MeanField/tests/quadrature/policy.cpp

#include <catch2/catch_test_macros.hpp>
#include <catch2/matchers/catch_matchers_floating_point.hpp>

#include <array>
#include <cmath>
#include <concepts>
#include <memory>
#include <stdexcept>
#include <string_view>
#include <type_traits>
#include <utility>

#include <mfem.hpp>

import mean_field;
import test_helpers;

using namespace mean_field;

namespace {
    template <typename T>
    concept HasRuntimeSpaceOrders = requires(T value) { value.space_orders; };

    static_assert(mean_field::field::FieldTag<field::Gravity>);
    static_assert(mean_field::field::FieldTag<field::Displacement>);
    static_assert(mean_field::field::FieldTag<field::Density>);
    static_assert(mean_field::field::FieldTag<field::Enthalpy>);
    static_assert(mean_field::field::FieldTag<field::BarotropicConstant>);
    static_assert(field::Gravity::constraintsAreValid);
    static_assert(std::same_as<
                  field::RelationTargetT<field::Gravity::Flux>,
                  field::Gravity::Potential>);
    static_assert(!HasRuntimeSpaceOrders<utils::Args>);

    std::string_view get_term_name(const quadrature::Term term) {
        switch (term) {
        case quadrature::Term::gravity_hdiv_mass:
            return "gravity_hdiv_mass";
        case quadrature::Term::gravity_divergence:
            return "gravity_divergence";
        case quadrature::Term::gravity_source:
            return "gravity_source";
        case quadrature::Term::gravity_force:
            return "gravity_force";
        case quadrature::Term::gravity_boundary:
            return "gravity_boundary";
        case quadrature::Term::centrifugal:
            return "centrifugal";
        case quadrature::Term::density_projection:
            return "density_projection";
        case quadrature::Term::eos_closure:
            return "eos_closure";
        case quadrature::Term::hydrostatic_equilibrium:
            return "hydrostatic_equilibrium";
        case quadrature::Term::isobaric_surface:
            return "isobaric_surface";
        case quadrature::Term::mesh_extension:
            return "mesh_extension";
        case quadrature::Term::mass_conservation:
            return "mass_conservation";
        case quadrature::Term::mass_normalization:
            return "mass_normalization";
        case quadrature::Term::center_of_mass:
            return "center_of_mass";
        case quadrature::Term::quadrupole:
            return "quadrupole";
        case quadrature::Term::gravitational_energy:
            return "gravitational_energy";
        case quadrature::Term::pressure_integral:
            return "pressure_integral";
        case quadrature::Term::virial:
            return "virial";
        case quadrature::Term::error_norm:
            return "error_norm";
        case quadrature::Term::pressure_force:
            return "pressure_force";
        }

        return "unknown";
    }

    quadrature::Query make_query(
        const quadrature::Term term,
        const int base_order
    ) {
        return {.term = term, .base_order = base_order};
    }

    template <typename FieldT, typename QuantityT>
    concept CanMakeFec = requires { FieldT::template make_fec<QuantityT>(3); };
} // namespace

TEST_CASE(
    "Quadrature Policy Computes Base Orders",
    tags::unit &tags::quadrature
) {
    const quadrature::Policy policy(quadrature::make_rule_set(quadrature::Mode::production));

    quadrature::Query generic_query = {
        .term                  = quadrature::Term::gravitational_energy,
        .trial_order           = 3,
        .test_order            = 4,
        .coefficient_order     = 2,
        .geometry_weight_order = 5
    };

    const quadrature::Resolution generic_resolution = policy.resolve(generic_query);
    CHECK(generic_resolution.base_order == 14);
    CHECK(generic_resolution.boost == 0);
    CHECK(generic_resolution.order == 14);
    CHECK_FALSE(generic_resolution.used_fixed_order);

    quadrature::Query divergence_query = {
        .term                  = quadrature::Term::gravity_divergence,
        .trial_order           = 3,
        .test_order            = 2,
        .coefficient_order     = 1,
        .geometry_weight_order = 4
    };

    CHECK(policy.resolve(divergence_query).base_order == 9);

    divergence_query.trial_order = 0;
    CHECK(policy.resolve(divergence_query).base_order == 7);

    quadrature::Query explicit_query = {
        .term                  = quadrature::Term::gravity_hdiv_mass,
        .trial_order           = 20,
        .test_order            = 20,
        .coefficient_order     = 20,
        .geometry_weight_order = 20,
        .base_order            = 11
    };

