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MeanField_SERiF/tests/model/moving_equilibrium.cpp
Emily Boudreaux cb20faeb3d test(tests): added test suite 
The test suite is extensive. Note that LLMs were used to aid in the development of the test suite. All LLM generated code was manually reviewed.
2026-11-09 13:53:17 -05:00

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#include <algorithm>
#include <array>
#include <cmath>
#include <limits>
#include <memory>
#include <numbers>
#include <tuple>
#include <utility>
#include <variant>
#include <catch2/catch_approx.hpp>
#include <catch2/catch_test_macros.hpp>
#include "mfem/linalg/solvers.hpp"
#include "mfem/general/communication.hpp"
#include "serif/equations/angular_momentum.hpp"
#include "serif/equations/barotropic_density.hpp"
#include "serif/equations/primal_gravity.hpp"
#include "serif/equations/surface_potential.hpp"
#include "serif/equations/mass_normalization.hpp"
#include "serif/backend/mfem/model/equilibrium.hpp"
#include "serif/model/eos_reference.hpp"
#include "serif/solver/preconditioner/default_preconditioners.hpp"
#include "serif/tests/deformation/mesh.hpp"
#include "serif/tests/equations/gravity_fixture.hpp"
// MeanField's prepared_stellar_equilibrium.cpp checks the complete moving root
// against its children and centered differences. Keep both checks: child parity
// verifies composition, while finite differences verify the assembled derivative.
namespace {
namespace model = serif::model;
namespace backend = model::backend::mfem;
namespace execution = serif::operators::backend::mfem;
namespace dependencies = serif::utils::dependencies;
namespace equations = serif::equations;
namespace deformation = serif::geometry::deformation;
namespace surface = serif::geometry::surface;
namespace blocks = serif::discretization::blocks;
namespace tests = serif::tests::equations;
using Polytrope = serif::eos::models::Polytrope;
using Density = blocks::density::mass;
using Potential = blocks::gravity::potential;
using Constant = blocks::barotropic_constant::mass_normalization;
using Omega = blocks::rotation::angular_velocity;
using Shape = blocks::surface_deformation::coefficients;
using ShapeRow = blocks::surface_deformation::shape_equilibrium;
using Displacement = blocks::displacement::vector;
using Kind = blocks::RepresentedValueKind;
using Vector = mfem::Vector;
using InteriorRows = dependencies::KeyList<Density, Potential, Constant, Omega>;
/** @brief Own paired stellar/vacuum meshes and all resources borrowed by the public model binding. */
struct Fixture {
stroid::StroidMesh generated{serif::tests::deformation::make_mesh(1)};
tests::gravity::GravityFixture fields;
mfem::FiniteElementSpace reference_displacement{&fields.mesh, &fields.enthalpy_collection, 3, mfem::Ordering::byNODES};
mfem::FiniteElementSpace compactification_space{&fields.mesh, generated.exterior_coordinate->space->FEColl()};
mfem::GridFunction compactification{&compactification_space};
/** @brief Preserve the generator's exterior coordinate on the identically numbered mesh copy. */
explicit Fixture(const mfem::Ordering::Type ordering) : fields(mfem::Mesh(*generated.mesh), ordering) {
REQUIRE(compactification.Size() == generated.exterior_coordinate->values->Size());
compactification = *generated.exterior_coordinate->values;
}
};
/** @brief Exercise all stellar equations at a valid, deliberately unconverged rotating state. */
[[nodiscard]] auto physical_model(const double index = 1.5) {
const auto definition = [](const auto& physics) {
const auto eos = model::borrow_eos(physics.equation_of_state());
const auto& rotation = physics.template specification<model::FixedAngularMomentum>();
const auto& axis = rotation.axis();
const auto& center = rotation.center();
return model::EquilibriumEquations{
.interior_equations = equations::EquationRegistry{
equations::BarotropicDensityBalance{eos, serif::dimensions::PressureValue{0.025}, axis, center}, equations::PrimalPoissonBalance{2.3},
equations::MassNormalization{physics.template specification<model::FixedTotalMass>().target().value()},
equations::AngularMomentumConstraint{rotation.target().value(), axis, center}
},
.shape_force = equations::SurfacePotentialBalance{axis, center},
.surface_condition = surface::Isobaric{serif::dimensions::PressureValue{0.025}}
};
};
return model::make_stellar_model(Polytrope{index, 0.25}, definition,
model::FixedTotalMass{serif::dimensions::MassValue{1.1}},
model::FixedAngularMomentum{{.angular_momentum = serif::dimensions::AngularMomentumValue{0.14},
.axis = {0.2, -0.3, 1.0}, .center = {0.03, -0.02, 0.01}}});
}
/** @brief Use the production radial lift and vacuum extension with nine independent surface harmonics. */
[[nodiscard]] auto discretize(const std::shared_ptr<Fixture>& fixture) {
const auto& fields = fixture->fields;
const auto bindings = dependencies::make_dependency_context(
dependencies::borrow<Density>(fields.density_binding), dependencies::borrow<Potential>(fields.potential_binding),
dependencies::borrow<Constant>(fields.constant_binding), dependencies::borrow<Omega>(fields.angular_velocity_binding),
dependencies::borrow<Displacement>(fields.displacement_binding));
const auto reference = deformation::backend::mfem::deformation_discretization(
fields.enthalpy_space, fixture->reference_displacement, *fixture->generated.reference_mesh);
const deformation::DomainDeformation<deformation::SphericalHarmonicSurface> geometry{
.surface = {.maximum_degree = 2}, .stellar_interior = {}, .vacuum = {}
};
return backend::with_deformation(backend::make_stellar_discretization(fixture, bindings, fixture->compactification, fields.mapper), geometry, reference);
}
/** @brief Populate all physical fields, scalar constraints and surface modes in the moving-star fixture. */
template <typename Layout, typename ShapeCoefficients>
[[nodiscard]] model::StellarState<Layout> initial_state(const Layout& layout, tests::gravity::GravityFixture& fields, const ShapeCoefficients& shape) {
model::StellarState state(layout);
const auto initialize = [&]<typename Term>(const Vector& values) {
const auto destination = state.template get<Term>();
