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FESADev/src/fesa/analysis/linear_frequency_procedure.cpp
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#include "fesa/analysis/linear_frequency_procedure.h"
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <limits>
#include <memory>
#include <new>
#include <sstream>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>
#include "analysis/eigen_reduction.h"
#include "fesa/analysis/analysis_model.h"
#include "fesa/assembly/parallel_for.h"
#include "fesa/assembly/sparse_assembler.h"
#include "fesa/elements/element_factory.h"
#include "fesa/elements/mitc4_shell.h"
#include "fesa/fem/dof_manager.h"
#include "fesa/math/sparse_matrix.h"
#include "fesa/solvers/eigen/mkl_feast_eigen_solver.h"
namespace fesa {
namespace {
Status Failure(const std::string& code, const std::string& identity,
const std::string& message) {
return Status::Failure(
FailureCategory::kSolver,
{{Severity::kError, code, {}, "FREQUENCY", identity, message}});
}
double Dot(const Vector& left, const Vector& right) {
return left.Dot(right);
}
double Norm(const Vector& vector) {
double result = 0.0;
for (std::size_t i = 0; i < vector.Size(); ++i)
result = std::hypot(result, vector[i]);
return result;
}
double Ratio(double numerator, double denominator) {
if (std::isfinite(numerator) && std::isfinite(denominator) &&
denominator > 0.0)
return numerator / denominator;
return numerator == 0.0 && denominator == 0.0
? 0.0
: (std::numeric_limits<double>::infinity)();
}
double D(std::size_t dof, double length) {
return dof % 6U < 3U ? length : 1.0;
}
Status MetricFailure(const char* metric, double value, std::size_t column) {
std::ostringstream message;
message << std::setprecision(17) << metric << "=" << value << "; limit=1e-10";
return Failure("eigenpair-validation-failed",
"solver-column=" + std::to_string(column), message.str());
}
double FrobeniusNorm(const SparseMatrix& matrix) {
double norm = 0.0;
for (const double value : matrix.Values()) norm = std::hypot(norm, value);
return norm;
}
double MaximumEdgeLength(const Domain& domain) {
double maximum = 0.0;
for (std::size_t shell = 0U; shell < domain.ShellElements().Size(); ++shell) {
const auto& nodes = domain.ShellElements()[shell].NodeIndices();
for (std::size_t edge = 0U; edge < 4U; ++edge) {
const auto& first = domain.Nodes()[nodes[edge]].coordinates;
const auto& second = domain.Nodes()[nodes[(edge + 1U) % 4U]].coordinates;
maximum =
(std::max)(maximum, std::hypot(std::hypot(first[0U] - second[0U],
first[1U] - second[1U]),
first[2U] - second[2U]));
}
}
return maximum;
}
Result<EigenAnalysisState> ExecuteCandidate(const Domain& domain,
const EigenSolver& solver) {
const FrequencyStepDefinition* frequency = domain.Frequency();
if (frequency == nullptr || domain.Steps().Size() != 1U) {
return Result<EigenAnalysisState>::Failure(
Failure("invalid-frequency-procedure", "step",
"The domain has no sole frequency step."));
}
if (frequency->requested_mode_count <= 0) {
return Result<EigenAnalysisState>::Failure(
Failure("invalid-frequency-request", "requested-mode-count",
"Frequency requested mode count must be positive."));
}
Result<AnalysisModel> model = AnalysisModel::Create(domain);
if (!model.HasValue())
return Result<EigenAnalysisState>::Failure(model.GetStatus());
const ElementFactory factory;
std::vector<std::unique_ptr<Element>> owned;
std::vector<std::unique_ptr<ShellReferenceElement>> references;