    CHECK(policy.resolve(explicit_query).base_order == 11);
    CHECK(policy.resolve(explicit_query).order == 11);
}

TEST_CASE(
    "Quadrature Policy Composes Global and Term Boosts",
    tags::unit &tags::quadrature
) {
    quadrature::RuleSet rule_set     = quadrature::make_rule_set(quadrature::Mode::production, 3);
    rule_set.gravity_hdiv_mass.boost = 5;
    rule_set.error_norm.boost        = 2;
    const quadrature::Policy policy(rule_set);

    const quadrature::Resolution mass_resolution = policy.resolve(make_query(quadrature::Term::gravity_hdiv_mass, 7));
    CHECK(mass_resolution.base_order == 7);
    CHECK(mass_resolution.boost == 8);
    CHECK(mass_resolution.order == 15);
    CHECK_FALSE(mass_resolution.used_fixed_order);

    const quadrature::Resolution error_resolution = policy.resolve(make_query(quadrature::Term::error_norm, 7));
    CHECK(error_resolution.boost == 5);
    CHECK(error_resolution.order == 12);

    const quadrature::Resolution source_resolution = policy.resolve(make_query(quadrature::Term::gravity_source, 7));
    CHECK(source_resolution.boost == 3);
    CHECK(source_resolution.order == 10);
}

TEST_CASE(
    "Quadrature Fixed Orders Have Defined Precedence",
    tags::unit &tags::quadrature
) {
    quadrature::RuleSet rule_set           = quadrature::make_rule_set(quadrature::Mode::production, 4);
    rule_set.fallback.fixed_order          = 17;
    rule_set.gravity_hdiv_mass.fixed_order = 23;
    rule_set.gravity_hdiv_mass.boost       = 100;
    rule_set.gravity_source.boost          = 100;
    const quadrature::Policy policy(rule_set);

    const quadrature::Resolution term_resolution = policy.resolve(make_query(quadrature::Term::gravity_hdiv_mass, 8));
    CHECK(term_resolution.base_order == 8);
    CHECK(term_resolution.boost == 0);
    CHECK(term_resolution.order == 23);
    CHECK(term_resolution.used_fixed_order);

    const quadrature::Resolution fallback_resolution = policy.resolve(make_query(quadrature::Term::gravity_source, 8));
    CHECK(fallback_resolution.base_order == 8);
    CHECK(fallback_resolution.boost == 0);
    CHECK(fallback_resolution.order == 17);
    CHECK(fallback_resolution.used_fixed_order);
}

TEST_CASE(
    "Quadrature Modes Apply Their Expected Baseline Boosts",
    tags::unit &tags::quadrature
) {
    constexpr int base_order   = 6;
    constexpr int global_boost = 3;

    for (const quadrature::Mode mode :
         {quadrature::Mode::fast, quadrature::Mode::production, quadrature::Mode::convergence}) {
        const quadrature::Policy policy(quadrature::make_rule_set(mode, global_boost));
        const quadrature::Resolution resolution = policy.resolve(make_query(quadrature::Term::error_norm, base_order));
        CHECK(resolution.boost == global_boost);
        CHECK(resolution.order == base_order + global_boost);
    }

    const quadrature::Policy reference_policy(quadrature::make_rule_set(quadrature::Mode::reference, global_boost));
    const quadrature::Resolution reference_resolution =
        reference_policy.resolve(make_query(quadrature::Term::error_norm, base_order));
    CHECK(reference_resolution.boost == global_boost + 8);
    CHECK(reference_resolution.order == base_order + global_boost + 8);
}

