perf(allocations): reduced overall allocations by 95%, increaseed jacobian applicatin by 2x

This commit uses global pre allocated work space to dramatically reduce memory usage and allocation time

libmeanfield/interface/mapping/compactification/compactification.cppm

@@ -31,6 +31,16 @@ export namespace mean_field::mapping::compactification {
     public:
         virtual ~ExteriorDomainMap() = default;
 
+        /*
+         * Return true when, with the reference and compactification data held
+         * fixed, both outputs of Evaluate are affine functions of the
+         * displaced position and displacement Jacobian.  This is the contract
+         * required by the exact determinant-polynomial geometry preflight.
+         */
+        [[nodiscard]] virtual bool IsAffineInDisplacement() const noexcept {
+            return false;
+        }
+
         [[nodiscard]] virtual MappingStatus Evaluate(
             const ExteriorMapInput &input,
             ExteriorMapResult &result

libmeanfield/interface/mapping/compactification/kelvin.cppm

@@ -12,6 +12,10 @@ export namespace mean_field::mapping::compactification {
     public:
         explicit KelvinCompactification(options::KelvinCompactificationOptions options);
 
+        [[nodiscard]] bool IsAffineInDisplacement() const noexcept override {
+            return true;
+        }
+
         [[nodiscard]] MappingStatus Evaluate(
             const ExteriorMapInput &input,
             ExteriorMapResult &result
@@ -45,4 +49,4 @@ export namespace mean_field::mapping::compactification {
 
         options::KelvinCompactificationOptions m_options;
     };
-} // namespace mean_field::mapping::compactification
+} // namespace mean_field::mapping::compactification

libmeanfield/interface/mapping/domain_mapper.cppm

@@ -80,6 +80,7 @@ export namespace mean_field::mapping {
             mfem::Vector m_shape;
             mfem::DenseMatrix m_reference_dshape;
             mfem::DenseMatrix m_mesh_dshape;
+            mfem::DenseMatrix m_reference_field_jacobian;
             mfem::Vector m_field_value;
             mfem::DenseMatrix m_field_jacobian;
 

libmeanfield/interface/mapping/prepared_cache.cppm

@@ -0,0 +1,42 @@
+module;
+
+#include <mfem.hpp>
+#include <vector>
+
+export module mean_field:mapping.prepared_cache;
+import :mapping.types;
+
+export namespace mean_field::mapping {
+    // Flat, owning storage for prepared volume contexts. Load into reusable
+    // workspaces: no MFEM buffers or pointer aliases are owned per quadrature
+    // point. The layout retains every public context field without recomputing
+    // inverses or changing the mapper's numerical contract.
+    class VolumeMappingCache {
+    public:
+        void SetSize(
+            int point_count,
+            int dimension
+        );
+        void Store(
+            int point,
+            const VolumeMappingContext &context
+        );
+        void Load(
+            int point,
+            VolumeMappingContext &context
+        ) const;
+        void LoadInverseJacobian(
+            int point,
+            mfem::DenseMatrix &inverse
+        ) const;
+        [[nodiscard]] int GetPointCount() const;
+        [[nodiscard]] int GetDimension() const;
+
+    private:
+        [[nodiscard]] const double *GetPointData(int point) const;
+        std::vector<double> m_data;
+        int m_point_count{0};
+        int m_dimension{0};
+        int m_point_stride{0};
+    };
+} // namespace mean_field::mapping