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feat(topology): Added TMOP support

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Meshes generated purley algebraically tend to be poorly conditioned. Incorporated MFEM's TMOP support based on a metric of ideal shape and unit size
This commit is contained in:
Emily Boudreaux
2026-04-07 12:19:58 -04:00
parent a5ddf6a62f
commit 5a82311251
22 changed files with 545 additions and 101 deletions
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253
tests/stroidTest.cpp
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@@ -17,6 +17,8 @@
#include <algorithm>
#include <array>
#include <limits>
#include <print>
#include <complex>
namespace {
@@ -32,10 +34,10 @@ std::filesystem::path GetSourceRoot() {
return std::filesystem::current_path();
}
Config LoadConfigFromRepo(const std::filesystem::path& relative_path) {
Config cfg;
cfg.load((GetSourceRoot() / relative_path).string());
return cfg;
std::unique_ptr<Config> LoadConfigFromRepo(const std::filesystem::path& relative_path) {
auto cfg_ptr = std::make_unique<Config>();
cfg_ptr->load((GetSourceRoot() / relative_path).string());
return cfg_ptr;
}
@@ -122,13 +124,13 @@ std::unique_ptr<mfem::Mesh> BuildProjectedMesh(const Config& cfg) {
double ComputeStellarVolumeWithDomainLFIntegrator(mfem::Mesh& mesh, const Config& cfg) {
const int mesh_max_attr = mesh.attributes.Size() > 0 ? mesh.attributes.Max() : 0;
const int cfg_max_attr = static_cast<int>(std::max({cfg->core_id, cfg->envelope_id, cfg->vacuum_id}));
const int cfg_max_attr = static_cast<int>(std::max({cfg->core_id.value(), cfg->envelope_id.value(), cfg->vacuum_id.value()}));
const int coeff_size = std::max(1, std::max(mesh_max_attr, cfg_max_attr));
mfem::Vector attr_coeff(coeff_size);
attr_coeff = 0.0;
attr_coeff(static_cast<int>(cfg->core_id) - 1) = 1.0;
attr_coeff(static_cast<int>(cfg->envelope_id) - 1) = 1.0;
attr_coeff(static_cast<int>(cfg->core_id.value()) - 1) = 1.0;
attr_coeff(static_cast<int>(cfg->envelope_id.value()) - 1) = 1.0;
mfem::PWConstCoefficient stellar_coeff(attr_coeff);
mfem::L2_FECollection fec(0, mesh.Dimension());
@@ -233,6 +235,26 @@ ConditioningStats CollectConditioningStats(const mfem::Mesh& mesh, const std::se
return stats;
}
std::optional<double> EvalGridFunctionAtPoint(
mfem::Mesh& mesh,
const mfem::Vector& x,
const mfem::GridFunction& u ){
mfem::Array<int> elem_ids;
mfem::Array<mfem::IntegrationPoint> ips;
mfem::DenseMatrix P(x.Size(), 1);
P.SetCol(0, x);
mesh.FindPoints(P, elem_ids, ips, false);
if (elem_ids.Size() > 0 && elem_ids[0] >= 0) {
return u.GetValue(elem_ids[0], ips[0]);
} else {
return std::nullopt;
}
}
} // namespace
/**
@@ -270,7 +292,8 @@ TEST_F(stroidTest, BuildSkeleton_DefaultCounts) {
* `src/lib/topology/topology.cpp` (`vacuum_shells`, `inf_bdr_quads`) and config parsing path.
*/
TEST_F(stroidTest, BuildSkeleton_ExternalDomainCounts) {
const Config cfg = LoadConfigFromRepo("configs/test_external_domain.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_external_domain.toml");
const auto& cfg = *cfg_ptr;
const std::unique_ptr<mfem::Mesh> mesh = stroid::topology::BuildSkeleton(cfg);
ASSERT_NE(mesh, nullptr);
@@ -289,19 +312,20 @@ TEST_F(stroidTest, BuildSkeleton_ExternalDomainCounts) {
* `core_id`, `envelope_id`, `vacuum_id`, `surface_bdr_id`, `inf_bdr_id` in config fixtures.
