/stellar_recipe.cppm
         libmeanfield/interface/preconditioning/preconditioning.cppm
         libmeanfield/interface/normalization/plan.cppm
         libmeanfield/interface/normalization/physical_riesz.cppm
@@ -346,10 +353,18 @@ add_executable(tests
         tests/normalization/stellar_equilibrium.cpp
         tests/user-api/stellar_equilibrium.cpp
         tests/solver/preconditioning_diagnostics.cpp
+        tests/solver/stellar_equilibrium_architecture.cpp
+        tests/solver/stellar_equilibrium_architecture_internal.cpp
+        tests/solver/stellar_equilibrium_runtime.cpp
 )
 
 target_link_libraries(tests PRIVATE mean_field test_mod Catch2::Catch2 Boost::boost)
 
+# A deliberately opt-in API workbench. It is compiled explicitly during API
+# verification but temporary user experiments do not break the default build.
+add_executable(sandbox EXCLUDE_FROM_ALL sandbox.cpp)
+target_link_libraries(sandbox PRIVATE mean_field)
+
 add_executable(mpi_tests
         tests/mpi/mpi_test_main.cpp
         tests/mpi/distributed_execution.cpp
@@ -416,6 +431,26 @@ catch_discover_tests(
         WORKING_DIRECTORY "${CMAKE_SOURCE_DIR}"
 )
 
+add_test(
+        NAME mpi_single_rank_stellar_root
+        COMMAND
+        ${MPIEXEC_EXECUTABLE}
+        ${MPIEXEC_NUMPROC_FLAG} 1
+        ${MPIEXEC_PREFLAGS}
+        $<TARGET_FILE:mpi_tests>
+        ${MPIEXEC_POSTFLAGS}
+        "[single-rank]"
+)
+set_tests_properties(
+        mpi_single_rank_stellar_root
+        PROPERTIES
+        LABELS "mpi;single-rank"
+        PROCESSORS 1
+        RESOURCE_LOCK mean_field_mpi
+        TIMEOUT 600
+        WORKING_DIRECTORY "${CMAKE_SOURCE_DIR}"
+)
+
 foreach (mean_field_mpi_ranks IN ITEMS 2 4)
     add_test(
             NAME mpi_${mean_field_mpi_ranks}_ranks
@@ -425,7 +460,7 @@ foreach (mean_field_mpi_ranks IN ITEMS 2 4)
             ${MPIEXEC_PREFLAGS}
             $<TARGET_FILE:mpi_tests>
             ${MPIEXEC_POSTFLAGS}
-            "[mpi]"
+            "[mpi]~[single-rank]"
     )
     set_tests_properties(
             mpi_${mean_field_mpi_ranks}_ranks