TEST_CASE(
    "Quadrature Policy Routes Every Term to Its Control",
    tags::unit &tags::quadrature
) {
    quadrature::RuleSet rule_set;
    rule_set.gravity_hdiv_mass.boost       = 1;
    rule_set.gravity_divergence.boost      = 2;
    rule_set.gravity_source.boost          = 3;
    rule_set.gravity_force.boost           = 19;
    rule_set.gravity_boundary.boost        = 4;
    rule_set.centrifugal.boost             = 18;
    rule_set.density_projection.boost      = 5;
    rule_set.eos_closure.boost             = 6;
    rule_set.hydrostatic_equilibrium.boost = 7;
    rule_set.isobaric_surface.boost        = 8;
    rule_set.mesh_extension.boost          = 9;
    rule_set.mass_conservation.boost       = 10;
    rule_set.mass_normalization.boost      = 11;
    rule_set.center_of_mass.boost          = 12;
    rule_set.quadrupole.boost              = 13;
    rule_set.gravitational_energy.boost    = 14;
    rule_set.pressure_integral.boost       = 15;
    rule_set.virial.boost                  = 16;
    rule_set.error_norm.boost              = 17;
    const quadrature::Policy policy(rule_set);

    const std::array<std::pair<quadrature::Term, int>, 19> cases = {
        {{quadrature::Term::gravity_hdiv_mass, 1},
         {quadrature::Term::gravity_divergence, 2},
         {quadrature::Term::gravity_source, 3},
         {quadrature::Term::gravity_force, 19},
         {quadrature::Term::gravity_boundary, 4},
         {quadrature::Term::centrifugal, 18},
         {quadrature::Term::density_projection, 5},
         {quadrature::Term::eos_closure, 6},
         {quadrature::Term::hydrostatic_equilibrium, 7},
         {quadrature::Term::isobaric_surface, 8},
         {quadrature::Term::mesh_extension, 9},
         {quadrature::Term::mass_conservation, 10},
         {quadrature::Term::mass_normalization, 11},
         {quadrature::Term::center_of_mass, 12},
         {quadrature::Term::quadrupole, 13},
         {quadrature::Term::gravitational_energy, 14},
         {quadrature::Term::pressure_integral, 15},
         {quadrature::Term::virial, 16},
         {quadrature::Term::error_norm, 17}}
    };

    for (const auto &[term, expected_boost] : cases) {
        DYNAMIC_SECTION(get_term_name(term)) {
            const quadrature::Resolution resolution = policy.resolve(make_query(term, 20));
            CHECK(resolution.boost == expected_boost);
            CHECK(resolution.order == 20 + expected_boost);
        }
    }
}

TEST_CASE(
    "Quadrature Policy Rejects Invalid Orders",
    tags::unit &tags::quadrature
) {
    const quadrature::Policy policy(quadrature::make_rule_set(quadrature::Mode::production));

    quadrature::Query negative_component_query = {.term = quadrature::Term::error_norm, .trial_order = -1};
    REQUIRE_THROWS_AS(policy.resolve(negative_component_query), std::invalid_argument);

    quadrature::Query negative_base_query = {.term = quadrature::Term::error_norm, .base_order = -1};
    REQUIRE_THROWS_AS(policy.resolve(negative_base_query), std::invalid_argument);

    quadrature::RuleSet negative_fixed_rule_set;
    negative_fixed_rule_set.error_norm.fixed_order = -1;
    const quadrature::Policy negative_fixed_policy(negative_fixed_rule_set);
    REQUIRE_THROWS_AS(
        negative_fixed_policy.resolve(make_query(quadrature::Term::error_norm, 3)), std::invalid_argument
    );

    quadrature::RuleSet negative_resolved_rule_set;
    negative_resolved_rule_set.fallback.boost = -4;
    const quadrature::Policy negative_resolved_policy(negative_resolved_rule_set);
    REQUIRE_THROWS_AS(
        negative_resolved_policy.resolve(make_query(quadrature::Term::error_norm, 3)), std::invalid_argument
    );
}

TEST_CASE(
    "MFEM Rule Factory Returns the Resolved Rule",
    tags::unit &tags::quadrature
) {
    quadrature::RuleSet rule_set = quadrature::make_rule_set(quadrature::Mode::production, 2);
    rule_set.error_norm.boost    = 3;
    const quadrature::RuleFactory factory{quadrature::Policy(rule_set)};
    const quadrature::MfemRule selected_rule =
        factory.get(make_query(quadrature::Term::error_norm, 4), mfem::Geometry::CUBE);
    const mfem::IntegrationRule &expected_rule = mfem::IntRules.Get(mfem::Geometry::CUBE, 9);

