MeanField/tests/operators/gravity_field.cpp

#include "profile.h"
#include <array>
#include <catch2/catch_test_macros.hpp>
#include <catch2/matchers/catch_matchers_floating_point.hpp>
#include <cmath>
#include <mfem.hpp>

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<form>(blocks::density_field.mass_term);
    constexpr auto displacement_block      = blocks::get_value_block<form>(blocks::displacement_field.geometry_term);
    constexpr auto gravity_gradient_block  = blocks::get_value_block<form>(blocks::gravity_field.gradient_term);
    constexpr auto gravity_potential_block = blocks::get_value_block<form>(blocks::gravity_field.poisson_term);
    constexpr auto gravity_gradient_residual_block =
        blocks::get_residual_block<form>(blocks::gravity_field.gradient_term);
    constexpr auto gravity_poisson_residual_block =
        blocks::get_residual_block<form>(blocks::gravity_field.poisson_term);

    blocks::form_layout<form> make_gravity_layout(const fem::FEM &f) {
        const std::array<int, form::value_block_count> value_sizes{
            f.densityFes->GetTrueVSize(), f.displacementFes->GetTrueVSize(), f.gravityFluxFes->GetTrueVSize(),
            f.gravityPotentialFes->GetTrueVSize()
        };

        const std::array<int, form::residual_block_count> residual_sizes{
            f.gravityFluxFes->GetTrueVSize(), f.gravityPotentialFes->GetTrueVSize()
        };

        return blocks::form_layout<form>(value_sizes, residual_sizes);
    }

    template <typename Block>
    void set_block(
        mfem::Vector &vector,
        const mfem::Array<int> &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 <typename Block>
    mfem::Vector get_block(
        const mfem::Vector &vector,
        const mfem::Array<int> &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<double>(i + 1) + phase) +
                        0.2 * std::cos(0.19 * static_cast<double>(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<int> 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<double>::infinity()};
        double maximum_stellar_determinant{0.0};
        double minimum_vacuum_determinant{std::numeric_limits<double>::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<double>::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<double>(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<int> gravity_dofs;
        mfem::Array<int> displacement_dofs;
        mfem::Array<int> 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_form>;
    gravity_layout make_gravity_jacobian_layout(const fem::FEM &f) {
        const std::array<int, gravity_form::value_block_count> value_sizes{
            f.densityFes->GetTrueVSize(), f.displacementFes->GetTrueVSize(), f.gravityFluxFes->GetTrueVSize(),
            f.gravityPotentialFes->GetTrueVSize()
        };

        const std::array<int, gravity_form::residual_block_count> residual_sizes{
            f.gravityFluxFes->GetTrueVSize(), f.gravityPotentialFes->GetTrueVSize()
        };

        return gravity_layout(value_sizes, residual_sizes);
    }

    template <int index>
    void set_value_block(
        mfem::Vector &vector,
        const gravity_layout &layout,
        const blocks::value_block<index> 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 <int index>
    mfem::Vector get_value_block(
        const mfem::Vector &vector,
        const gravity_layout &layout,
        const blocks::value_block<index> 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 <int index>
    mfem::Vector get_residual_block(
        const mfem::Vector &vector,
        const gravity_layout &layout,
        const blocks::residual_block<index> 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 <int index>
    void fill_value_block(
        mfem::Vector &vector,
        const gravity_layout &layout,
        const blocks::value_block<index> block,
        const double scale,
        const double phase
    ) {
        for (int i = 0; i < layout.size(block); ++i) {
            const double index_value = static_cast<double>(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<int> 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<double>(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 <int index>
    mfem::Vector make_read_only_value_view(
        const mfem::Vector &vector,
        const mfem::Array<int> &offsets,
        const blocks::value_block<index>
    ) {
        const int offset = offsets[index];
        const int size   = offsets[index + 1] - offset;
        return mfem::Vector(const_cast<mfem::real_t *>(vector.GetData()) + offset, size);
    }

    void check_linearization_context_matches_state(
        const operators::context::gravity_field::GravityFieldLinearizationContext &context,
        const mfem::Vector &state,
        const mfem::Array<int> &state_offsets,
        MPI_Comm communicator
    ) {
        using form                   = blocks::gravity_field_form;

        constexpr auto density_block = utils::blocks::get_value_block<form>(blocks::density_field.mass_term);
        constexpr auto displacement_block =
            utils::blocks::get_value_block<form>(blocks::displacement_field.geometry_term);
        constexpr auto gravity_gradient_block =
            utils::blocks::get_value_block<form>(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<int> 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<form> 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<form> 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<form> 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<form> 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<form> 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<form> 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<int> 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::gravity_field_form>(
        blocks::displacement_field.geometry_term
    );

    constexpr auto gravity_gradient_block =
        mean_field::utils::blocks::get_value_block<blocks::gravity_field_form>(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<blocks::gravity_field_form> 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<double>::epsilon());

            const double vacuum_action_fraction =
                vacuum_action_norm / std::max(reference_norm, std::numeric_limits<double>::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<double>::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<DirectionCase> 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<double>::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<mfem::Operator *>(&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<mfem::Operator *>(&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<double, 3> difference_steps{8.0e-2, 4.0e-2, 2.0e-2};
    std::array<double, difference_steps.size()> 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<double, 3> difference_steps{8.0e-2, 4.0e-2, 2.0e-2};
    std::array<double, difference_steps.size()> 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<mfem::Operator *>(&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<mfem::Operator *>(&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<double, 3> difference_steps{8.0e-2, 4.0e-2, 2.0e-2};

    std::array<double, difference_steps.size()> errors{};
    std::array<double, difference_steps.size()> 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<mfem::Operator *>(&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<form>(blocks::displacement_field.geometry_term);

    constexpr auto gravity_gradient_block =
        mean_field::utils::blocks::get_value_block<form>(blocks::gravity_field.gradient_term);

    constexpr auto gravity_gradient_residual_block =
        mean_field::utils::blocks::get_residual_block<form>(blocks::gravity_field.gradient_term);

    const std::array<int, form::value_block_count> value_sizes{
        f.densityFes->GetTrueVSize(), f.displacementFes->GetTrueVSize(), f.gravityFluxFes->GetTrueVSize(),
        f.gravityPotentialFes->GetTrueVSize()
    };

    const std::array<int, form::residual_block_count> residual_sizes{
        f.gravityFluxFes->GetTrueVSize(), f.gravityPotentialFes->GetTrueVSize()
    };

    const blocks::form_layout<form> 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<double>::epsilon());

            const double unexplained_fraction_of_gap =
                unexplained_gap_norm / std::max(total_gap_norm, std::numeric_limits<double>::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<double>::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));
        }
    }
}