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PolynomialReconstruction.cpp
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Stéphane Del Pino authoredStéphane Del Pino authored
PolynomialReconstruction.cpp 69.14 KiB
#include <scheme/PolynomialReconstruction.hpp>
#include <algebra/Givens.hpp>
#include <algebra/ShrinkMatrixView.hpp>
#include <algebra/ShrinkVectorView.hpp>
#include <algebra/SmallMatrix.hpp>
#include <analysis/GaussLegendreQuadratureDescriptor.hpp>
#include <analysis/GaussQuadratureDescriptor.hpp>
#include <analysis/QuadratureFormula.hpp>
#include <analysis/QuadratureManager.hpp>
#include <geometry/CubeTransformation.hpp>
#include <geometry/LineTransformation.hpp>
#include <geometry/PrismTransformation.hpp>
#include <geometry/PyramidTransformation.hpp>
#include <geometry/SquareTransformation.hpp>
#include <geometry/TetrahedronTransformation.hpp>
#include <geometry/TriangleTransformation.hpp>
#include <mesh/MeshData.hpp>
#include <mesh/MeshDataManager.hpp>
#include <mesh/MeshFlatFaceBoundary.hpp>
#include <mesh/NamedBoundaryDescriptor.hpp>
#include <mesh/StencilDescriptor.hpp>
#include <mesh/StencilManager.hpp>
#include <scheme/DiscreteFunctionDPkVariant.hpp>
#include <scheme/DiscreteFunctionUtils.hpp>
#include <scheme/DiscreteFunctionVariant.hpp>
template <size_t Dimension>
PUGS_INLINE auto
symmetrize_vector(const TinyVector<Dimension>& normal, const TinyVector<Dimension>& u)
{
return u - 2 * dot(u, normal) * normal;
}
template <size_t Dimension>
PUGS_INLINE auto
symmetrize_matrix(const TinyVector<Dimension>& normal, const TinyMatrix<Dimension>& A)
{
const TinyMatrix S = TinyMatrix<Dimension>{identity} - 2 * tensorProduct(normal, normal);
return S * A * S;
}
template <size_t Dimension>
PUGS_INLINE auto
symmetrize_coordinates(const TinyVector<Dimension>& origin,
const TinyVector<Dimension>& normal,
const TinyVector<Dimension>& u)
{
return u - 2 * dot(u - origin, normal) * normal;
}
class PolynomialReconstruction::MutableDiscreteFunctionDPkVariant
{
public:
using Variant = std::variant<DiscreteFunctionDPk<1, double>,
DiscreteFunctionDPk<1, TinyVector<1>>,
DiscreteFunctionDPk<1, TinyVector<2>>,
DiscreteFunctionDPk<1, TinyVector<3>>,
DiscreteFunctionDPk<1, TinyMatrix<1>>,
DiscreteFunctionDPk<1, TinyMatrix<2>>,
DiscreteFunctionDPk<1, TinyMatrix<3>>,
DiscreteFunctionDPk<2, double>,
DiscreteFunctionDPk<2, TinyVector<1>>,
DiscreteFunctionDPk<2, TinyVector<2>>,
DiscreteFunctionDPk<2, TinyVector<3>>,
DiscreteFunctionDPk<2, TinyMatrix<1>>,
DiscreteFunctionDPk<2, TinyMatrix<2>>,
DiscreteFunctionDPk<2, TinyMatrix<3>>,
DiscreteFunctionDPk<3, double>,
DiscreteFunctionDPk<3, TinyVector<1>>,
DiscreteFunctionDPk<3, TinyVector<2>>,
DiscreteFunctionDPk<3, TinyVector<3>>,
DiscreteFunctionDPk<3, TinyMatrix<1>>,
DiscreteFunctionDPk<3, TinyMatrix<2>>,
DiscreteFunctionDPk<3, TinyMatrix<3>>,
DiscreteFunctionDPkVector<1, double>,
DiscreteFunctionDPkVector<1, TinyVector<1>>,
DiscreteFunctionDPkVector<1, TinyVector<2>>,
DiscreteFunctionDPkVector<1, TinyVector<3>>,
DiscreteFunctionDPkVector<1, TinyMatrix<1>>,
DiscreteFunctionDPkVector<1, TinyMatrix<2>>,
DiscreteFunctionDPkVector<1, TinyMatrix<3>>,
DiscreteFunctionDPkVector<2, double>,
DiscreteFunctionDPkVector<2, TinyVector<1>>,
DiscreteFunctionDPkVector<2, TinyVector<2>>,
DiscreteFunctionDPkVector<2, TinyVector<3>>,
DiscreteFunctionDPkVector<2, TinyMatrix<1>>,