    REQUIRE(selected_rule.integration_rule != nullptr);
    CHECK(selected_rule.resolution.base_order == 4);
    CHECK(selected_rule.resolution.boost == 5);
    CHECK(selected_rule.resolution.order == 9);
    CHECK(selected_rule.integration_rule == &expected_rule);
    CHECK(selected_rule.integration_rule->GetNPoints() > 0);
}

TEST_CASE(
    "MFEM Quadrature Rule Integrates Tensor Polynomial Exactly",
    tags::unit &tags::quadrature
) {
    constexpr int polynomial_degree = 7;
    const quadrature::RuleFactory factory{quadrature::Policy(quadrature::make_rule_set(quadrature::Mode::production))};
    const quadrature::MfemRule selected_rule =
        factory.get(make_query(quadrature::Term::error_norm, polynomial_degree), mfem::Geometry::CUBE);
    double numerical_integral = 0.0;

    for (int i = 0; i < selected_rule.integration_rule->GetNPoints(); ++i) {
        const mfem::IntegrationPoint &integration_point = selected_rule.integration_rule->IntPoint(i);
        numerical_integral += integration_point.weight * std::pow(integration_point.x, polynomial_degree) *
                              std::pow(integration_point.y, polynomial_degree) *
                              std::pow(integration_point.z, polynomial_degree);
    }

    const double one_dimensional_integral = 1.0 / static_cast<double>(polynomial_degree + 1);
    const double analytic_integral = one_dimensional_integral * one_dimensional_integral * one_dimensional_integral;
    CHECK_THAT(numerical_integral, Catch::Matchers::WithinAbs(analytic_integral, 5.0e-14));
}

TEST_CASE(
    "Policy Controlled Hdiv Mass Assembly Matches Overintegrated Reference",
    tags::quadrature &tags::solver &tags::integration
) {
    mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D(1, 1, 1, mfem::Element::HEXAHEDRON, 1.0, 1.0, 1.0);
    mfem::RT_FECollection rt_collection(2, 3);
    mfem::FiniteElementSpace rt_space(&mesh, &rt_collection);
    const mfem::FiniteElement *rt_element       = rt_space.GetTypicalFE();
    mfem::ElementTransformation *transformation = mesh.GetElementTransformation(0);
    const int base_order                        = 2 * rt_element->GetOrder() + transformation->OrderW();

    const quadrature::RuleFactory production_factory{
        quadrature::Policy(quadrature::make_rule_set(quadrature::Mode::production))
    };
    const quadrature::MfemRule production_rule =
        production_factory.get(make_query(quadrature::Term::gravity_hdiv_mass, base_order), rt_element->GetGeomType());

    quadrature::RuleSet reference_rule_set     = quadrature::make_rule_set(quadrature::Mode::production);
    reference_rule_set.gravity_hdiv_mass.boost = 8;
    const quadrature::RuleFactory reference_factory{quadrature::Policy(reference_rule_set)};
    const quadrature::MfemRule reference_rule =
        reference_factory.get(make_query(quadrature::Term::gravity_hdiv_mass, base_order), rt_element->GetGeomType());

    mfem::BilinearForm production_mass(&rt_space);
    auto *production_integrator = new mfem::VectorFEMassIntegrator();
    production_integrator->SetIntegrationRule(*production_rule.integration_rule);
    production_mass.AddDomainIntegrator(production_integrator);
    production_mass.Assemble();
    production_mass.Finalize();

    mfem::BilinearForm reference_mass(&rt_space);
    auto *reference_integrator = new mfem::VectorFEMassIntegrator();
    reference_integrator->SetIntegrationRule(*reference_rule.integration_rule);
    reference_mass.AddDomainIntegrator(reference_integrator);
    reference_mass.Assemble();
    reference_mass.Finalize();

    mfem::Vector input(rt_space.GetVSize());
    mfem::Vector production_output(rt_space.GetVSize());
    mfem::Vector reference_output(rt_space.GetVSize());
    for (int i = 0; i < input.Size(); ++i) {
        input(i) = std::sin(0.37 * static_cast<double>(i + 1));
    }

    production_mass.Mult(input, production_output);
    reference_mass.Mult(input, reference_output);

    mfem::Vector difference(production_output);
    difference -= reference_output;
    const double relative_difference = difference.Norml2() / reference_output.Norml2();
    INFO("Production quadrature order = " << production_rule.resolution.order);
    INFO("Reference quadrature order = " << reference_rule.resolution.order);
    INFO("Relative operator difference = " << relative_difference);
    CHECK_THAT(relative_difference, Catch::Matchers::WithinAbs(0.0, 1.0e-12));
}

