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