DiscreteFunctionDPkVector<2, TinyMatrix<2>>,
DiscreteFunctionDPkVector<2, TinyMatrix<3>>,
DiscreteFunctionDPkVector<3, double>,
DiscreteFunctionDPkVector<3, TinyVector<1>>,
DiscreteFunctionDPkVector<3, TinyVector<2>>,
DiscreteFunctionDPkVector<3, TinyVector<3>>,
DiscreteFunctionDPkVector<3, TinyMatrix<1>>,
DiscreteFunctionDPkVector<3, TinyMatrix<2>>,
DiscreteFunctionDPkVector<3, TinyMatrix<3>>>;
private:
Variant m_mutable_discrete_function_dpk;
public:
PUGS_INLINE
const Variant&
mutableDiscreteFunctionDPk() const
{
return m_mutable_discrete_function_dpk;
}
template <typename DiscreteFunctionDPkT>
PUGS_INLINE auto&&
get() const
{
static_assert(is_discrete_function_dpk_v<DiscreteFunctionDPkT>, "invalid template argument");
#ifndef NDEBUG
if (not std::holds_alternative<DiscreteFunctionDPkT>(this->m_mutable_discrete_function_dpk)) {
std::ostringstream error_msg;
error_msg << "invalid discrete function type\n";
error_msg << "- required " << rang::fgB::red << demangle<DiscreteFunctionDPkT>() << rang::fg::reset << '\n';
error_msg << "- contains " << rang::fgB::yellow
<< std::visit([](auto&& f) -> std::string { return demangle<decltype(f)>(); },
this->m_mutable_discrete_function_dpk)
<< rang::fg::reset;
throw NormalError(error_msg.str());
}
#endif // NDEBUG
return std::get<DiscreteFunctionDPkT>(this->mutableDiscreteFunctionDPk());
}
template <size_t Dimension, typename DataType>
MutableDiscreteFunctionDPkVariant(const DiscreteFunctionDPk<Dimension, DataType>& discrete_function_dpk)
: m_mutable_discrete_function_dpk{discrete_function_dpk}
{
static_assert(std::is_same_v<DataType, double> or // std::is_same_v<DataType, TinyVector<1, double>> or //
std::is_same_v<DataType, TinyVector<2, double>> or //
std::is_same_v<DataType, TinyVector<3, double>> or //
std::is_same_v<DataType, TinyMatrix<1, 1, double>> or //
std::is_same_v<DataType, TinyMatrix<2, 2, double>> or //
std::is_same_v<DataType, TinyMatrix<3, 3, double>>,
"DiscreteFunctionDPk with this DataType is not allowed in variant");
}
template <size_t Dimension, typename DataType>
MutableDiscreteFunctionDPkVariant(const DiscreteFunctionDPkVector<Dimension, DataType>& discrete_function_dpk)
: m_mutable_discrete_function_dpk{discrete_function_dpk}
{
static_assert(std::is_same_v<DataType, double> or //
std::is_same_v<DataType, TinyVector<1, double>> or //
std::is_same_v<DataType, TinyVector<2, double>> or //
std::is_same_v<DataType, TinyVector<3, double>> or //
std::is_same_v<DataType, TinyMatrix<1, 1, double>> or //
std::is_same_v<DataType, TinyMatrix<2, 2, double>> or //
std::is_same_v<DataType, TinyMatrix<3, 3, double>>,
"DiscreteFunctionDPkVector with this DataType is not allowed in variant");
}
MutableDiscreteFunctionDPkVariant& operator=(MutableDiscreteFunctionDPkVariant&&) = default;
MutableDiscreteFunctionDPkVariant& operator=(const MutableDiscreteFunctionDPkVariant&) = default;
MutableDiscreteFunctionDPkVariant(const MutableDiscreteFunctionDPkVariant&) = default;
MutableDiscreteFunctionDPkVariant(MutableDiscreteFunctionDPkVariant&&) = default;
MutableDiscreteFunctionDPkVariant() = delete;
~MutableDiscreteFunctionDPkVariant() = default;
};
template <typename ConformTransformationT>
void
_computeEjkMean(const QuadratureFormula<1>& quadrature,
const ConformTransformationT& T,
const TinyVector<1>& Xj,
const double Vi,
const size_t degree,
const size_t dimension,
SmallArray<double>& inv_Vj_wq_detJ_ek,
