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Merge branch 'ebourne_split_metric_tensor' into 'main'
Create metric tensor operator See merge request gysela-developpers/gyselalibxx!683
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| Original file line number | Diff line number | Diff line change |
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| #pragma once | ||
| #include <type_traits> | ||
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| #include <sll/view.hpp> | ||
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| /** | ||
| * @brief An operator for calculating the metric tensor. | ||
| * @tparam Mapping The mapping providing the Jacobian operator. | ||
| * @tparam PositionCoordinate The coordinate type where the metric tensor can be evaluated. | ||
| */ | ||
| template <class Mapping, class PositionCoordinate> | ||
| class MetricTensor | ||
| { | ||
| public: | ||
| /// The type of the Jacobian matrix and its inverse | ||
| using Matrix_2x2 = std::array<std::array<double, 2>, 2>; | ||
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| private: | ||
| Mapping m_mapping; | ||
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| public: | ||
| /** | ||
| * @brief A constructor for the metric tensor operator. | ||
| * | ||
| * @param[in] mapping The mapping which can be used to calculate the Jacobian. | ||
| */ | ||
| MetricTensor(Mapping mapping) : m_mapping(mapping) {} | ||
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| /** | ||
| * @brief Compute the metric tensor assignd to the mapping. | ||
| * | ||
| * The metric tensor matrix is defined as: | ||
| * @f$ G = (J_{\mathcal{F}})^T J_{\mathcal{F}} @f$. | ||
| * with @f$ J_{\mathcal{F}} @f$ the Jacobian matrix. | ||
| * | ||
| * @param[in] coord | ||
| * The coordinate where we evaluate the metric tensor. | ||
| * @param[out] matrix | ||
| * The metric tensor matrix. | ||
| */ | ||
| void operator()(Matrix_2x2& matrix, PositionCoordinate const& coord) const | ||
| { | ||
| const double J_11 = m_mapping.jacobian_11(coord); | ||
| const double J_12 = m_mapping.jacobian_12(coord); | ||
| const double J_21 = m_mapping.jacobian_21(coord); | ||
| const double J_22 = m_mapping.jacobian_22(coord); | ||
| matrix[0][0] = (J_11 * J_11 + J_21 * J_21); | ||
| matrix[0][1] = (J_11 * J_12 + J_21 * J_22); | ||
| matrix[1][0] = (J_11 * J_12 + J_21 * J_22); | ||
| matrix[1][1] = (J_12 * J_12 + J_22 * J_22); | ||
| } | ||
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| /** | ||
| * @brief Compute the inverse metric tensor associated to the mapping. | ||
| * | ||
| * @param[in] coord | ||
| * The coordinate where we evaluate the metric tensor. | ||
| * @param[out] matrix | ||
| * The metric tensor matrix. | ||
| */ | ||
| void inverse(Matrix_2x2& matrix, PositionCoordinate const& coord) const | ||
| { | ||
| const double J_11 = m_mapping.jacobian_11(coord); | ||
| const double J_12 = m_mapping.jacobian_12(coord); | ||
| const double J_21 = m_mapping.jacobian_21(coord); | ||
| const double J_22 = m_mapping.jacobian_22(coord); | ||
| const double jacob_2 = m_mapping.jacobian(coord) * m_mapping.jacobian(coord); | ||
| matrix[0][0] = (J_12 * J_12 + J_22 * J_22) / jacob_2; | ||
| matrix[0][1] = (-J_11 * J_12 - J_21 * J_22) / jacob_2; | ||
| matrix[1][0] = (-J_11 * J_12 - J_21 * J_22) / jacob_2; | ||
| matrix[1][1] = (J_11 * J_11 + J_21 * J_21) / jacob_2; | ||
| } | ||
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| /** | ||
| * @brief Compute the covariant vector from the contravariant vector | ||
| * | ||
| * @param[in] contravariant_vector | ||
| * The metric tensor matrix. | ||
| * @param[in] coord | ||
| * The coordinate where we want to compute the convariant vector. | ||
| * | ||
| * @return A vector of the covariant | ||
| */ | ||
| std::array<double, 2> to_covariant( | ||
| std::array<double, 2> const& contravariant_vector, | ||
| PositionCoordinate const& coord) const | ||
| { | ||
| Matrix_2x2 inv_metric_tensor; | ||
| inverse(inv_metric_tensor, coord); | ||
| std::array<double, 2> covariant_vector; | ||
| covariant_vector[0] = inv_metric_tensor[0][0] * contravariant_vector[0] | ||
| + inv_metric_tensor[0][1] * contravariant_vector[1]; | ||
| covariant_vector[1] = inv_metric_tensor[1][0] * contravariant_vector[0] | ||
| + inv_metric_tensor[1][1] * contravariant_vector[1]; | ||
| return covariant_vector; | ||
| } | ||
| }; |
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