TEST_CASE(
    "HDiv Mass Helper Resolves the MFEM Baseline",
    tags::unit &tags::quadrature &tags::solver
) {
    mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D(1, 1, 1, mfem::Element::HEXAHEDRON);
    mfem::RT_FECollection rt_collection(2, 3);
    mfem::FiniteElementSpace rt_space(&mesh, &rt_collection);

    quadrature::RuleSet rule_set     = quadrature::make_rule_set(quadrature::Mode::production);
    rule_set.gravity_hdiv_mass.boost = 3;
    quadrature::RuleFactory factory{quadrature::Policy(std::move(rule_set))};

    const mfem::FiniteElement &element                = *rt_space.GetTypicalFE();
    const mfem::ElementTransformation &transformation = *mesh.GetElementTransformation(0);
    mfem::VectorFEMassIntegrator integrator;

    const quadrature::Resolution resolution = factory.configure_gravity_hdiv_mass(
        integrator, quadrature::QuadratureRole::discretization, element, transformation
    );
    const int expected_base_order = 2 * element.GetOrder() + transformation.OrderW();

    CHECK(resolution.base_order == expected_base_order);
    CHECK(resolution.boost == 3);
    CHECK(resolution.order == expected_base_order + 3);
}

TEST_CASE(
    "Gravity Divergence Helper Resolves Preconditioner Rule",
    tags::unit &tags::quadrature &tags::solver
) {
    mfem::Mesh mesh = mfem::Mesh::MakeCartesian3D(1, 1, 1, mfem::Element::HEXAHEDRON);
    mfem::RT_FECollection rt_collection(2, 3);
    mfem::L2_FECollection l2_collection(2, 3);
    mfem::FiniteElementSpace rt_space(&mesh, &rt_collection);
    mfem::FiniteElementSpace l2_space(&mesh, &l2_collection);

    quadrature::RuleSet rule_set        = quadrature::make_rule_set(quadrature::Mode::production);
    rule_set.gravity_divergence.boost   = 2;
    rule_set.roles.preconditioner.boost = 3;
    quadrature::RuleFactory factory{quadrature::Policy(std::move(rule_set))};

    const mfem::FiniteElement &trial_element          = *rt_space.GetTypicalFE();
    const mfem::FiniteElement &test_element           = *l2_space.GetTypicalFE();
    const mfem::ElementTransformation &transformation = *mesh.GetElementTransformation(0);
    mfem::VectorFEDivergenceIntegrator integrator;

    const quadrature::Resolution resolution = factory.configure_gravity_divergence(
        integrator, quadrature::QuadratureRole::preconditioner, trial_element, test_element, transformation
    );
    const int expected_base_order =
        std::max(0, trial_element.GetOrder() - 1) + test_element.GetOrder() + transformation.OrderW();

    CHECK(resolution.base_order == expected_base_order);
    CHECK(resolution.boost == 5);
    CHECK(resolution.order == expected_base_order + 5);
}

TEST_CASE(
    "Field Registry Encodes Spaces Orders And Stable Pair Constraints",
    tags::unit &tags::quadrature &tags::initialization
) {
    CHECK(mean_field::field::Density::Scalar::familyOrder == 2);
    CHECK(mean_field::field::Gravity::Potential::familyOrder == 2);
    CHECK(mean_field::field::Gravity::Flux::familyOrder == 2);
    CHECK(mean_field::field::Displacement::Vector::familyOrder == 3);
    CHECK(mean_field::field::Enthalpy::Scalar::familyOrder == 3);

    CHECK((std::same_as<mean_field::field::Density::Scalar::Space, mean_field::field::L2>));
    CHECK((std::same_as<mean_field::field::Gravity::Potential::Space, mean_field::field::L2>));
    CHECK((std::same_as<mean_field::field::Gravity::Flux::Space, mean_field::field::RT>));
    CHECK((std::same_as<mean_field::field::Displacement::Vector::Space, mean_field::field::H1>));
    CHECK((std::same_as<mean_field::field::Enthalpy::Scalar::Space, mean_field::field::H1>));

