perf(jacobian-action): major updates to jacobian action application by removing redudant quadrature work. ~5x increase in speed

libmeanfield/interface/mapping/domain_mapper.cppm

@@ -78,6 +78,7 @@ export namespace mean_field::mapping {
             int m_dimension;
 
             mfem::Vector m_shape;
+            mfem::DenseMatrix m_reference_dshape;
             mfem::DenseMatrix m_mesh_dshape;
             mfem::Vector m_field_value;
             mfem::DenseMatrix m_field_jacobian;
@@ -178,7 +179,8 @@ export namespace mean_field::mapping {
             const mfem::IntegrationPoint &integration_point,
             Workspace &workspace,
             mfem::Vector &value,
-            mfem::DenseMatrix &jacobian
+            mfem::DenseMatrix &jacobian,
+            const mfem::DenseMatrix *inverse_mesh_jacobian
         ) const;
 
         [[nodiscard]] MappingStatus EvaluateCompactificationCoordinate(
@@ -186,7 +188,19 @@ export namespace mean_field::mapping {
             mfem::ElementTransformation &transformation,
             const mfem::IntegrationPoint &integration_point,
             Workspace &workspace,
-            CompactificationPointData &point_data
+            CompactificationPointData &point_data,
+            const mfem::DenseMatrix *inverse_mesh_jacobian
+        ) const;
+
+        [[nodiscard]] MappingStatus EvaluatePointVariationImpl(
+            const ElementMappingData &element_data,
+            const ElementDisplacementData &direction,
+            mfem::ElementTransformation &transformation,
+            const mfem::IntegrationPoint &integration_point,
+            const MappingPointContext &base_context,
+            Workspace &workspace,
+            MappingPointVariation &variation,
+            const mfem::DenseMatrix *inverse_mesh_jacobian
         ) const;
 
         [[nodiscard]] static mfem::ElementTransformation &SelectFaceElementTransformation(