ElementView view;
owned.reserve(model.Value().ActiveElements().size());
view.reserve(model.Value().ActiveElements().size());
for (const EntityIndex index : model.Value().ActiveElements()) {
auto element = factory.Create(domain.Elements()[index], domain);
if (!element.HasValue())
return Result<EigenAnalysisState>::Failure(element.GetStatus());
auto reference = factory.BindShellReference(*element.Value());
if (reference == nullptr) {
return Result<EigenAnalysisState>::Failure(Failure(
"unsupported-frequency-element", std::to_string(index),
"The frequency procedure supports MITC4 shell elements only."));
}
view.emplace_back(*element.Value());
owned.push_back(std::move(element.Value()));
references.push_back(std::move(reference));
}
DofManager dofs;
const Status dof_status = dofs.Build(model.Value(), view);
if (!dof_status.IsOk())
return Result<EigenAnalysisState>::Failure(dof_status);
const SerialParallelFor serial;
auto stiffness = SparseAssembler::Assemble(view, dofs, serial);
if (!stiffness.HasValue())
return Result<EigenAnalysisState>::Failure(stiffness.GetStatus());
std::vector<double> density(domain.Materials().Size(), 0.0);
for (const auto& item : domain.Densities()) {
if (item.material_index >= density.size() ||
density[item.material_index] != 0.0 || !(item.rho > 0.0) ||
!std::isfinite(item.rho)) {
return Result<EigenAnalysisState>::Failure(Failure(
"invalid-material-density", std::to_string(item.material_index),
"Invalid or duplicate material density."));
}
density[item.material_index] = item.rho;
}
for (std::size_t i = 0; i < dofs.PrescribedValues().Size(); ++i) {
if (dofs.PrescribedValues()[i] != 0.0) {
return Result<EigenAnalysisState>::Failure(
Status::Failure(FailureCategory::kInput,
{{Severity::kError,
"unsupported-eigen-boundary",
frequency->frequency_location,
"BOUNDARY",
{},
"Frequency requires homogeneous constraints."}}));
}
}
std::vector<Matrix> nodal_mass(domain.Nodes().size(), Matrix(6U, 6U));
std::vector<double> drilling(domain.Nodes().size(), 0.0);
for (std::size_t shell = 0U; shell < domain.ShellElements().Size(); ++shell) {
const auto& definition = domain.ShellElements()[shell];
if (!(density[definition.MaterialIndex()] > 0.0)) {
return Result<EigenAnalysisState>::Failure(
Failure("missing-frequency-density",
std::to_string(definition.MaterialIndex()),
"Every active shell material requires a positive density."));
}
const auto& element = references[shell];
auto mass = element->Mass(density[definition.MaterialIndex()]);
auto shell_stiffness = element->Stiffness();
if (!mass.HasValue())
return Result<EigenAnalysisState>::Failure(mass.GetStatus());
if (!shell_stiffness.HasValue())
return Result<EigenAnalysisState>::Failure(shell_stiffness.GetStatus());
for (std::size_t local_node = 0U; local_node < 4U; ++local_node) {
const std::size_t node = definition.NodeIndices()[local_node];
drilling[node] += shell_stiffness.Value().drilling_stiffness;
for (std::size_t a = 0U; a < 6U; ++a) {
for (std::size_t b = 0U; b < 6U; ++b) {
nodal_mass[node](a, b) += mass.Value().lumped_global24(
6U * local_node + a, 6U * local_node + b);
}
}
}
}
const double length = MaximumEdgeLength(domain);
std::vector<std::uint8_t> mask(dofs.FullDofCount(), 0U);
for (const std::size_t index : dofs.ConstrainedDofs()) mask[index] = 1U;
auto reduction = eigen_internal::BuildEigenReduction(
stiffness.Value(), nodal_mass, domain.ShellNodeInitialFrames(), mask,
drilling, length);