    CHECK(mean_field::field::Density::Scalar::rankValue == 0);
    CHECK(mean_field::field::Gravity::Potential::rankValue == 0);
    CHECK(mean_field::field::Gravity::Flux::rankValue == 1);
    CHECK(mean_field::field::Displacement::Vector::rankValue == 1);
    CHECK(mean_field::field::Enthalpy::Scalar::rankValue == 0);
    CHECK(mean_field::field::Gravity::Flux::familyOrder == mean_field::field::Gravity::Potential::familyOrder);

    CHECK(std::is_empty_v<mean_field::field::Field<mean_field::field::Gravity>>);
    CHECK(std::is_empty_v<mean_field::field::Field<mean_field::field::Displacement>>);
    CHECK(std::is_empty_v<mean_field::field::Field<mean_field::field::Density>>);
    CHECK(std::is_empty_v<mean_field::field::Field<mean_field::field::Enthalpy>>);

    STATIC_CHECK(field::RegisteredQuantity<field::BarotropicConstant::Scalar>);
    STATIC_CHECK(field::GlobalScalarQuantity<field::BarotropicConstant::Scalar>);
    STATIC_CHECK_FALSE(field::FieldQuantity<field::BarotropicConstant::Scalar>);

    STATIC_CHECK(field::BarotropicConstant::Scalar::storageKind == field::StorageKind::global_scalar);
    STATIC_CHECK(field::BarotropicConstant::Scalar::staticBlockSize == 1);

    STATIC_CHECK(field::Enthalpy::Scalar::storageKind == field::StorageKind::finite_element);
    STATIC_CHECK(field::Enthalpy::Scalar::staticBlockSize == field::dynamicBlockSize);

    STATIC_CHECK_FALSE(CanMakeFec<field::Field<field::BarotropicConstant>, field::BarotropicConstant::Scalar>);
}

TEST_CASE(
    "Field Forms Produce Typed Quadrature Queries",
    tags::unit &tags::quadrature
) {
    using GravityField                     = field::Field<field::Gravity>;
    using DensityField                     = field::Field<field::Density>;
    using EnthalpyField                    = field::Field<field::Enthalpy>;

    constexpr quadrature::Query hdiv_query = GravityField::make_query<field::Gravity::Form::HDivMass>(
        quadrature::QuadratureRole::discretization, 2, {}, utils::DOMAINS::ALL, quadrature::MappingKind::general
    );
    constexpr quadrature::Query divergence_query = GravityField::make_query<field::Gravity::Form::DivergenceCoupling>(
        quadrature::QuadratureRole::preconditioner, 2
    );
    constexpr quadrature::Query source_query = GravityField::make_query<field::Gravity::Form::SourceProjection>(
        quadrature::QuadratureRole::projection, 2, {}, utils::DOMAINS::STELLAR
    );
    constexpr quadrature::Query center_of_mass_query = DensityField::make_query<field::Density::Form::CenterOfMass>(
        quadrature::QuadratureRole::diagnostic, 2, std::array<int, 1>{1}, utils::DOMAINS::STELLAR
    );
    constexpr quadrature::Query eos_closure_query = EnthalpyField::make_query<field::Enthalpy::Form::EosClosureSource>(
        quadrature::QuadratureRole::discretization, 2, std::array<int, 1>{6}, utils::DOMAINS::STELLAR,
        quadrature::MappingKind::general
    );
    constexpr quadrature::Query equilibrium_gravity_query =
        EnthalpyField::make_query<field::Enthalpy::Form::EquilibriumGravity>(
            quadrature::QuadratureRole::discretization, 2, {}, utils::DOMAINS::STELLAR, quadrature::MappingKind::general
        );