SmallArray<double>& mean_of_ejk)
{
using Rd = TinyVector<1>;
mean_of_ejk.fill(0);
for (size_t i_q = 0; i_q < quadrature.numberOfPoints(); ++i_q) {
const double wq = quadrature.weight(i_q);
const Rd& xi_q = quadrature.point(i_q);
const double detT = T.jacobianDeterminant();
const Rd X_Xj = T(xi_q) - Xj;
const double x_xj = X_Xj[0];
{
size_t k = 0;
inv_Vj_wq_detJ_ek[k++] = wq * detT / Vi;
for (; k <= degree; ++k) {
inv_Vj_wq_detJ_ek[k] = x_xj * inv_Vj_wq_detJ_ek[k - 1];
}
}
for (size_t k = 1; k < dimension; ++k) {
mean_of_ejk[k - 1] += inv_Vj_wq_detJ_ek[k];
}
}
}
template <typename ConformTransformationT>
void
_computeEjkMean(const QuadratureFormula<2>& quadrature,
const ConformTransformationT& T,
const TinyVector<2>& Xj,
const double Vi,
const size_t degree,
const size_t dimension,
SmallArray<double>& inv_Vj_wq_detJ_ek,
SmallArray<double>& mean_of_ejk)
{
using Rd = TinyVector<2>;
mean_of_ejk.fill(0);
for (size_t i_q = 0; i_q < quadrature.numberOfPoints(); ++i_q) {
const double wq = quadrature.weight(i_q);
const Rd& xi_q = quadrature.point(i_q);
const double detT = [&] {
if constexpr (std::is_same_v<TriangleTransformation<2>, std::decay_t<decltype(T)>>) {
return T.jacobianDeterminant();
} else {
return T.jacobianDeterminant(xi_q);
}
}();
const Rd X_Xj = T(xi_q) - Xj;
const double x_xj = X_Xj[0];
const double y_yj = X_Xj[1];
{
size_t k = 0;
inv_Vj_wq_detJ_ek[k++] = wq * detT / Vi;
for (; k <= degree; ++k) {
inv_Vj_wq_detJ_ek[k] = x_xj * inv_Vj_wq_detJ_ek[k - 1];
}
for (size_t i_y = 1; i_y <= degree; ++i_y) {
const size_t begin_i_y_1 = ((i_y - 1) * (2 * degree - i_y + 4)) / 2;
for (size_t l = 0; l <= degree - i_y; ++l) {
inv_Vj_wq_detJ_ek[k++] = y_yj * inv_Vj_wq_detJ_ek[begin_i_y_1 + l];
}
}
}
for (size_t k = 1; k < dimension; ++k) {
mean_of_ejk[k - 1] += inv_Vj_wq_detJ_ek[k];
}
}
}
template <typename ConformTransformationT>
void
_computeEjkMean(const QuadratureFormula<3>& quadrature,
const ConformTransformationT& T,
const TinyVector<3>& Xj,
const double Vi,
const size_t degree,
const size_t dimension,
SmallArray<double>& inv_Vj_wq_detJ_ek,
SmallArray<double>& mean_of_ejk)
{
using Rd = TinyVector<3>;
mean_of_ejk.fill(0);
for (size_t i_q = 0; i_q < quadrature.numberOfPoints(); ++i_q) {
const double wq = quadrature.weight(i_q);
const Rd& xi_q = quadrature.point(i_q);
const double detT = [&] { if constexpr (std::is_same_v<TetrahedronTransformation, std::decay_t<decltype(T)>>) {
return T.jacobianDeterminant();
} else {
return T.jacobianDeterminant(xi_q);
}
}();
const Rd X_Xj = T(xi_q) - Xj;
const double x_xj = X_Xj[0];
const double y_yj = X_Xj[1];
const double z_zj = X_Xj[2];
{
size_t k = 0;
inv_Vj_wq_detJ_ek[k++] = wq * detT / Vi;
for (; k <= degree; ++k) {
inv_Vj_wq_detJ_ek[k] = x_xj * inv_Vj_wq_detJ_ek[k - 1];
}
for (size_t i_y = 1; i_y <= degree; ++i_y) {
const size_t begin_i_y_1 = ((i_y - 1) * (2 * degree - i_y + 4)) / 2;
for (size_t l = 0; l <= degree - i_y; ++l) {
inv_Vj_wq_detJ_ek[k++] = y_yj * inv_Vj_wq_detJ_ek[begin_i_y_1 + l];
}
}
for (size_t i_z = 1; i_z <= degree; ++i_z) {
const size_t begin_i_z_1 = ((i_z - 1) * (3 * (degree + 2) * (degree + 3) + (i_z - (3 * degree + 8)) * i_z)) / 6;
for (size_t i_y = 0; i_y <= degree - i_z; ++i_y) {
const size_t begin_i_y_1 = (i_y * (2 * degree - i_y + 3)) / 2 + begin_i_z_1;
for (size_t l = 0; l <= degree - i_y - i_z; ++l) {