if (!reduction.HasValue())
return Result<EigenAnalysisState>::Failure(reduction.GetStatus());
const std::size_t request =
static_cast<std::size_t>(frequency->requested_mode_count);
if (request > reduction.Value().whitened_operator.Rows()) {
return Result<EigenAnalysisState>::Failure(Status::Failure(
FailureCategory::kModel,
{{Severity::kError, "insufficient-finite-modes",
frequency->frequency_location, "FREQUENCY", std::to_string(request),
"Requested modes exceed finite dimension " +
std::to_string(reduction.Value().whitened_operator.Rows())}}));
}
double zero_scale = (std::numeric_limits<double>::infinity)();
for (std::size_t e = 0; e < domain.ShellElements().Size(); ++e) {
const auto material_id = domain.ShellElements()[e].MaterialIndex();
const auto* material = dynamic_cast<const IsotropicLinearElasticMaterial*>(
&domain.Materials()[material_id]);
if (material == nullptr)
return Result<EigenAnalysisState>::Failure(
Failure("invalid-eigenvalue-result", "material",
"Unsupported frequency material."));
zero_scale = (std::min)(zero_scale,
(material->YoungsModulus() / density[material_id]) /
length / length);
}
auto backend = solver.Solve(
reduction.Value().whitened_operator, request, zero_scale);
if (!backend.HasValue())
return Result<EigenAnalysisState>::Failure(backend.GetStatus());
EigenAnalysisState state(std::move(backend.Value()));
state.full_dof_count = dofs.FullDofCount();
state.free_dof_count = reduction.Value().free_count;
state.mass_null_dimension = reduction.Value().null_count;
state.finite_dimension = reduction.Value().whitened_operator.Rows();
state.characteristic_length = length;
state.eta_mz = reduction.Value().eta_mz;
state.eta_kz = reduction.Value().eta_kz;
state.eta_pz = reduction.Value().eta_pz;
state.null_checks_applicable = state.mass_null_dimension != 0U;
state.constraint_mask = mask;
state.prescribed_displacement.assign(state.full_dof_count, 0.0);
for (const auto& node : reduction.Value().nodes)
state.nodal_reduction.push_back(node.record);
// The controls use the actual constrained, length-scaled pencil, including
// positive partial-BC drilling stiffness. Full constrained rows are
// reactions.
const SparseMatrix& k = stiffness.Value();
const SparseMatrix& a = reduction.Value().whitened_operator;
double stiffness_norm = 0.0;
for (const auto row : dofs.FreeDofs()) {
for (std::size_t entry = k.RowOffsets()[row];
entry < k.RowOffsets()[row + 1U]; ++entry) {
const auto col = k.ColumnIndices()[entry];
if (!mask[col])
stiffness_norm =
std::hypot(stiffness_norm,
D(row, length) * k.Values()[entry] * D(col, length));
}
}
double mass_norm = 0.0;
for (std::size_t node = 0; node < nodal_mass.size(); ++node) {
for (std::size_t row = 0; row < 6U; ++row) {
for (std::size_t col = 0; col < 6U; ++col) {
if (!mask[6U * node + row] && !mask[6U * node + col]) {
mass_norm = std::hypot(
mass_norm,
D(row, length) * nodal_mass[node](row, col) * D(col, length));
}
}
}
}
const double a_norm = FrobeniusNorm(a);
state.vectors = Matrix(request, state.full_dof_count);
const std::size_t count = state.backend.eigenvalues.size();
std::vector<Vector> all_modes;
std::vector<Vector> all_mass_times;
all_modes.reserve(count);
all_mass_times.reserve(count);
std::size_t cluster = 1U;
for (std::size_t column = 0; column < count; ++column) {
const double lambda = state.backend.eigenvalues[column];
const double mu = lambda / state.backend.operator_scale;