    constexpr quadrature::Query equilibrium_constant_query =
        EnthalpyField::make_query<field::Enthalpy::Form::EquilibriumConstant>(
            quadrature::QuadratureRole::discretization, 2, {}, utils::DOMAINS::STELLAR, quadrature::MappingKind::general
        );
    constexpr quadrature::Query rotation_query = EnthalpyField::make_query<field::Enthalpy::Form::EquilibriumRotation>(
        quadrature::QuadratureRole::discretization, 2, std::array<int, 1>{2}, utils::DOMAINS::STELLAR,
        quadrature::MappingKind::general
    );
    constexpr quadrature::Query isobaric_surface_query =
        EnthalpyField::make_query<field::Enthalpy::Form::IsobaricSurface>(
            quadrature::QuadratureRole::discretization, 2, {}, utils::DOMAINS::STELLAR, quadrature::MappingKind::general
        );
    constexpr quadrature::Query mesh_extension_query =
        field::Field<field::Displacement>::make_query<field::Displacement::Form::MeshExtension>(
            quadrature::QuadratureRole::discretization, 2, {}, utils::DOMAINS::ALL, quadrature::MappingKind::general
        );
    constexpr quadrature::Query mass_normalization_query =
        DensityField::make_query<field::Density::Form::MassNormalization>(
            quadrature::QuadratureRole::discretization, 2, {}, utils::DOMAINS::STELLAR, quadrature::MappingKind::general
        );
    constexpr quadrature::Query pressure_integral_query =
        EnthalpyField::make_query<field::Enthalpy::Form::PressureIntegral>(
            quadrature::QuadratureRole::diagnostic, 2, std::array<int, 1>{9}, utils::DOMAINS::STELLAR,
            quadrature::MappingKind::general
        );

    STATIC_CHECK(mean_field::field::Gravity::Form::SourceProjection::dynamicOrderCount == 0);
    STATIC_CHECK(hdiv_query.base_order.has_value());
    STATIC_CHECK(*hdiv_query.base_order == 8);
    STATIC_CHECK(*divergence_query.base_order == 6);
    STATIC_CHECK(*source_query.base_order == 6);
    STATIC_CHECK(*center_of_mass_query.base_order == 5);
    STATIC_CHECK(*eos_closure_query.base_order == 13);
    STATIC_CHECK(*equilibrium_gravity_query.base_order == 7);
    STATIC_CHECK(*rotation_query.base_order == 7);
    STATIC_CHECK(*isobaric_surface_query.base_order == 8);
    STATIC_CHECK(*mesh_extension_query.base_order == 6);
    STATIC_CHECK(*mass_normalization_query.base_order == 4);
    STATIC_CHECK(*pressure_integral_query.base_order == 14);
    STATIC_CHECK(*equilibrium_constant_query.base_order == 5);

    CHECK(equilibrium_constant_query.term == quadrature::Term::hydrostatic_equilibrium);
    CHECK(hdiv_query.term == mean_field::quadrature::Term::gravity_hdiv_mass);
    CHECK(hdiv_query.role == mean_field::quadrature::QuadratureRole::discretization);
    CHECK(hdiv_query.domain == mean_field::utils::DOMAINS::ALL);
    CHECK(hdiv_query.mapping == mean_field::quadrature::MappingKind::general);
    CHECK(source_query.term == mean_field::quadrature::Term::gravity_source);
    CHECK(center_of_mass_query.term == mean_field::quadrature::Term::center_of_mass);
    CHECK(eos_closure_query.term == mean_field::quadrature::Term::eos_closure);
    CHECK(equilibrium_gravity_query.term == mean_field::quadrature::Term::hydrostatic_equilibrium);
    CHECK(rotation_query.term == mean_field::quadrature::Term::hydrostatic_equilibrium);
    CHECK(isobaric_surface_query.term == mean_field::quadrature::Term::isobaric_surface);
    CHECK(mesh_extension_query.term == mean_field::quadrature::Term::mesh_extension);
    CHECK(mass_normalization_query.term == mean_field::quadrature::Term::mass_normalization);
    CHECK(pressure_integral_query.term == mean_field::quadrature::Term::pressure_integral);

    CHECK_THROWS_AS(
        (GravityField::make_query<mean_field::field::Gravity::Form::HDivMass>(
            mean_field::quadrature::QuadratureRole::discretization, -1
        )),
        std::invalid_argument
    );
    CHECK_THROWS_AS(
        (DensityField::make_query<mean_field::field::Density::Form::CenterOfMass>(
            mean_field::quadrature::QuadratureRole::diagnostic, 2, std::array<int, 1>{-1}
        )),
        std::invalid_argument
    );
}