REQUIRE(destination.size() == static_cast<std::size_t>(values.Size()));
std::copy_n(values.GetData(), values.Size(), destination.begin());
};
initialize.template operator()<Density>(fields.density());
initialize.template operator()<Potential>(fields.potential());
state.template get<Constant>()[0] = 0.72;
state.template get<Omega>()[0] = 0.31;
std::ranges::copy(shape, state.template get<Shape>().begin());
return state;
}
/** @brief Make an independent physical candidate without sharing any mutable field storage. */
template <typename Layout>
[[nodiscard]] model::StellarState<Layout> perturbed_state(const model::StellarState<Layout>& original, const double step, const Vector& direction) {
REQUIRE(original.values().size() == static_cast<std::size_t>(direction.Size()));
model::StellarState result(original);
for (int index = 0; index < direction.Size(); ++index) {
result.values()[static_cast<std::size_t>(index)] += step * direction[index];
}
return result;
}
/** @brief Copy a frozen residual before evaluating another candidate. */
template <typename System>
[[nodiscard]] Vector residual(const System& system) {
Vector result(static_cast<int>(system.residual().size()));
std::copy(system.residual().begin(), system.residual().end(), result.GetData());
return result;
}
/** @brief Check each equation separately so large gravity rows cannot hide missing scalar or shape rows. */
template <typename Layout>
void check_rows(const Vector& actual, const Vector& expected, const Layout& layout, double relative_tolerance, double absolute_tolerance) {
REQUIRE(actual.Size() == expected.Size());
int offset = 0;
for (std::size_t row = 0; row < layout.residual_sizes.size(); ++row) {
CAPTURE(row);
double error_squared = 0.0, reference_squared = 0.0;
for (std::size_t entry = 0; entry < layout.residual_sizes[row]; ++entry) {
const double difference = actual[offset] - expected[offset];
error_squared += difference * difference;
reference_squared += expected[offset] * expected[offset];
++offset;
}
CHECK(std::sqrt(error_squared) <= absolute_tolerance + relative_tolerance * std::sqrt(reference_squared));
}
}
/** @brief Compare cached scalar functionals with the independently retained moving volume actions. */
template <typename Row, typename Evaluator>
void check_scalar_row(const Evaluator& evaluator, const backend::PhysicalSystem& physical) {
const auto& layout = evaluator.layout();
const auto& cache = evaluator.cache();
const auto volume = cache.template share<typename execution::volume_keys::Scoped<Row>::Linearization>();
const auto& shape = cache.template get<model::computations::ShapeDerivatives>();
const auto reference = backend::volume_row_action(volume, layout, backend::ColumnContribution{
static_cast<int>(layout.template offset<Kind::value, Shape>()), shape.tangent});
const auto& cached = cache.template get<model::computations::ScalarResidualRow<Row>>();
const Vector direction = tests::deterministic(reference.action()->Width(), 0.47);
const Vector dual = tests::constant(1, 0.37);
Vector expected(1), actual(1), expected_transpose, actual_transpose(direction.Size());
reference.action()->Mult(direction, expected);
cached.action()->Mult(direction, actual);
CHECK(actual[0] == Catch::Approx(expected[0]).margin(2.0e-12));
reference.action()->MultTranspose(dual, expected_transpose);
cached.action()->MultTranspose(dual, actual_transpose);
CHECK(tests::relative_error(actual_transpose, expected_transpose) < 2.0e-12);
const auto check_column = [&]<typename Column>() {
const int offset = static_cast<int>(layout.template offset<Kind::value, Column>());
const int size = static_cast<int>(layout.template size<Kind::value, Column>());
const auto selected = physical.block(static_cast<int>(layout.template offset<Kind::residual, Row>()), 1, offset, size);
Vector input(size), selected_transpose;
std::copy_n(direction.GetData() + offset, size, input.GetData());
Vector complete(direction.Size());
complete = 0.0;
std::copy_n(input.GetData(), size, complete.GetData() + offset);
cached.action()->Mult(complete, expected);
selected.action()->Mult(input, actual);
CHECK(actual[0] == Catch::Approx(expected[0]).margin(2.0e-12));
selected.action()->MultTranspose(dual, selected_transpose);
Vector expected_column(expected_transpose.GetData() + offset, size);
CHECK(tests::relative_error(selected_transpose, expected_column) < 2.0e-12);
};
check_column.template operator()<Density>();
check_column.template operator()<Shape>();
check_column.template operator()<Omega>();
}
/** @brief Place the volume and surface children, then independently enforce both physical traces. */
template <typename Evaluator, typename Layout>
void check_composition(const Evaluator& evaluator, const model::StellarState<Layout>& state,
const backend::PhysicalSystem& physical, const serif::discretization::backend::mfem::DofSelection& boundary) {
const auto& layout = evaluator.layout();
const auto& cache = evaluator.cache();
Vector expected(static_cast<int>(layout.template total_size<Kind::residual>()));
expected = 0.0;
[&]<typename... Rows>(dependencies::KeyList<Rows...>) {
const auto place = [&]<typename Row>() {
const auto& child = cache.template get<typename execution::volume_keys::Scoped<Row>::Linearization>();
REQUIRE(static_cast<std::size_t>(child.residual.Size()) == layout.template size<Kind::residual, Row>());
std::copy_n(child.residual.GetData(), child.residual.Size(), expected.GetData() + layout.template offset<Kind::residual, Row>());
};
(place.template operator()<Rows>(), ...);
}(InteriorRows{});
const auto& surface_child = cache.template get<model::computations::ShapeContribution>();
REQUIRE(surface_child.residual.size() == 1);
for (const auto& contribution : surface_child.residual) {
std::copy(contribution.values.begin(), contribution.values.end(), expected.GetData() + contribution.row_offset);
}
const int shape_row = static_cast<int>(layout.template offset<Kind::residual, ShapeRow>());
const int shape_size = static_cast<int>(layout.template size<Kind::residual, ShapeRow>());
Vector shape_residual(expected.GetData() + shape_row, shape_size);
REQUIRE(shape_residual.Norml2() > 1.0e-8);
// Compare each retained surface child coupling with the corresponding assembled block.
