perf(shell): route local products through MKL and reduce Hessian storage work

src/fesa/elements/mitc4_shell.cpp

@@ -8,6 +8,7 @@
 #include <utility>
 
 #include "fesa/model/model_types.h"
+#include "math/dense_blas_internal.h"
 
 namespace fesa {
 
@@ -223,28 +224,18 @@ Matrix ScaledMatrix(const Matrix& source, double factor) {
   return result;
 }
 
-/// @brief Lifts a local matrix by a deterministic serial congruence product.
-/// @note The loop and accumulation order are part of reproducible stiffness.
+/// @brief Lifts a local matrix through MKL and mirrors the upper triangle.
 Matrix Congruence(const Matrix& local, const Matrix& transformation) {
   if (local.Rows() != local.Columns() ||
       local.Rows() != transformation.Rows()) {
     throw std::invalid_argument{
         "MITC4 congruence dimensions are incompatible."};
   }
-  Matrix result{transformation.Columns(), transformation.Columns()};
+  Matrix result = dense_blas_internal::MultiplyTransposeLeft(
+      transformation, local.Multiply(transformation));
   for (std::size_t row = 0U; row < result.Rows(); ++row) {
     for (std::size_t column = row; column < result.Columns(); ++column) {
-      double value = 0.0;
-      for (std::size_t local_row = 0U; local_row < local.Rows(); ++local_row) {
-        for (std::size_t local_column = 0U; local_column < local.Columns();
-             ++local_column) {
-          value += transformation(local_row, row) *
-                   local(local_row, local_column) *
-                   transformation(local_column, column);
-        }
-      }
-      result(row, column) = value;
-      result(column, row) = value;
+      result(column, row) = result(row, column);
     }
   }
   return result;
@@ -611,7 +602,8 @@ Matrix Mitc4Shell::TransverseShearSectionMatrix() const {
   return result;
 }
 
-Result<Mitc4Stiffness> Mitc4Shell::Stiffness() const {
+Result<Mitc4Stiffness> Mitc4Shell::Stiffness() const try {
+  const dense_blas_internal::ScopedLocalDenseThreads local_threads{};
   const Matrix constitutive = MaterialConstitutive5();
   const Matrix tying_samples = CovariantTyingShearSamples20();
   Matrix physical_local{kPhysicalDofCount, kPhysicalDofCount};
@@ -627,17 +619,12 @@ Result<Mitc4Stiffness> Mitc4Shell::Stiffness() const {
     const Matrix strain = StrainDisplacement(
         point.natural_coordinates[0], point.natural_coordinates[1],
         point.natural_coordinates[2], &tying_samples);
+    const Matrix integrand = dense_blas_internal::MultiplyTransposeLeft(
+        strain, constitutive.Multiply(strain));
     for (std::size_t row = 0U; row < kPhysicalDofCount; ++row) {
       for (std::size_t column = row; column < kPhysicalDofCount; ++column) {
-        double integrand = 0.0;
-        for (std::size_t first = 0U; first < 5U; ++first) {
-          for (std::size_t second = 0U; second < 5U; ++second) {
-            integrand += strain(first, row) * constitutive(first, second) *
-                         strain(second, column);
-          }
-        }
         const double contribution =
-            integrand * geometry.jacobian * point.weight;
+            integrand(row, column) * geometry.jacobian * point.weight;
         physical_local(row, column) += contribution;
         if (row != column) {
           physical_local(column, row) += contribution;
@@ -714,6 +701,8 @@ Result<Mitc4Stiffness> Mitc4Shell::Stiffness() const {
       Mitc4Stiffness{std::move(physical_local), std::move(physical_global),
                      std::move(drilling_global), std::move(stabilized_global),
                      drilling_stiffness});
+} catch (const std::exception& error) {
+  return StiffnessFailure(source_location_, identity_, error.what());
 }
 
 Result<Mitc4Mass> Mitc4Shell::Mass(const double density) const {