*/
TEST_F(stroidTest, BuildSkeleton_ExternalDomainAttributes) {
const Config cfg = LoadConfigFromRepo("configs/test_external_domain.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_external_domain.toml");
const auto& cfg = *cfg_ptr;
const std::unique_ptr<mfem::Mesh> mesh = stroid::topology::BuildSkeleton(cfg);
ASSERT_NE(mesh, nullptr);
const auto volume_attr_counts = CountVolumeAttributes(*mesh);
EXPECT_EQ(volume_attr_counts.at(static_cast<int>(cfg->core_id)), 1);
EXPECT_EQ(volume_attr_counts.at(static_cast<int>(cfg->envelope_id)), 6);
EXPECT_EQ(volume_attr_counts.at(static_cast<int>(cfg->vacuum_id)), 6);
EXPECT_EQ(volume_attr_counts.at(static_cast<int>(cfg->core_id.value())), 1);
EXPECT_EQ(volume_attr_counts.at(static_cast<int>(cfg->envelope_id.value())), 6);
EXPECT_EQ(volume_attr_counts.at(static_cast<int>(cfg->vacuum_id.value())), 6);
const auto boundary_attr_counts = CountBoundaryAttributes(*mesh);
EXPECT_EQ(boundary_attr_counts.at(static_cast<int>(cfg->surface_bdr_id)), 6);
EXPECT_EQ(boundary_attr_counts.at(static_cast<int>(cfg->inf_bdr_id)), 6);
EXPECT_EQ(boundary_attr_counts.at(static_cast<int>(cfg->surface_bdr_id.value())), 6);
EXPECT_EQ(boundary_attr_counts.at(static_cast<int>(cfg->inf_bdr_id.value())), 6);
}
@@ -333,7 +357,8 @@ TEST_F(stroidTest, Finalize_RefinementIncreasesElements) {
* If this fails: inspect refine-loop count and any topology-side early exits in `Finalize`.
*/
TEST_F(stroidTest, Finalize_DefaultRefinementScalesHexCountByEightPowerL) {
const Config cfg = LoadConfigFromRepo("configs/test_refinement_l2.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_refinement_l2.toml");
const auto& cfg = *cfg_ptr;
const std::unique_ptr<mfem::Mesh> mesh = stroid::topology::BuildSkeleton(cfg);
const int initial_elements = mesh->GetNE();
@@ -352,7 +377,8 @@ TEST_F(stroidTest, Finalize_DefaultRefinementScalesHexCountByEightPowerL) {
* If this fails: inspect `Finalize` and verify external-domain elements are not excluded from refinement.
*/
TEST_F(stroidTest, Finalize_ExternalDomainRefinementScalesHexCountByEightPowerL) {
const Config cfg = LoadConfigFromRepo("configs/test_external_domain_refinement_l1.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_external_domain_refinement_l1.toml");
const auto& cfg = *cfg_ptr;
const std::unique_ptr<mfem::Mesh> mesh = stroid::topology::BuildSkeleton(cfg);
const int initial_elements = mesh->GetNE();
@@ -371,7 +397,9 @@ TEST_F(stroidTest, Finalize_ExternalDomainRefinementScalesHexCountByEightPowerL)
* If this fails: inspect `Finalize` orientation/refinement calls and any attribute mutation side effects.
*/
TEST_F(stroidTest, Finalize_ExternalDomainConformingAndRefined) {
const Config cfg = LoadConfigFromRepo("configs/test_external_domain.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_external_domain.toml");
const auto& cfg = *cfg_ptr;
const std::unique_ptr<mfem::Mesh> mesh = stroid::topology::BuildSkeleton(cfg);
const int initial_elements = mesh->GetNE();
@@ -381,13 +409,13 @@ TEST_F(stroidTest, Finalize_ExternalDomainConformingAndRefined) {
EXPECT_GT(mesh->GetNE(), initial_elements);
const auto volume_attr_counts = CountVolumeAttributes(*mesh);
EXPECT_GT(volume_attr_counts.at(static_cast<int>(cfg->core_id)), 0);
EXPECT_GT(volume_attr_counts.at(static_cast<int>(cfg->envelope_id)), 0);
EXPECT_GT(volume_attr_counts.at(static_cast<int>(cfg->vacuum_id)), 0);
EXPECT_GT(volume_attr_counts.at(static_cast<int>(cfg->core_id.value())), 0);
EXPECT_GT(volume_attr_counts.at(static_cast<int>(cfg->envelope_id.value())), 0);
EXPECT_GT(volume_attr_counts.at(static_cast<int>(cfg->vacuum_id.value())), 0);
const auto boundary_attr_counts = CountBoundaryAttributes(*mesh);
EXPECT_GT(boundary_attr_counts.at(static_cast<int>(cfg->surface_bdr_id)), 0);
EXPECT_GT(boundary_attr_counts.at(static_cast<int>(cfg->inf_bdr_id)), 0);
EXPECT_GT(boundary_attr_counts.at(static_cast<int>(cfg->surface_bdr_id.value())), 0);
EXPECT_GT(boundary_attr_counts.at(static_cast<int>(cfg->inf_bdr_id.value())), 0);
}
/**
@@ -399,16 +427,18 @@ TEST_F(stroidTest, Finalize_ExternalDomainConformingAndRefined) {
* notably `src/lib/topology/topology.cpp` and `src/lib/utils/mesh_utils.cpp`.