for (const auto& contribution : surface_child.jacobian) {
const auto selected = physical.block(contribution.row_offset, contribution.block.action()->Height(),
contribution.column_offset, contribution.block.action()->Width());
const Vector direction = tests::deterministic(contribution.block.action()->Width(), 0.47);
const Vector dual = tests::deterministic(contribution.block.action()->Height(), 0.71);
Vector actual(contribution.block.action()->Height()), reference(contribution.block.action()->Height());
Vector actual_transpose(contribution.block.action()->Width()), reference_transpose(contribution.block.action()->Width());
selected.action()->Mult(direction, actual);
contribution.block.action()->Mult(direction, reference);
CHECK(tests::relative_error(actual, reference) < 2.0e-13);
selected.action()->MultTranspose(dual, actual_transpose);
contribution.block.action()->MultTranspose(dual, reference_transpose);
CHECK(tests::relative_error(actual_transpose, reference_transpose) < 2.0e-13);
}
const auto density = state.template get<Density>();
REQUIRE(boundary.size() > 0);
REQUIRE(boundary.size() < static_cast<int>(density.size()));
const double surface_density = serif::eos::evaluate<serif::dimensions::MassDensity>(
evaluator.model().equation_of_state(), serif::dimensions::PressureValue{0.025}).value();
const int density_row = static_cast<int>(layout.template offset<Kind::residual, Density>());
for (const int row : boundary.reduced_dofs()) {
expected[density_row + row] = density[row] - surface_density;
}
const auto infinity = serif::discretization::backend::mfem::select_boundary_dofs<
serif::discretization::domain::InfinitySurfaceBoundary>(
evaluator.binding().discretization->template binding<Potential>());
REQUIRE(infinity.size() > 0);
const int potential_row = static_cast<int>(layout.template offset<Kind::residual, Potential>());
for (const int row : infinity.reduced_dofs()) {
expected[potential_row + row] = state.template get<Potential>()[row];
}
check_rows(residual(physical), expected, layout, 2.0e-13, 2.0e-13);
// Each strong trace must reach its own scalar field alone, including in the transpose.
const auto check_trace = [&]<typename Field>(const auto& selected) {
Vector dual(expected.Size()), transpose;
dual = 0.0;
Vector expected_transpose(physical.jacobian().action()->Width());
expected_transpose = 0.0;
const int row_offset = static_cast<int>(layout.template offset<Kind::residual, Field>());
const int column_offset = static_cast<int>(layout.template offset<Kind::value, Field>());
for (const int row : selected.reduced_dofs()) {
dual[row_offset + row] = 0.17 + 0.01 * (row % 7);
expected_transpose[column_offset + row] = dual[row_offset + row];
}
physical.jacobian().action()->MultTranspose(dual, transpose);
CHECK(tests::relative_error(transpose, expected_transpose) < 2.0e-13);
};
check_trace.template operator()<Density>(boundary);
check_trace.template operator()<Potential>(infinity);
}
/** @brief Compare every physical state column and a mixed perturbation through the public evaluation path. */
template <typename Evaluator, typename Layout>
void check_derivatives(Evaluator& evaluator, const model::StellarState<Layout>& state) {
const auto& layout = evaluator.layout();
const auto evaluation = evaluator.evaluate(state);
REQUIRE(evaluation);
const auto frozen = *evaluation;
const Vector direction_seed = tests::deterministic(static_cast<int>(state.values().size()), 0.43);
const Vector dual = tests::deterministic(frozen->jacobian().action()->Height(), 1.17);
Vector transpose, block_transpose;
frozen->jacobian().action()->MultTranspose(dual, transpose);
const auto blocks = frozen->block(0, dual.Size(), 0, static_cast<int>(state.values().size()));
blocks.action()->MultTranspose(dual, block_transpose);
CHECK(tests::relative_error(transpose, block_transpose) < 2.0e-12);
// The final iteration moves all physical fields and the surface simultaneously.
int offset = 0;
for (std::size_t column = 0; column <= layout.state_sizes.size(); ++column) {
CAPTURE(column);
Vector direction(direction_seed);
if (column < layout.state_sizes.size()) {
direction = 0.0;
std::copy_n(direction_seed.GetData() + offset, layout.state_sizes[column], direction.GetData() + offset);
offset += static_cast<int>(layout.state_sizes[column]);
}
Vector action, block_action;
frozen->jacobian().action()->Mult(direction, action);
blocks.action()->Mult(direction, block_action);
REQUIRE(action.Norml2() > 1.0e-10);
check_rows(action, block_action, layout, 2.0e-12, 2.0e-12);
CHECK((action * dual) == Catch::Approx(direction * transpose).epsilon(2.0e-12).margin(2.0e-12));
constexpr double step = 1.0e-5;
const auto plus = evaluator.evaluate(perturbed_state(state, step, direction));
REQUIRE(plus);
Vector difference = residual(**plus);
const auto minus = evaluator.evaluate(perturbed_state(state, -step, direction));
REQUIRE(minus);
difference -= residual(**minus);
difference /= 2.0 * step;
check_rows(action, difference, layout, 2.0e-6, 2.0e-9);
if (column == Layout::template index<Kind::value, Shape>()) {
// Shape must affect each interior equation and the surface potential, not only its own row.