TEST_CASE(
    "Field Factories Construct The Registered MFEM Collections",
    tags::unit &tags::quadrature &tags::initialization
) {
    using GravityField      = field::Field<field::Gravity>;
    using DisplacementField = field::Field<field::Displacement>;
    using DensityField      = field::Field<field::Density>;
    using EnthalpyField     = field::Field<field::Enthalpy>;

    std::unique_ptr<mfem::FiniteElementCollection> density_collection =
        DensityField::make_fec<field::Density::Scalar>(3);
    std::unique_ptr<mfem::FiniteElementCollection> potential_collection =
        GravityField::make_fec<field::Gravity::Potential>(3);
    std::unique_ptr<mfem::FiniteElementCollection> flux_collection = GravityField::make_fec<field::Gravity::Flux>(3);
    std::unique_ptr<mfem::FiniteElementCollection> displacement_collection =
        DisplacementField::make_fec<field::Displacement::Vector>(3);
    std::unique_ptr<mfem::FiniteElementCollection> enthalpy_collection =
        EnthalpyField::make_fec<field::Enthalpy::Scalar>(3);

    CHECK(dynamic_cast<mfem::L2_FECollection *>(density_collection.get()) != nullptr);
    CHECK(dynamic_cast<mfem::L2_FECollection *>(potential_collection.get()) != nullptr);
    CHECK(dynamic_cast<mfem::RT_FECollection *>(flux_collection.get()) != nullptr);
    CHECK(dynamic_cast<mfem::H1_FECollection *>(displacement_collection.get()) != nullptr);
    CHECK(dynamic_cast<mfem::H1_FECollection *>(enthalpy_collection.get()) != nullptr);

    CHECK_THROWS_AS((DensityField::make_fec<mean_field::field::Density::Scalar>(0)), std::invalid_argument);
}

TEST_CASE(
    "FEM Setup Realizes Every Registered Field Independently",
    tags::integration &tags::initialization &tags::solver
) {
    const utils::Args args = test_utils::setup_args();
    const fem::FEM fem     = fem::setup_fem(args.mesh_file, args, 0);

    REQUIRE(fem.okay());
    REQUIRE(fem.mesh != nullptr);
    REQUIRE(fem.densityFes != nullptr);
    REQUIRE(fem.gravityPotentialFes != nullptr);
    REQUIRE(fem.gravityFluxFes != nullptr);
    REQUIRE(fem.displacementFes != nullptr);
    REQUIRE(fem.enthalpyFes != nullptr);

    CHECK(fem.densityFes.get() != fem.gravityPotentialFes.get());
    CHECK(fem.densityFec.get() != fem.gravityPotentialFec.get());

    CHECK(fem.densityFes->GetMaxElementOrder() == mean_field::field::Density::Scalar::familyOrder);
    CHECK(fem.gravityPotentialFes->GetMaxElementOrder() == mean_field::field::Gravity::Potential::familyOrder);
    CHECK(fem.gravityFluxFes->GetMaxElementOrder() == mean_field::field::Gravity::Flux::familyOrder + 1);
    CHECK(fem.displacementFes->GetMaxElementOrder() == mean_field::field::Displacement::Vector::familyOrder);
    CHECK(fem.enthalpyFes->GetMaxElementOrder() == mean_field::field::Enthalpy::Scalar::familyOrder);

    CHECK(fem.densityFes->GetVDim() == 1);
    CHECK(fem.gravityPotentialFes->GetVDim() == 1);
    CHECK(fem.gravityFluxFes->GetVDim() == 1);
    CHECK(fem.displacementFes->GetVDim() == fem.mesh->SpaceDimension());
    CHECK(fem.displacementFes->GetOrdering() == mfem::Ordering::byNODES);
    CHECK(fem.enthalpyFes->GetVDim() == 1);

    using DomainSchema = mean_field::utils::domain::CoreEnvelopeVacuumDomainSchema;

    const mean_field::field::FieldDofMap densityMap =
        mean_field::field::make_field_dof_map<mean_field::field::Density, DomainSchema>(*fem.densityFes);
    const mean_field::field::FieldDofMap displacementMap =
        mean_field::field::make_field_dof_map<mean_field::field::Displacement, DomainSchema>(*fem.displacementFes);

    CHECK(densityMap.full_size() == fem.densityFes->GetTrueVSize());
    CHECK(densityMap.reduced_size() < densityMap.full_size());
    CHECK(displacementMap.full_size() == fem.displacementFes->GetTrueVSize());
    CHECK(displacementMap.reduced_size() == displacementMap.full_size());
}