if (column != 0U && mu - state.backend.eigenvalues[column - 1U] /
state.backend.operator_scale >
1e-8)
++cluster;
Vector y = eigen_internal::RestoreScaledMode(
reduction.Value(), state.backend.eigenvectors, column);
Vector physical(y.Size());
std::size_t pivot = 0U;
for (std::size_t dof = 0; dof < y.Size(); ++dof) {
physical[dof] = D(dof, length) * y[dof];
if (!std::isfinite(physical[dof]))
return Result<EigenAnalysisState>::Failure(
MetricFailure("initial_modal_mass", physical[dof],
state.backend.column_ids[column]));
if (std::abs(y[dof]) > std::abs(y[pivot])) pivot = dof;
}
Vector mass_times = eigen_internal::MultiplyNodalMass(nodal_mass, physical);
const double initial_mass = Dot(physical, mass_times);
if (!(initial_mass > 0.0) || !std::isfinite(initial_mass))
return Result<EigenAnalysisState>::Failure(
MetricFailure("initial_modal_mass", initial_mass,
state.backend.column_ids[column]));
const double normalization =
(y[pivot] < 0.0 ? -1.0 : 1.0) / std::sqrt(initial_mass);
for (std::size_t dof = 0; dof < physical.Size(); ++dof) {
physical[dof] *= normalization;
if (!std::isfinite(physical[dof]) ||
(mask[dof] && physical[dof] != 0.0)) {
return Result<EigenAnalysisState>::Failure(
Failure("invalid-eigenvalue-result", std::to_string(column),
"Recovered mode is nonfinite or violates constraints."));
}
y[dof] = physical[dof] / D(dof, length);
}
// All stored physical metrics are recomputed from the final normalized phi.
mass_times = eigen_internal::MultiplyNodalMass(nodal_mass, physical);
const double modal_mass = Dot(physical, mass_times);
Vector ky = k.Multiply(physical);
Vector residual(physical.Size());
for (std::size_t dof = 0; dof < physical.Size(); ++dof) {
ky[dof] = mask[dof] ? 0.0 : D(dof, length) * ky[dof];
residual[dof] =
mask[dof] ? 0.0 : ky[dof] - lambda * D(dof, length) * mass_times[dof];
}
const double energy = Dot(y, ky);
const double y_norm = Norm(y);
const double pencil_scale = stiffness_norm + std::abs(lambda) * mass_norm;
const double eta_r = Ratio(Norm(residual), pencil_scale * y_norm);
const double eta_norm = std::abs(modal_mass - 1.0);
const double eta_energy = Ratio(std::abs(energy - lambda * modal_mass),
(pencil_scale * y_norm) * y_norm);
const double rayleigh = energy / modal_mass;
Vector x(a.Rows());
for (std::size_t row = 0; row < x.Size(); ++row) {
x[row] = state.backend.eigenvectors(row, column) * normalization;
if (!std::isfinite(x[row]))
return Result<EigenAnalysisState>::Failure(
Failure("invalid-eigenvalue-result", std::to_string(column),
"Recovered mode is nonfinite or violates constraints."));
}
Vector ax = a.Multiply(x);
Vector whitened_residual = ax;
whitened_residual.Axpy(-lambda, x);
const double x_norm = Norm(x);
const double eta_w =
Ratio(Norm(whitened_residual), (a_norm + std::abs(lambda)) * x_norm);
for (std::size_t row = 0; row < ax.Size(); ++row)
ax[row] = ax[row] / state.backend.operator_scale - mu * x[row];
const double rho_b = Ratio(Norm(ax), x_norm);
for (const auto& metric :
std::initializer_list<std::pair<const char*, double>>{
{"eta_r", eta_r},
{"eta_w", eta_w},
{"rho_b", rho_b},
{"eta_norm", eta_norm},
{"eta_energy", eta_energy}}) {
if (!std::isfinite(metric.second) || metric.second > 1e-10)
return Result<EigenAnalysisState>::Failure(MetricFailure(
metric.first, metric.second, state.backend.column_ids[column]));
}
if (!std::isfinite(rayleigh))
return Result<EigenAnalysisState>::Failure(
Failure("invalid-eigenvalue-result", std::to_string(column),