*/
TEST_F(stroidTest, Finalize_ExternalDomainKeepsOnlyExpectedMaterialAndBoundaryIDs) {
const Config cfg = LoadConfigFromRepo("configs/test_external_domain.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_external_domain.toml");
const auto& cfg = *cfg_ptr;
const std::unique_ptr<mfem::Mesh> mesh = stroid::topology::BuildSkeleton(cfg);
stroid::topology::Finalize(*mesh, cfg);
const auto volume_attr_counts = CountVolumeAttributes(*mesh);
const std::set<int> expected_volume_ids = {
static_cast<int>(cfg->core_id),
static_cast<int>(cfg->envelope_id),
static_cast<int>(cfg->vacuum_id)
static_cast<int>(cfg->core_id.value()),
static_cast<int>(cfg->envelope_id.value()),
static_cast<int>(cfg->vacuum_id.value())
};
for (const auto& [attr, count] : volume_attr_counts) {
EXPECT_TRUE(expected_volume_ids.contains(attr));
@@ -418,8 +448,8 @@ TEST_F(stroidTest, Finalize_ExternalDomainKeepsOnlyExpectedMaterialAndBoundaryID
const auto boundary_attr_counts = CountBoundaryAttributes(*mesh);
const std::set<int> expected_boundary_ids = {
static_cast<int>(cfg->surface_bdr_id),
static_cast<int>(cfg->inf_bdr_id)
static_cast<int>(cfg->surface_bdr_id.value()),
static_cast<int>(cfg->inf_bdr_id.value())
};
for (const auto& [attr, count] : boundary_attr_counts) {
EXPECT_TRUE(expected_boundary_ids.contains(attr));
@@ -496,7 +526,8 @@ TEST_F(stroidTest, ApplyEquiangular_BasicTransform) {
* `configs/test_flattening.toml`.
*/
TEST_F(stroidTest, ApplySpheroidal_FlattensZ) {
const Config cfg = LoadConfigFromRepo("configs/test_flattening.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_flattening.toml");
const auto& cfg = *cfg_ptr;
mfem::Vector pos(3);
pos(0) = 0.0;
@@ -571,9 +602,9 @@ TEST_F(stroidTest, TransformPoint_IsContinuousAcrossCoreAndStarInterfaces) {
dir(2) = -0.4;
mfem::Vector near_core_left = dir;
near_core_left *= cfg->r_core * (1.0 - eps);
near_core_left *= cfg->r_core.value() * (1.0 - eps);
mfem::Vector near_core_right = dir;
near_core_right *= cfg->r_core * (1.0 + eps);
near_core_right *= cfg->r_core.value() * (1.0 + eps);
const mfem::Vector core_left_mapped = TransformCopy(near_core_left, cfg);
const mfem::Vector core_right_mapped = TransformCopy(near_core_right, cfg);
@@ -583,9 +614,9 @@ TEST_F(stroidTest, TransformPoint_IsContinuousAcrossCoreAndStarInterfaces) {
EXPECT_LT(diff.Norml2(), 1e-3);
mfem::Vector near_star_left = dir;
near_star_left *= cfg->r_star * (1.0 - eps);
near_star_left *= cfg->r_star.value() * (1.0 - eps);
mfem::Vector near_star_right = dir;
near_star_right *= cfg->r_star * (1.0 + eps);
near_star_right *= cfg->r_star.value() * (1.0 + eps);
const mfem::Vector star_left_mapped = TransformCopy(near_star_left, cfg);
const mfem::Vector star_right_mapped = TransformCopy(near_star_right, cfg);
@@ -684,7 +715,9 @@ TEST_F(stroidTest, EndToEnd_BuildFinalizePromoteProject) {
* If this fails: inspect external-domain topology assembly and projection loops over mixed attributes.