int row_offset = 0;
for (std::size_t row = 0; row < layout.residual_sizes.size(); ++row) {
Vector row_action(action.GetData() + row_offset, static_cast<int>(layout.residual_sizes[row]));
CHECK(row_action.Norml2() > 1.0e-10);
row_offset += row_action.Size();
}
}
}
const auto restored = evaluator.evaluate(state);
REQUIRE(restored);
check_rows(residual(**restored), residual(*frozen), layout, 0.0, 0.0);
}
/** @brief Check the assembled solver coordinates, including strong rows, scalar constraints and native surface modes. */
template <typename Evaluator, typename Layout>
void check_normalized_system(Evaluator& evaluator, const model::StellarState<Layout>& state,
const serif::discretization::backend::mfem::DofSelection& boundary) {
namespace normalization = serif::solver::normalization;
namespace dimensions = serif::dimensions;
const auto evaluation = evaluator.evaluate(state);
REQUIRE(evaluation);
const auto frozen = *evaluation;
REQUIRE(frozen->physical() == evaluator.cache().template get<model::keys::PhysicalSystem>());
const auto& layout = evaluator.layout();
const auto& coordinates = frozen->coordinates();
const auto& scales = frozen->reference_scales();
CHECK(scales.mass.value() == Catch::Approx(1.1));
CHECK(scales.radius.value() > 0.0);
CHECK(scales.radius.value() != 1.0);
REQUIRE(coordinates.state_size() == state.values().size());
REQUIRE(coordinates.residual_size() == frozen->residual().size());
CHECK(coordinates.state_factors().front() != 1.0);
Vector expected_residual(static_cast<int>(frozen->residual().size()));
coordinates.normalize_residual(frozen->physical()->residual(), {expected_residual.GetData(), frozen->residual().size()});
check_rows(residual(*frozen), expected_residual, layout, 0.0, 0.0);
const double radius = scales.radius.value();
const std::size_t density_row = layout.template offset<Kind::residual, Density>();
for (const int row : boundary.reduced_dofs()) {
CHECK(coordinates.residual_factors()[density_row + row] == Catch::Approx(1.0 / scales.density.value()).epsilon(2.0e-13));
}
const auto& density_metric = evaluator.cache().template get<normalization::ReferenceVolumeMetric<Density>>();
const auto& selected_rows = boundary.reduced_dofs();
int interior = 0;
while (std::find(selected_rows.begin(), selected_rows.end(), interior) != selected_rows.end()) {
++interior;
}
REQUIRE(interior < static_cast<int>(state.template get<Density>().size()));
// The density balance residual is a barotropic pressure potential, a specific energy.
CHECK(coordinates.residual_factors()[density_row + interior] == Catch::Approx(1.0 /
(scales.specific_energy.value() * std::sqrt(density_metric[interior] * radius * radius * radius))).epsilon(2.0e-13));
CHECK(coordinates.state_factors()[layout.template offset<Kind::value, Constant>()] == Catch::Approx(1.0 / scales.specific_energy.value()).epsilon(2.0e-13));
const auto infinity = serif::discretization::backend::mfem::select_boundary_dofs<
serif::discretization::domain::InfinitySurfaceBoundary>(
evaluator.binding().discretization->template binding<Potential>());
for (const int row : infinity.reduced_dofs()) {
CHECK(coordinates.residual_factors()[layout.template offset<Kind::residual, Potential>() + row] ==
Catch::Approx(1.0 / scales.specific_energy.value()).epsilon(2.0e-13));
}
CHECK(coordinates.residual_factors()[layout.template offset<Kind::residual, Constant>()] == Catch::Approx(1.0 / scales.mass.value()).epsilon(2.0e-13));
CHECK(coordinates.residual_factors()[layout.template offset<Kind::residual, Omega>()] == Catch::Approx(1.0 / scales.angular_momentum.value()).epsilon(2.0e-13));
const auto& surface_metric = evaluator.cache().template get<deformation::keys::SurfaceMetric>();
for (std::size_t mode = 0; mode < state.template get<Shape>().size(); ++mode) {
CHECK(coordinates.state_factors()[layout.template offset<Kind::value, Shape>() + mode] == Catch::Approx(std::sqrt(surface_metric[mode]) / (radius * radius)).epsilon(2.0e-13));
CHECK(coordinates.residual_factors()[layout.template offset<Kind::residual, ShapeRow>() + mode] == Catch::Approx(1.0 / scales.specific_energy.value()).epsilon(2.0e-13));
}
const Vector seed = tests::deterministic(static_cast<int>(state.values().size()), 0.43);
const Vector dual = tests::deterministic(static_cast<int>(coordinates.residual_size()), 1.17);
Vector transpose;
frozen->jacobian().MultTranspose(dual, transpose);
for (const int selected : {-1, 0, 1}) {
CAPTURE(selected);
Vector direction(seed);
if (selected >= 0) {
direction = 0.0;
const std::size_t offset = selected == 0 ? layout.template offset<Kind::value, Shape>() : layout.template offset<Kind::value, Constant>();
const std::size_t count = selected == 0 ? state.template get<Shape>().size() : 1;
std::copy_n(seed.GetData() + offset, count, direction.GetData() + offset);
}
Vector physical_direction(static_cast<int>(state.values().size())), action, physical_action, expected_action(static_cast<int>(coordinates.residual_size()));
coordinates.denormalize_state({direction.GetData(), coordinates.state_size()}, {physical_direction.GetData(), coordinates.state_size()});
frozen->jacobian().Mult(direction, action);
frozen->physical()->jacobian().action()->Mult(physical_direction, physical_action);
coordinates.normalize_residual({physical_action.GetData(), coordinates.residual_size()}, {expected_action.GetData(), coordinates.residual_size()});
check_rows(action, expected_action, layout, 2.0e-13, 2.0e-13);
CHECK((action * dual) == Catch::Approx(direction * transpose).epsilon(3.0e-12).margin(3.0e-12));
constexpr double step = 2.0e-6;
const auto plus = evaluator.evaluate(perturbed_state(state, step, physical_direction));
REQUIRE(plus);