"Nonfinite Rayleigh quotient."));
state.eigenpair_checks.push_back(
{column + 1U, state.backend.column_ids[column], lambda, modal_mass,
rayleigh, eta_r, eta_w, rho_b, eta_norm, eta_energy,
state.backend.backend_res_available[column],
state.backend.backend_res[column]});
if (column < request) {
std::optional<double> frequency_value;
if (lambda >= 0.0) {
frequency_value = std::sqrt(lambda) / (2.0 * std::acos(-1.0));
if (!std::isfinite(*frequency_value) ||
(lambda > 0.0 && *frequency_value == 0.0))
return Result<EigenAnalysisState>::Failure(
Failure("invalid-eigenvalue-result", std::to_string(column),
"Cycle frequency conversion failed."));
}
state.modes.push_back(
{column + 1U, lambda,
static_cast<std::uint8_t>(std::abs(mu) <= 1e-9 ? 0U : 1U), cluster,
frequency_value});
for (std::size_t dof = 0; dof < physical.Size(); ++dof)
state.vectors(column, dof) = physical[dof];
}
all_modes.push_back(std::move(physical));
all_mass_times.push_back(std::move(mass_times));
}
double gram_norm = 0.0;
for (std::size_t left = 0; left < count; ++left) {
for (std::size_t right = 0; right < count; ++right) {
const double gram = Dot(all_modes[left], all_mass_times[right]);
gram_norm = std::hypot(gram_norm, gram - (left == right ? 1.0 : 0.0));
if (left != right)
state.max_eta_orth =
(std::max)(state.max_eta_orth,
Ratio(std::abs(gram),
std::sqrt(
state.eigenpair_checks[left].modal_mass *
state.eigenpair_checks[right].modal_mass)));
}
}
state.eta_gram = gram_norm / std::sqrt(static_cast<double>(count));
if (!std::isfinite(state.eta_gram) || state.eta_gram > 1e-10 ||
!std::isfinite(state.max_eta_orth) || state.max_eta_orth > 1e-10) {
return Result<EigenAnalysisState>::Failure(
MetricFailure("eta_gram", state.eta_gram, 0U));
}
state.backend.eigenvectors = Matrix(0U, 0U);
return Result<EigenAnalysisState>::Success(std::move(state));
}
} // namespace
Result<EigenAnalysisState> LinearFrequencyProcedureExecutor::Execute(
const Domain& domain) const {
try {
const MklFeastEigenSolver default_solver;
auto result = ExecuteCandidate(domain, solver_ ? *solver_ : default_solver);
if (!result.HasValue()) {
auto diagnostics = result.GetStatus().Diagnostics();
for (auto& diagnostic : diagnostics) {
if (diagnostic.location.file.empty())
diagnostic.location = domain.Frequency() != nullptr
? domain.Frequency()->frequency_location
: SourceLocation{domain.SourcePath(), 0U};
}
return Result<EigenAnalysisState>::Failure(Status::Failure(
result.GetStatus().Category().value_or(FailureCategory::kSolver),
std::move(diagnostics)));
}
return result;
} catch (const std::invalid_argument&) {
return Result<EigenAnalysisState>::Failure(
Failure("invalid-eigenvalue-result", "modal-workspace",
"Modal product inputs must be finite and shape compatible."));
} catch (const std::bad_alloc&) {
return Result<EigenAnalysisState>::Failure(
Failure("eigen-allocation-failed", "modal-workspace",
"Allocation failed after dimension checks; requested modes "
"were not reduced."));
} catch (const std::length_error&) {
return Result<EigenAnalysisState>::Failure(
Failure("eigen-index-overflow", "modal-workspace",
"Requested workspace exceeds container capacity."));
} catch (const std::runtime_error&) {
return Result<EigenAnalysisState>::Failure(
Failure("eigen-multiplication-failed", "modal-workspace",
"Modal sparse multiplication failed."));
}
}
} // namespace fesa
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