*/
TEST_F(stroidTest, EndToEnd_ExternalDomainBuildFinalizePromoteProject) {
const Config cfg = LoadConfigFromRepo("configs/test_external_domain.toml");
const auto cfg_ptr= LoadConfigFromRepo("configs/test_external_domain.toml");
const auto& cfg = *cfg_ptr;
const std::unique_ptr<mfem::Mesh> mesh = stroid::topology::BuildSkeleton(cfg);
stroid::topology::Finalize(*mesh, cfg);
stroid::topology::PromoteToHighOrder(*mesh, cfg);
@@ -705,8 +738,12 @@ TEST_F(stroidTest, EndToEnd_ExternalDomainBuildFinalizePromoteProject) {
* that may leak starside nodes into vacuum geometry.
*/
TEST_F(stroidTest, Volume_StellarDomainMatchesWithAndWithoutExternalDomain) {
const Config no_external_cfg = LoadConfigFromRepo("configs/test_volume_no_external.toml");
const Config with_external_cfg = LoadConfigFromRepo("configs/test_volume_with_external.toml");
const auto no_external_cfg_ptr = LoadConfigFromRepo("configs/test_volume_no_external.toml");
const auto with_external_cfg_ptr = LoadConfigFromRepo("configs/test_volume_with_external.toml");
const auto& no_external_cfg = *no_external_cfg_ptr;
const auto& with_external_cfg = *with_external_cfg_ptr;
const std::unique_ptr<mfem::Mesh> no_external_mesh = stroid::topology::BuildSkeleton(no_external_cfg);
stroid::topology::Finalize(*no_external_mesh, no_external_cfg);
@@ -719,12 +756,12 @@ TEST_F(stroidTest, Volume_StellarDomainMatchesWithAndWithoutExternalDomain) {
stroid::topology::ProjectMesh(*with_external_mesh, with_external_cfg);
const std::set<int> stellar_attrs_no_external = {
static_cast<int>(no_external_cfg->core_id),
static_cast<int>(no_external_cfg->envelope_id)
static_cast<int>(no_external_cfg->core_id.value()),
static_cast<int>(no_external_cfg->envelope_id.value())
};
const std::set<int> stellar_attrs_with_external = {
static_cast<int>(with_external_cfg->core_id),
static_cast<int>(with_external_cfg->envelope_id)
static_cast<int>(with_external_cfg->core_id.value()),
static_cast<int>(with_external_cfg->envelope_id.value())
};
const double stellar_volume_no_external = ComputeMeshVolumeForAttributes(*no_external_mesh, stellar_attrs_no_external);
@@ -744,7 +781,9 @@ TEST_F(stroidTest, Volume_StellarDomainMatchesWithAndWithoutExternalDomain) {
* If this fails: inspect `ComputeMeshVolume*` helpers and region attribute IDs in config fixtures.
*/
TEST_F(stroidTest, Volume_ExternalMeshExcludesVacuumWhenRequested) {
const Config cfg = LoadConfigFromRepo("configs/test_volume_with_external.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_volume_with_external.toml");
const auto& cfg = *cfg_ptr;
const std::unique_ptr<mfem::Mesh> mesh = stroid::topology::BuildSkeleton(cfg);
stroid::topology::Finalize(*mesh, cfg);
@@ -752,10 +791,10 @@ TEST_F(stroidTest, Volume_ExternalMeshExcludesVacuumWhenRequested) {
stroid::topology::ProjectMesh(*mesh, cfg);
const std::set<int> stellar_attrs = {
static_cast<int>(cfg->core_id),
static_cast<int>(cfg->envelope_id)
static_cast<int>(cfg->core_id.value()),
static_cast<int>(cfg->envelope_id.value())
};
const std::set<int> vacuum_attr = {static_cast<int>(cfg->vacuum_id)};
const std::set<int> vacuum_attr = {static_cast<int>(cfg->vacuum_id.value())};
const double total_volume = ComputeMeshVolume(*mesh);
const double stellar_volume = ComputeMeshVolumeForAttributes(*mesh, stellar_attrs);
@@ -775,7 +814,8 @@ TEST_F(stroidTest, Volume_ExternalMeshExcludesVacuumWhenRequested) {
* `IntegrateElementVolume`.