CHECK(evaluator.cache().report().template status<normalization::keys::Scales>() == dependencies::PreparationStatus::reused);
CHECK(evaluator.cache().report().template status<normalization::keys::Normalization>() == dependencies::PreparationStatus::reused);
CHECK(evaluator.cache().report().template status<deformation::keys::SurfaceMetric>() == dependencies::PreparationStatus::reused);
Vector difference = residual(**plus);
const auto minus = evaluator.evaluate(perturbed_state(state, -step, physical_direction));
REQUIRE(minus);
difference -= residual(**minus);
difference /= 2.0 * step;
check_rows(action, difference, layout, 3.0e-6, 3.0e-8);
}
const auto restored = evaluator.evaluate(state);
REQUIRE(restored);
check_rows(residual(**restored), residual(*frozen), layout, 0.0, 0.0);
Vector repeated;
frozen->jacobian().MultTranspose(dual, repeated);
CHECK(tests::relative_error(repeated, transpose) == 0.0);
}
/** @brief Check the dimensional inverse, solver-coordinate adapter and independently measured linear residual. */
template <typename Prepared, typename Layout>
void check_stellar_linear_solve(const Prepared& prepared, const Layout& layout,
const serif::discretization::backend::mfem::DofSelection& boundary) {
const auto& system = *prepared.system();
const auto& coordinates = system.coordinates();
const int size = system.jacobian().Width();
REQUIRE(size == system.jacobian().Height());
REQUIRE(coordinates.state_factors().front() != 1.0);
REQUIRE(coordinates.residual_factors().front() != 1.0);
CHECK(prepared.contract() == serif::solver::preconditioner::ApplicationContract::fixed_linear);
const Vector normalized_direction = tests::deterministic(size, 0.37);
Vector physical_direction(size), physical_rhs, normalized_rhs(size);
coordinates.denormalize_state({normalized_direction.GetData(), coordinates.state_size()},
{physical_direction.GetData(), coordinates.state_size()});
system.physical()->jacobian().action()->Mult(physical_direction, physical_rhs);
coordinates.normalize_residual({physical_rhs.GetData(), coordinates.residual_size()},
{normalized_rhs.GetData(), coordinates.residual_size()});
Vector physical_correction(size), expected_correction(size), normalized_correction(size), preconditioned_action;
prepared.physical_preconditioner().Mult(physical_rhs, physical_correction);
coordinates.normalize_state({physical_correction.GetData(), coordinates.state_size()},
{expected_correction.GetData(), coordinates.state_size()});
prepared.preconditioner().Mult(normalized_rhs, normalized_correction);
CHECK(tests::relative_error(normalized_correction, expected_correction) < 3.0e-13);
system.physical()->jacobian().action()->Mult(physical_correction, preconditioned_action);
for (const int row : boundary.reduced_dofs()) {
const int index = static_cast<int>(layout.template offset<Kind::residual, Density>()) + row;
CHECK(preconditioned_action[index] == Catch::Approx(physical_rhs[index]).epsilon(2.0e-11).margin(2.0e-12));
}
// The joint surface/scalar Schur solve must enforce every border equation and mutual coupling.
for (const std::size_t index : {layout.template offset<Kind::residual, Constant>(), layout.template offset<Kind::residual, Omega>()}) {
CHECK(preconditioned_action[static_cast<int>(index)] == Catch::Approx(physical_rhs[static_cast<int>(index)]).epsilon(2.0e-11).margin(2.0e-12));
}
for (std::size_t mode = 0; mode < layout.template size<Kind::residual, ShapeRow>(); ++mode) {
const int index = static_cast<int>(layout.template offset<Kind::residual, ShapeRow>() + mode);
CHECK(preconditioned_action[index] == Catch::Approx(physical_rhs[index]).epsilon(2.0e-11).margin(2.0e-12));
}
mfem::FGMRESSolver krylov;
krylov.SetRelTol(1.0e-10);
krylov.SetAbsTol(1.0e-13);
krylov.SetMaxIter(400);
krylov.SetKDim(100);
krylov.SetPrintLevel(0);
krylov.SetPreconditioner(prepared.preconditioner());
krylov.SetOperator(system.jacobian());
for (const bool newton_right_hand_side : {false, true}) {
CAPTURE(newton_right_hand_side);
Vector solve_rhs(physical_rhs);
if (newton_right_hand_side) {
solve_rhs = residual(*system.physical());
solve_rhs *= -1.0;
}
coordinates.normalize_residual({solve_rhs.GetData(), coordinates.residual_size()},
{normalized_rhs.GetData(), coordinates.residual_size()});
Vector solution(size);
solution = 0.0;
krylov.Mult(normalized_rhs, solution);
CAPTURE(krylov.GetNumIterations(), krylov.GetFinalNorm());
CHECK(krylov.GetConverged());
coordinates.denormalize_state({solution.GetData(), coordinates.state_size()},
{physical_correction.GetData(), coordinates.state_size()});
system.physical()->jacobian().action()->Mult(physical_correction, preconditioned_action);
Vector measured_residual(preconditioned_action);
measured_residual -= solve_rhs;
Vector normalized_residual(size);
coordinates.normalize_residual({measured_residual.GetData(), coordinates.residual_size()},
{normalized_residual.GetData(), coordinates.residual_size()});
CHECK(normalized_residual.Norml2() / normalized_rhs.Norml2() < 2.0e-10);
CHECK(measured_residual.Norml2() / solve_rhs.Norml2() < 2.0e-8);
check_rows(preconditioned_action, solve_rhs, layout, 2.0e-7, 2.0e-9);
}
}
/** @brief Prepare the production stellar recipe selectively and retain its complete frozen numerical state. */
void check_moving_preconditioner() {
namespace normalization = serif::solver::normalization;
namespace preconditioner = serif::solver::preconditioner;
using InverseKey = preconditioner::keys::Preconditioner;
using PreparedKey = model::preconditioning::PreparedSystem;
using Status = dependencies::PreparationStatus;
#ifdef MFEM_USE_MPI
// The AMG backend borrows the application's MPI session; the test is its application owner.