inv_Vj_wq_detJ_ek[k++] = z_zj * inv_Vj_wq_detJ_ek[begin_i_y_1 + l];
}
}
}
}
for (size_t k = 1; k < dimension; ++k) {
mean_of_ejk[k - 1] += inv_Vj_wq_detJ_ek[k];
}
}
}
template <typename NodeListT, size_t Dimension>
void _computeEjkMean(const TinyVector<Dimension>& Xj,
const NodeValue<const TinyVector<Dimension>>& xr,
const NodeListT& node_list,
const CellType& cell_type,
const double Vi,
const size_t degree,
const size_t basis_dimension,
SmallArray<double>& inv_Vj_wq_detJ_ek,
SmallArray<double>& mean_of_ejk);
template <typename NodeListT>
void
_computeEjkMean(const TinyVector<1>& Xj,
const NodeValue<const TinyVector<1>>& xr,
const NodeListT& node_list,
const CellType& cell_type,
const double Vi,
const size_t degree,
const size_t basis_dimension,
SmallArray<double>& inv_Vj_wq_detJ_ek,
SmallArray<double>& mean_of_ejk)
{
if (cell_type == CellType::Line) {
const LineTransformation<1> T{xr[node_list[0]], xr[node_list[1]]};
const auto& quadrature = QuadratureManager::instance().getLineFormula(GaussLegendreQuadratureDescriptor{degree});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
} else {
throw NotImplementedError("unexpected cell type: " + std::string{name(cell_type)});
}
}
template <typename NodeListT>
void
_computeEjkMeanInSymmetricCell(const TinyVector<1>& origin,
const TinyVector<1>& normal,
const TinyVector<1>& Xj,
const NodeValue<const TinyVector<1>>& xr,
const NodeListT& node_list,
const CellType& cell_type,
const double Vi,
const size_t degree,
const size_t basis_dimension,
SmallArray<double>& inv_Vj_wq_detJ_ek,
SmallArray<double>& mean_of_ejk)
{
if (cell_type == CellType::Line) {
const auto x0 = symmetrize_coordinates(origin, normal, xr[node_list[1]]);
const auto x1 = symmetrize_coordinates(origin, normal, xr[node_list[0]]);
const LineTransformation<1> T{x0, x1};
const auto& quadrature = QuadratureManager::instance().getLineFormula(GaussLegendreQuadratureDescriptor{degree});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
} else {
throw NotImplementedError("unexpected cell type: " + std::string{name(cell_type)});
}
}
template <typename ConformTransformationT>
void _computeEjkBoundaryMean(const QuadratureFormula<1>& quadrature,
const ConformTransformationT& T,
const TinyVector<2>& Xj,
const double Vi,
const size_t degree,
const size_t dimension,
SmallArray<double>& inv_Vj_alpha_p_1_wq_X_prime_orth_ek,
SmallArray<double>& mean_of_ejk);
template <>
void
_computeEjkBoundaryMean(const QuadratureFormula<1>& quadrature,
const LineTransformation<2>& T,
const TinyVector<2>& Xj,
const double Vi,
const size_t degree,
const size_t dimension,
SmallArray<double>& inv_Vj_alpha_p_1_wq_X_prime_orth_ek,
SmallArray<double>& mean_of_ejk)
{
using Rd = TinyVector<2>;
const double velocity_perp_e1 = T.velocity()[1];
for (size_t i_q = 0; i_q < quadrature.numberOfPoints(); ++i_q) {
const double wq = quadrature.weight(i_q);
const TinyVector<1> xi_q = quadrature.point(i_q);
const Rd X_Xj = T(xi_q) - Xj;
const double x_xj = X_Xj[0]; const double y_yj = X_Xj[1];
{
size_t k = 0;
inv_Vj_alpha_p_1_wq_X_prime_orth_ek[k++] = x_xj * wq * velocity_perp_e1 / Vi;
for (; k <= degree; ++k) {
inv_Vj_alpha_p_1_wq_X_prime_orth_ek[k] =
x_xj * inv_Vj_alpha_p_1_wq_X_prime_orth_ek[k - 1] * ((1. * k) / (k + 1));
}
for (size_t i_y = 1; i_y <= degree; ++i_y) {
const size_t begin_i_y_1 = ((i_y - 1) * (2 * degree - i_y + 4)) / 2;
for (size_t l = 0; l <= degree - i_y; ++l) {