*/
TEST_F(stroidTest, Volume_SphericalStellarDomainMatchesAnalyticSphere) {
const Config cfg = LoadConfigFromRepo("configs/test_volume_spherical_no_external.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_volume_spherical_no_external.toml");
const auto& cfg = *cfg_ptr;
const std::unique_ptr<mfem::Mesh> mesh = stroid::topology::BuildSkeleton(cfg);
stroid::topology::Finalize(*mesh, cfg);
@@ -783,12 +823,12 @@ TEST_F(stroidTest, Volume_SphericalStellarDomainMatchesAnalyticSphere) {
stroid::topology::ProjectMesh(*mesh, cfg);
const std::set<int> stellar_attrs = {
static_cast<int>(cfg->core_id),
static_cast<int>(cfg->envelope_id)
static_cast<int>(cfg->core_id.value()),
static_cast<int>(cfg->envelope_id.value())
};
const double measured_volume = ComputeMeshVolumeForAttributes(*mesh, stellar_attrs);
const double analytic_volume = 4.0 / 3.0 * kPi * std::pow(cfg->r_star, 3.0);
const double analytic_volume = 4.0 / 3.0 * kPi * std::pow(cfg->r_star.value(), 3.0);
const double rel_err = std::abs(measured_volume - analytic_volume) / analytic_volume;
EXPECT_LT(rel_err, 1e-2);
@@ -804,11 +844,12 @@ TEST_F(stroidTest, Volume_SphericalStellarDomainMatchesAnalyticSphere) {
* and MFEM assembly setup in this test file.
*/
TEST_F(stroidTest, Volume_SphericalStellarDomainDomainLFIntegratorMatchesAnalyticSphere) {
const Config cfg = LoadConfigFromRepo("configs/test_volume_spherical_with_external.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_volume_spherical_with_external.toml");
const auto& cfg = *cfg_ptr;
std::unique_ptr<mfem::Mesh> mesh = BuildProjectedMesh(cfg);
const double measured_volume = ComputeStellarVolumeWithDomainLFIntegrator(*mesh, cfg);
const double analytic_volume = 4.0 / 3.0 * kPi * std::pow(cfg->r_star, 3.0);
const double analytic_volume = 4.0 / 3.0 * kPi * std::pow(cfg->r_star.value(), 3.0);
const double rel_err = std::abs(measured_volume - analytic_volume) / analytic_volume;
EXPECT_LT(rel_err, 1e-2);
@@ -823,7 +864,9 @@ TEST_F(stroidTest, Volume_SphericalStellarDomainDomainLFIntegratorMatchesAnalyti
* refinement/order config used by `configs/test_volume_spherical_no_external.toml`.
*/
TEST_F(stroidTest, Conditioning_DefaultMeshHasPositiveJacobiansAndReasonableShape) {
const Config cfg = LoadConfigFromRepo("configs/test_volume_spherical_no_external.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_volume_spherical_no_external.toml");
const auto& cfg = *cfg_ptr;
const std::unique_ptr<mfem::Mesh> mesh = BuildProjectedMesh(cfg);
const ConditioningStats stats = CollectConditioningStats(*mesh, {});
@@ -845,12 +888,14 @@ TEST_F(stroidTest, Conditioning_DefaultMeshHasPositiveJacobiansAndReasonableShap
* assignment in `BuildSkeleton`.
*/
TEST_F(stroidTest, Conditioning_ExternalMeshPerRegionHasPositiveJacobians) {
const Config cfg = LoadConfigFromRepo("configs/test_volume_spherical_with_external.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_volume_spherical_with_external.toml");
const auto& cfg = *cfg_ptr;
const std::unique_ptr<mfem::Mesh> mesh = BuildProjectedMesh(cfg);
const ConditioningStats core_stats = CollectConditioningStats(*mesh, {static_cast<int>(cfg->core_id)});
const ConditioningStats envelope_stats = CollectConditioningStats(*mesh, {static_cast<int>(cfg->envelope_id)});
const ConditioningStats vacuum_stats = CollectConditioningStats(*mesh, {static_cast<int>(cfg->vacuum_id)});
const ConditioningStats core_stats = CollectConditioningStats(*mesh, {static_cast<int>(cfg->core_id.value())});
const ConditioningStats envelope_stats = CollectConditioningStats(*mesh, {static_cast<int>(cfg->envelope_id.value())});
const ConditioningStats vacuum_stats = CollectConditioningStats(*mesh, {static_cast<int>(cfg->vacuum_id.value())});
ASSERT_GT(core_stats.samples, 0);
ASSERT_GT(envelope_stats.samples, 0);
@@ -874,7 +919,9 @@ TEST_F(stroidTest, Conditioning_ExternalMeshPerRegionHasPositiveJacobians) {
* `src/lib/utils/mesh_utils.cpp`, then trace upstream mapping changes.