if (!mfem::Mpi::IsInitialized()) {
mfem::Mpi::Init();
}
#endif
auto fixture = std::make_shared<Fixture>(mfem::Ordering::byNODES);
std::weak_ptr<Fixture> lifetime = fixture;
Vector right_hand_side, frozen_correction, frozen_action;
auto retained = [&]() {
const auto physics = physical_model();
const auto discretization = discretize(fixture);
using Description = decltype(model::resolve_equilibrium_equations(physics));
using Plan = model::EquilibriumPlan<Polytrope, Description>;
const std::array shape{0.004, -0.002, 0.001, 0.003, -0.001, 0.002, -0.003, 0.001, 0.002};
const auto layout = backend::equilibrium_layout<Plan>(discretization, shape);
const auto state = initial_state(layout, fixture->fields, shape);
const auto recipe = preconditioner::make_primal_preconditioner(layout);
static_assert(dependencies::ContainsKey<Density, typename decltype(recipe)::Values>);
static_assert(dependencies::ContainsKey<Potential, typename decltype(recipe)::Values>);
static_assert(dependencies::ContainsKey<Shape, typename decltype(recipe)::Values>);
static_assert(!dependencies::ContainsKey<::serif::tests::equations::Enthalpy, typename Plan::Values>);
const auto configured = ::serif::model::make_discretization(::serif::model::DiscretizationOptions{
.model = physics, .finite_elements = discretization,
.normalization = normalization::make_normalization(normalization::NormalizationOptions{
.scheme = normalization::LaneEmdenApproximation{.n = 3.0, .central_density = serif::dimensions::DensityValue{0.9}}, .coordinates = normalization::Dimensionless{},
.gravitational_constant = serif::dimensions::QuantityValue<serif::dimensions::GravitationalConstant>{2.3 / (4.0 * std::numbers::pi)}
}),
.preconditioner = recipe
});
serif::discretization::quadrature::RuleSet rules;
rules.set_fallback_control({.fixed_order = 8});
const execution::VolumeOptions volume_options{.quadrature_policy = serif::discretization::quadrature::Policy{rules}};
auto evaluator = backend::bind_stellar_model(configured, state, volume_options);
const auto physical = evaluator.evaluate(state);
REQUIRE(physical);
CHECK(evaluator.cache().report().template status<InverseKey>() == Status::not_required);
CHECK(evaluator.cache().report().template status<PreparedKey>() == Status::not_required);
const auto prepared = evaluator.prepare_linear_system(state);
if (!prepared) {
UNSCOPED_INFO("Failed computation index: " << prepared.error().computation_index);
if (std::holds_alternative<preconditioner::Failure>(prepared.error().error)) {
UNSCOPED_INFO(std::get<preconditioner::Failure>(prepared.error().error).message);
}
}
REQUIRE(prepared);
const auto first = *prepared;
CHECK(first->system() == *physical);
CHECK(evaluator.cache().report().template status<model::keys::PhysicalSystem>() == Status::reused);
CHECK(evaluator.cache().report().template status<InverseKey>() == Status::computed);
const auto repeated = evaluator.prepare_linear_system(state);
REQUIRE(repeated);
CHECK(*repeated == first);
CHECK(evaluator.cache().report().computed_count() == 0);
CHECK(evaluator.cache().report().template status<InverseKey>() == Status::reused);
const auto boundary = serif::discretization::backend::mfem::select_boundary_dofs<
serif::discretization::domain::StellarSurfaceBoundary>(fixture->fields.density_binding);
check_stellar_linear_solve(*first, layout, boundary);
right_hand_side = tests::deterministic(static_cast<int>(state.values().size()), 0.82);
frozen_correction.SetSize(right_hand_side.Size());
first->preconditioner().Mult(right_hand_side, frozen_correction);
first->system()->jacobian().Mult(right_hand_side, frozen_action);
const Vector first_residual = residual(*first->system());
auto candidate = state;
candidate.template get<Density>()[0] += 0.01;
candidate.template get<Shape>()[0] += 0.0002;
const auto trial = evaluator.evaluate(candidate);
REQUIRE(trial);
CHECK(*trial != first->system());
CHECK(evaluator.cache().report().template status<InverseKey>() == Status::not_required);
CHECK(evaluator.cache().report().template status<PreparedKey>() == Status::not_required);
CHECK(tests::relative_error(residual(*first->system()), first_residual) == 0.0);
const auto updated = evaluator.prepare_linear_system(candidate);
REQUIRE(updated);
CHECK(*updated != first);
CHECK((*updated)->system() == *trial);
CHECK(evaluator.cache().report().template status<InverseKey>() == Status::computed);
const auto rebuilt = evaluator.prepare_linear_system(candidate, dependencies::make_dependency_context(), dependencies::PreparationMode::rebuild);
REQUIRE(rebuilt);
CHECK(*rebuilt != *updated);
CHECK(evaluator.cache().report().template status<model::keys::PhysicalSystem>() == Status::computed);
CHECK(evaluator.cache().report().template status<InverseKey>() == Status::computed);
Vector repeated_correction(right_hand_side.Size()), repeated_action;
first->preconditioner().Mult(right_hand_side, repeated_correction);
first->system()->jacobian().Mult(right_hand_side, repeated_action);
CHECK(tests::relative_error(repeated_correction, frozen_correction) == 0.0);
CHECK(tests::relative_error(repeated_action, frozen_action) == 0.0);
// At n=1.5 the exact density Jacobian is undefined at zero density; reject the EOS trial.