inv_Vj_alpha_p_1_wq_X_prime_orth_ek[k++] = y_yj * inv_Vj_alpha_p_1_wq_X_prime_orth_ek[begin_i_y_1 + l];
}
}
}
for (size_t k = 1; k < dimension; ++k) {
mean_of_ejk[k - 1] += inv_Vj_alpha_p_1_wq_X_prime_orth_ek[k];
}
}
}
template <MeshConcept MeshType>
void
_computeEjkMeanByBoundary(const MeshType& mesh,
const TinyVector<2>& Xj,
const CellId& cell_id,
const auto& cell_to_face_matrix,
const auto& face_to_node_matrix,
const auto& cell_face_is_reversed,
const CellValue<const double>& Vi,
const size_t degree,
const size_t basis_dimension,
SmallArray<double>& inv_Vj_alpha_p_1_wq_X_prime_orth_ek,
SmallArray<double>& mean_of_ejk)
{
const auto& quadrature = QuadratureManager::instance().getLineFormula(GaussLegendreQuadratureDescriptor(degree + 1));
auto xr = mesh.xr();
mean_of_ejk.fill(0);
auto cell_face_list = cell_to_face_matrix[cell_id];
for (size_t i_face = 0; i_face < cell_face_list.size(); ++i_face) {
bool is_reversed = cell_face_is_reversed[cell_id][i_face];
const FaceId face_id = cell_face_list[i_face];
auto face_node_list = face_to_node_matrix[face_id];
if (is_reversed) {
const LineTransformation<2> T{xr[face_node_list[1]], xr[face_node_list[0]]};
_computeEjkBoundaryMean(quadrature, T, Xj, Vi[cell_id], degree, basis_dimension,
inv_Vj_alpha_p_1_wq_X_prime_orth_ek, mean_of_ejk);
} else {
const LineTransformation<2> T{xr[face_node_list[0]], xr[face_node_list[1]]};
_computeEjkBoundaryMean(quadrature, T, Xj, Vi[cell_id], degree, basis_dimension,
inv_Vj_alpha_p_1_wq_X_prime_orth_ek, mean_of_ejk);
}
}
}
void
_computeEjkMeanByBoundaryInSymmetricCell(const TinyVector<2>& origin,
const TinyVector<2>& normal,
const TinyVector<2>& Xj,
const CellId& cell_id,
const NodeValue<const TinyVector<2>>& xr,
const auto& cell_to_face_matrix,
const auto& face_to_node_matrix,
const auto& cell_face_is_reversed,
const CellValue<const double>& Vi, const size_t degree,
const size_t basis_dimension,
SmallArray<double>& inv_Vj_alpha_p_1_wq_X_prime_orth_ek,
SmallArray<double>& mean_of_ejk)
{
const auto& quadrature = QuadratureManager::instance().getLineFormula(GaussLegendreQuadratureDescriptor(degree + 1));
mean_of_ejk.fill(0);
auto cell_face_list = cell_to_face_matrix[cell_id];
for (size_t i_face = 0; i_face < cell_face_list.size(); ++i_face) {
bool is_reversed = cell_face_is_reversed[cell_id][i_face];
const FaceId face_id = cell_face_list[i_face];
auto face_node_list = face_to_node_matrix[face_id];
const auto x0 = symmetrize_coordinates(origin, normal, xr[face_node_list[1]]);
const auto x1 = symmetrize_coordinates(origin, normal, xr[face_node_list[0]]);
if (is_reversed) {
const LineTransformation<2> T{x1, x0};
_computeEjkBoundaryMean(quadrature, T, Xj, Vi[cell_id], degree, basis_dimension,
inv_Vj_alpha_p_1_wq_X_prime_orth_ek, mean_of_ejk);
} else {
const LineTransformation<2> T{x0, x1};
_computeEjkBoundaryMean(quadrature, T, Xj, Vi[cell_id], degree, basis_dimension,
inv_Vj_alpha_p_1_wq_X_prime_orth_ek, mean_of_ejk);
}
}
}
template <typename NodeListT>
void
_computeEjkMean(const TinyVector<2>& Xj,
const NodeValue<const TinyVector<2>>& xr,
const NodeListT& node_list,
const CellType& cell_type,
const double Vi,
const size_t degree,
const size_t basis_dimension,
SmallArray<double>& inv_Vj_wq_detJ_ek,
SmallArray<double>& mean_of_ejk)
{
switch (cell_type) {
case CellType::Triangle: {
const TriangleTransformation<2> T{xr[node_list[0]], xr[node_list[1]], xr[node_list[2]]};