*/
TEST_F(stroidTest, Conditioning_DefaultMeshHasNoFlippedElementsOrBoundaryFaces) {
const Config cfg = LoadConfigFromRepo("configs/test_volume_spherical_no_external.toml");
const auto cfg_ptr = LoadConfigFromRepo("configs/test_volume_spherical_no_external.toml");
const auto& cfg = *cfg_ptr;
std::unique_ptr<mfem::Mesh> mesh = BuildProjectedMesh(cfg);
stroid::utils::MarkFlippedElements(*mesh);
@@ -887,3 +934,97 @@ TEST_F(stroidTest, Conditioning_DefaultMeshHasNoFlippedElementsOrBoundaryFaces)
EXPECT_FALSE(boundary_attr_counts.contains(500));
}
TEST_F(stroidTest, PolynomainalProjection) {
const auto cfg_ptr = LoadConfigFromRepo("configs/test_polynomial_projection.toml");
const auto& cfg = *cfg_ptr;
std::unique_ptr<mfem::Mesh> mesh = BuildProjectedMesh(cfg);
const int geom_order = mesh->GetNodes()->FESpace()->GetMaxElementOrder();
const int space_dim = mesh->Dimension();
mfem::H1_FECollection fec(geom_order, space_dim);
mfem::FiniteElementSpace fes(mesh.get(), &fec);
auto ProjectedFunction = [](const mfem::Vector& x) {
const double r = x.Norml2();
return 1 + 7 * r * r - 2 * r;
};
mfem::GridFunction projected_u(&fes);
mfem::FunctionCoefficient u_coeff(ProjectedFunction);
projected_u.ProjectCoefficient(u_coeff);
mfem::Vector x(space_dim);
x = 0.0;
for (double t = 0; t <= 1; t+= 0.01) {
x(0) = t;
double analytic_val = ProjectedFunction(x);
double projected_val = EvalGridFunctionAtPoint(*mesh, x, projected_u).value_or(std::numeric_limits<double>::quiet_NaN());
double rel_err = std::abs(projected_val - analytic_val) / analytic_val;
EXPECT_LT(rel_err, 1e-12);
}
}
TEST_F(stroidTest, TranscendtalProjection) {
const auto cfg_ptr = LoadConfigFromRepo("configs/test_polynomial_projection.toml");
const auto& cfg = *cfg_ptr;
std::unique_ptr<mfem::Mesh> mesh = BuildProjectedMesh(cfg);
const int geom_order = mesh->GetNodes()->FESpace()->GetMaxElementOrder();
const int space_dim = mesh->Dimension();
mfem::H1_FECollection fec(geom_order, space_dim);
mfem::FiniteElementSpace fes(mesh.get(), &fec);
auto ProjectedFunction = [](const mfem::Vector& x) {
const double r = x.Norml2();
if (r <= 1e-8) return 1.0;
return std::sin(r)/r;
};
auto expansion = [](const double t, const int order) {
double val = 0.0;
for (int k = 0; k < order; ++k) {
const double sign = (k % 2 == 0) ? 1.0 : -1.0;
const double term = sign * std::pow(t, 2 * k) / std::tgamma(2 * k + 2);
val += term;
}
return val;
};
auto expansion_err = [geom_order, &expansion](const double r) {
const double expansion_val = expansion(r, geom_order);
const double analytic_val = std::sin(r)/r;
return std::abs((expansion_val - analytic_val))/std::abs(analytic_val);
};
double max_estimated_truncation_error = 0.0;
for (double t = 0; t < 1; t+= 0.01) {
double trunc_err = expansion_err(t);
max_estimated_truncation_error = std::max(max_estimated_truncation_error, trunc_err);
}
mfem::GridFunction projected_u(&fes);
mfem::FunctionCoefficient u_coeff(ProjectedFunction);
projected_u.ProjectCoefficient(u_coeff);
mfem::Vector x(space_dim);
x = 0.0;
for (double t = 0; t <= 1; t+= 0.01) {
x(0) = t;
double analytic_val = ProjectedFunction(x);
double projected_val = EvalGridFunctionAtPoint(*mesh, x, projected_u).value_or(std::numeric_limits<double>::quiet_NaN());
double rel_err = std::abs(projected_val - analytic_val) / analytic_val;
EXPECT_LT(rel_err, 10*max_estimated_truncation_error);
}
}