auto singular = state;
std::ranges::fill(singular.template get<Density>(), 0.0);
singular.template get<Omega>()[0] = 0.0;
const auto preparations = evaluator.cache().preparation_count();
const auto rejected = evaluator.prepare_linear_system(singular);
REQUIRE_FALSE(rejected);
REQUIRE(std::holds_alternative<execution::PreparationRejection>(rejected.error().error));
CHECK(std::get<execution::PreparationRejection>(rejected.error().error).reason == execution::PreparationRejectionReason::EQUATION);
CHECK_FALSE(evaluator.cache().ready());
CHECK_FALSE(evaluator.cache().template contains<PreparedKey>());
CHECK(evaluator.cache().report().computed_count() == 0);
CHECK(evaluator.cache().report().reused_count() == 0);
CHECK(evaluator.cache().preparation_count() == preparations);
first->preconditioner().Mult(right_hand_side, repeated_correction);
first->system()->jacobian().Mult(right_hand_side, repeated_action);
CHECK(tests::relative_error(repeated_correction, frozen_correction) == 0.0);
CHECK(tests::relative_error(repeated_action, frozen_action) == 0.0);
CHECK(tests::relative_error(residual(*first->system()), first_residual) == 0.0);
const auto recovered = evaluator.prepare_linear_system(candidate);
REQUIRE(recovered);
CHECK(evaluator.cache().ready());
return first;
}();
fixture.reset();
CHECK_FALSE(lifetime.expired());
Vector repeated_correction(right_hand_side.Size()), repeated_action;
retained->preconditioner().Mult(right_hand_side, repeated_correction);
retained->system()->jacobian().Mult(right_hand_side, repeated_action);
CHECK(tests::relative_error(repeated_correction, frozen_correction) == 0.0);
CHECK(tests::relative_error(repeated_action, frozen_action) == 0.0);
retained.reset();
CHECK(lifetime.expired());
}
/** @brief Evaluate the full moving star in both native displacement orderings and retain its frozen actions. */
template <bool Normalize = false>
void check_moving_equilibrium(const mfem::Ordering::Type ordering) {
auto fixture = std::make_shared<Fixture>(ordering);
std::weak_ptr<Fixture> lifetime = fixture;
Vector direction, dual, action, transpose, normalized_action, normalized_transpose;
std::shared_ptr<const backend::NormalizedSystem> normalized_retained;
const auto exercise = [&]() {
auto& fields = fixture->fields;
const auto physics = physical_model();
const auto discretization = discretize(fixture);
using Description = decltype(model::resolve_equilibrium_equations(physics));
using Plan = model::EquilibriumPlan<Polytrope, Description>;
const std::array shape{0.004, -0.002, 0.001, 0.003, -0.001, 0.002, -0.003, 0.001, 0.002};
const auto layout = backend::equilibrium_layout<Plan>(discretization, shape);
REQUIRE(layout.state_sizes.size() == 5);
REQUIRE(layout.residual_sizes.size() == 5);
REQUIRE(layout.template total_size<Kind::value>() == layout.template total_size<Kind::residual>());
REQUIRE(shape.size() < static_cast<std::size_t>(fields.displacement_binding.size()));
const auto state = initial_state(layout, fields, shape);
const auto boundary = serif::discretization::backend::mfem::select_boundary_dofs<
serif::discretization::domain::StellarSurfaceBoundary>(fields.density_binding);
serif::discretization::quadrature::RuleSet rules;
rules.set_fallback_control({.fixed_order = 8});
const execution::VolumeOptions volume_options{.quadrature_policy = serif::discretization::quadrature::Policy{rules}};
auto evaluator = [&]() {
if constexpr (Normalize) {
namespace normalization = serif::solver::normalization;
using Reference = normalization::LaneEmdenApproximation<normalization::FromModel, serif::dimensions::DensityValue>;
const auto configured = ::serif::model::make_discretization(::serif::model::DiscretizationOptions{
.model = physics, .finite_elements = discretization,
.normalization = normalization::make_normalization(normalization::NormalizationOptions<Reference>{
.scheme = Reference{.n = 3.0, .central_density = serif::dimensions::DensityValue{0.9}},
.coordinates = normalization::Dimensionless{},
.gravitational_constant = serif::dimensions::QuantityValue<serif::dimensions::GravitationalConstant>{2.3 / (4.0 * std::numbers::pi)}
})
});
return backend::bind_stellar_model(configured, state, volume_options);
} else {
return backend::bind_stellar_model(physics, discretization, state, volume_options);
}
}();
const auto initial = evaluator.evaluate(state);
REQUIRE(initial);
const auto first = *initial;
using MassRow = model::computations::ScalarResidualRow<Constant>;
using AngularMomentumRow = model::computations::ScalarResidualRow<Omega>;
const auto mass_row = evaluator.cache().template share<MassRow>();
const auto angular_momentum_row = evaluator.cache().template share<AngularMomentumRow>();
CHECK(evaluator.cache().report().template status<MassRow>() == dependencies::PreparationStatus::computed);
CHECK(evaluator.cache().report().template status<AngularMomentumRow>() == dependencies::PreparationStatus::computed);
const auto repeated = evaluator.evaluate(state);
REQUIRE(repeated);
CHECK(*repeated == first);
CHECK(evaluator.cache().report().computed_count() == 0);
CHECK(evaluator.cache().template share<MassRow>() == mass_row);
CHECK(evaluator.cache().template share<AngularMomentumRow>() == angular_momentum_row);
// A successful trial is merely another result; the caller retains the previous candidate.