const auto& quadrature = QuadratureManager::instance().getTriangleFormula(GaussQuadratureDescriptor{degree});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
break;
}
case CellType::Quadrangle: {
const SquareTransformation<2> T{xr[node_list[0]], xr[node_list[1]], xr[node_list[2]], xr[node_list[3]]};
const auto& quadrature =
QuadratureManager::instance().getSquareFormula(GaussLegendreQuadratureDescriptor{degree + 1});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
break;
}
default: {
throw NotImplementedError("unexpected cell type: " + std::string{name(cell_type)});
}
}
}
template <typename NodeListT>
void
_computeEjkMeanInSymmetricCell(const TinyVector<2>& origin,
const TinyVector<2>& normal,
const TinyVector<2>& Xj,
const NodeValue<const TinyVector<2>>& xr, const NodeListT& node_list,
const CellType& cell_type,
const double Vi,
const size_t degree,
const size_t basis_dimension,
SmallArray<double>& inv_Vj_wq_detJ_ek,
SmallArray<double>& mean_of_ejk)
{
switch (cell_type) {
case CellType::Triangle: {
const auto x0 = symmetrize_coordinates(origin, normal, xr[node_list[2]]);
const auto x1 = symmetrize_coordinates(origin, normal, xr[node_list[1]]);
const auto x2 = symmetrize_coordinates(origin, normal, xr[node_list[0]]);
const TriangleTransformation<2> T{x0, x1, x2};
const auto& quadrature = QuadratureManager::instance().getTriangleFormula(GaussQuadratureDescriptor{degree});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
break;
}
case CellType::Quadrangle: {
const auto x0 = symmetrize_coordinates(origin, normal, xr[node_list[3]]);
const auto x1 = symmetrize_coordinates(origin, normal, xr[node_list[2]]);
const auto x2 = symmetrize_coordinates(origin, normal, xr[node_list[1]]);
const auto x3 = symmetrize_coordinates(origin, normal, xr[node_list[0]]);
const SquareTransformation<2> T{x0, x1, x2, x3};
const auto& quadrature =
QuadratureManager::instance().getSquareFormula(GaussLegendreQuadratureDescriptor{degree + 1});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
break;
}
default: {
throw NotImplementedError("unexpected cell type: " + std::string{name(cell_type)});
}
}
}
template <typename NodeListT>
void
_computeEjkMean(const TinyVector<3>& Xj,
const NodeValue<const TinyVector<3>>& xr,
const NodeListT& node_list,
const CellType& cell_type,
const double Vi,
const size_t degree,
const size_t basis_dimension,
SmallArray<double>& inv_Vj_wq_detJ_ek,
SmallArray<double>& mean_of_ejk)
{
if (cell_type == CellType::Tetrahedron) {
const TetrahedronTransformation T{xr[node_list[0]], xr[node_list[1]], xr[node_list[2]], xr[node_list[3]]};
const auto& quadrature = QuadratureManager::instance().getTetrahedronFormula(GaussQuadratureDescriptor{degree});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
} else if (cell_type == CellType::Prism) {
const PrismTransformation T{xr[node_list[0]], xr[node_list[1]], xr[node_list[2]], //
xr[node_list[3]], xr[node_list[4]], xr[node_list[5]]};
const auto& quadrature = QuadratureManager::instance().getPrismFormula(GaussQuadratureDescriptor{degree + 1});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
} else if (cell_type == CellType::Pyramid) {
const PyramidTransformation T{xr[node_list[0]], xr[node_list[1]], xr[node_list[2]], xr[node_list[3]],
xr[node_list[4]]};
const auto& quadrature = QuadratureManager::instance().getPyramidFormula(GaussQuadratureDescriptor{degree + 1});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
