feat(elements): implement certified full-integration Hex8 kernel

2026-10-09 01:03:43 +09:00
parent df0388ae2f
commit 9088af7b32
8 changed files with 1337 additions and 2 deletions
@@ -0,0 +1,32 @@
+#ifndef FESA_ELEMENTS_HEX8_GEOMETRY_H_
+#define FESA_ELEMENTS_HEX8_GEOMETRY_H_
+
+#include <array>
+
+#include "fesa/elements/hex8_element.h"
+
+namespace fesa::hex8_internal {
+using Triple = std::array<double, 3>;
+using Tensor = std::array<Triple, 3>;
+inline constexpr int kNodeSigns[8][3] = {{-1, -1, -1}, {1, -1, -1}, {1, 1, -1},
+                                         {-1, 1, -1},  {-1, -1, 1}, {1, -1, 1},
+                                         {1, 1, 1},    {-1, 1, 1}};
+/// @brief Distinguishes a witness from an exhausted conservative certificate.
+enum class Certificate { kPositive, kNonpositive, kUncertain, kNonfinite };
+/// @brief Certifies the closed natural cube with interval Bernstein bounds.
+/// @note Current addition rounding is enclosed when displacement is supplied.
+Certificate Certify(const Hex8Element::Coordinates& coordinates,
+                    const Vector* displacement = nullptr);
+/// @brief Evaluates trilinear shapes and natural derivatives in source order.
+void Shape(const Triple& natural, std::array<double, 8>& values,
+           std::array<Triple, 8>& derivatives);
+/// @brief Computes a three-column map Jacobian using translated coordinates.
+Tensor Jacobian(const Hex8Element::Coordinates& coordinates,
+                const std::array<Triple, 8>& derivatives);
+/// @brief Computes the signed determinant; no absolute value or clamp.
+double Determinant(const Tensor& matrix);
+/// @brief Computes the inverse for an already validated positive determinant.
+Tensor Inverse(const Tensor& matrix, double determinant);
+}  // namespace fesa::hex8_internal
+
+#endif  // FESA_ELEMENTS_HEX8_GEOMETRY_H_