const auto original = state;
auto copied = state;
CHECK(copied.values().data() != state.values().data());
copied.template get<Density>()[0] += 0.01;
copied.template get<Shape>()[0] += 0.0002;
auto moved = std::move(copied);
CHECK(std::ranges::equal(state.values(), original.values()));
const Vector first_residual = residual(*first);
const auto discarded = evaluator.evaluate(moved);
REQUIRE(discarded);
CHECK(evaluator.cache().template share<MassRow>() != mass_row);
CHECK(evaluator.cache().template share<AngularMomentumRow>() != angular_momentum_row);
CHECK(evaluator.cache().report().template status<MassRow>() == dependencies::PreparationStatus::computed);
CHECK(evaluator.cache().report().template status<AngularMomentumRow>() == dependencies::PreparationStatus::computed);
CHECK(*discarded != first);
CHECK(tests::relative_error(residual(**discarded), first_residual) > 1.0e-10);
CHECK(tests::relative_error(residual(*first), first_residual) == 0.0);
CHECK(std::ranges::equal(state.values(), original.values()));
const auto restored = evaluator.evaluate(state);
REQUIRE(restored);
if constexpr (Normalize) {
check_normalized_system(evaluator, state, boundary);
} else {
check_composition(evaluator, state, **restored, boundary);
check_scalar_row<Constant>(evaluator, **restored);
check_scalar_row<Omega>(evaluator, **restored);
check_derivatives(evaluator, state);
}
const auto evaluated = evaluator.evaluate(state);
REQUIRE(evaluated);
const auto retained = *evaluated;
const auto physical = [&]() {
if constexpr (Normalize) {
return retained->physical();
} else {
return retained;
}
}();
const auto preparations = evaluator.cache().preparation_count();
const Vector retained_residual = residual(*retained);
direction = tests::deterministic(static_cast<int>(state.values().size()), 0.61);
dual = tests::deterministic(static_cast<int>(state.values().size()), 1.31);
physical->jacobian().action()->Mult(direction, action);
physical->jacobian().action()->MultTranspose(dual, transpose);
if constexpr (Normalize) {
normalized_retained = retained;
normalized_retained->jacobian().Mult(direction, normalized_action);
normalized_retained->jacobian().MultTranspose(dual, normalized_transpose);
}
auto invalid = state;
invalid.template get<Shape>()[0] = std::numeric_limits<double>::quiet_NaN();
const auto rejected = evaluator.evaluate(invalid);
REQUIRE_FALSE(rejected);
CHECK(std::holds_alternative<deformation::DeformationFailure>(rejected.error().error));
CHECK(tests::relative_error(residual(*retained), retained_residual) == 0.0);
if constexpr (Normalize) {
CHECK_FALSE(evaluator.cache().template contains<serif::model::normalization::PreparedSystem>());
}
CHECK_FALSE(evaluator.cache().ready());
CHECK_FALSE(evaluator.cache().template contains<model::keys::PhysicalSystem>());
CHECK(evaluator.cache().report().computed_count() == 0);
CHECK(evaluator.cache().report().reused_count() == 0);
CHECK(evaluator.cache().preparation_count() == preparations);
const auto recovered = evaluator.evaluate(state);
REQUIRE(recovered);
CHECK(*recovered == retained);
CHECK(evaluator.cache().report().computed_count() == 0);
return physical;
};
auto retained = exercise();
fixture.reset();
CHECK_FALSE(lifetime.expired());
Vector repeated_action, repeated_transpose;
retained->jacobian().action()->Mult(direction, repeated_action);
retained->jacobian().action()->MultTranspose(dual, repeated_transpose);
CHECK(tests::relative_error(repeated_action, action) == 0.0);
CHECK(tests::relative_error(repeated_transpose, transpose) == 0.0);
retained.reset();
if constexpr (Normalize) {
CHECK_FALSE(lifetime.expired());
normalized_retained->jacobian().Mult(direction, repeated_action);
normalized_retained->jacobian().MultTranspose(dual, repeated_transpose);
CHECK(tests::relative_error(repeated_action, normalized_action) == 0.0);
CHECK(tests::relative_error(repeated_transpose, normalized_transpose) == 0.0);
normalized_retained.reset();
}
CHECK(lifetime.expired());
}
}
TEST_CASE("Complete moving stellar assembly preserves every coupled equation and boundary row", "[model][moving_equilibrium][integration]") {
SECTION("Component-block displacement ordering") {
check_moving_equilibrium(mfem::Ordering::byNODES);
}
SECTION("Interleaved displacement ordering") {
check_moving_equilibrium(mfem::Ordering::byVDIM);
}
}
TEST_CASE("Complete moving stellar normalization preserves solver coordinates and frozen ownership", "[model][moving_normalization][integration]") {
check_moving_equilibrium<true>(mfem::Ordering::byNODES);
}
TEST_CASE("Complete moving stellar preconditioning prepares a frozen solver system and solves its physical Jacobian", "[model][moving_preconditioner][integration]") {
#ifdef MFEM_USE_MPI
check_moving_preconditioner();
#else
SKIP("The default stellar recipe uses the one-process BoomerAMG backend, which requires an MPI-enabled MFEM build.");
#endif
}
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