} else if (cell_type == CellType::Hexahedron) {
const CubeTransformation T{xr[node_list[0]], xr[node_list[1]], xr[node_list[2]], xr[node_list[3]],
xr[node_list[4]], xr[node_list[5]], xr[node_list[6]], xr[node_list[7]]};
const auto& quadrature =
QuadratureManager::instance().getCubeFormula(GaussLegendreQuadratureDescriptor{degree + 1});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
} else {
throw NotImplementedError("unexpected cell type: " + std::string{name(cell_type)});
}
}
template <typename NodeListT>
void
_computeEjkMeanInSymmetricCell(const TinyVector<3>& origin,
const TinyVector<3>& normal,
const TinyVector<3>& Xj,
const NodeValue<const TinyVector<3>>& xr,
const NodeListT& node_list,
const CellType& cell_type,
const double Vi,
const size_t degree,
const size_t basis_dimension,
SmallArray<double>& inv_Vj_wq_detJ_ek,
SmallArray<double>& mean_of_ejk)
{
if (cell_type == CellType::Tetrahedron) {
const auto x0 = symmetrize_coordinates(origin, normal, xr[node_list[1]]);
const auto x1 = symmetrize_coordinates(origin, normal, xr[node_list[0]]);
const auto x2 = symmetrize_coordinates(origin, normal, xr[node_list[2]]);
const auto x3 = symmetrize_coordinates(origin, normal, xr[node_list[3]]);
const TetrahedronTransformation T{x0, x1, x2, x3};
const auto& quadrature = QuadratureManager::instance().getTetrahedronFormula(GaussQuadratureDescriptor{degree});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
} else if (cell_type == CellType::Prism) {
const auto x0 = symmetrize_coordinates(origin, normal, xr[node_list[1]]);
const auto x1 = symmetrize_coordinates(origin, normal, xr[node_list[0]]);
const auto x2 = symmetrize_coordinates(origin, normal, xr[node_list[2]]);
const auto x3 = symmetrize_coordinates(origin, normal, xr[node_list[4]]);
const auto x4 = symmetrize_coordinates(origin, normal, xr[node_list[3]]);
const auto x5 = symmetrize_coordinates(origin, normal, xr[node_list[5]]);
const PrismTransformation T{x0, x1, x2, //
x3, x4, x5};
const auto& quadrature = QuadratureManager::instance().getPrismFormula(GaussQuadratureDescriptor{degree + 1});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
} else if (cell_type == CellType::Pyramid) {
const auto x0 = symmetrize_coordinates(origin, normal, xr[node_list[3]]);
const auto x1 = symmetrize_coordinates(origin, normal, xr[node_list[2]]);
const auto x2 = symmetrize_coordinates(origin, normal, xr[node_list[1]]);
const auto x3 = symmetrize_coordinates(origin, normal, xr[node_list[0]]);
const auto x4 = symmetrize_coordinates(origin, normal, xr[node_list[4]]);
const PyramidTransformation T{x0, x1, x2, x3, x4};
const auto& quadrature = QuadratureManager::instance().getPyramidFormula(GaussQuadratureDescriptor{degree + 1});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
} else if (cell_type == CellType::Hexahedron) {
const auto x0 = symmetrize_coordinates(origin, normal, xr[node_list[3]]);
const auto x1 = symmetrize_coordinates(origin, normal, xr[node_list[2]]);
const auto x2 = symmetrize_coordinates(origin, normal, xr[node_list[1]]);
const auto x3 = symmetrize_coordinates(origin, normal, xr[node_list[0]]);
const auto x4 = symmetrize_coordinates(origin, normal, xr[node_list[7]]);
const auto x5 = symmetrize_coordinates(origin, normal, xr[node_list[6]]);
const auto x6 = symmetrize_coordinates(origin, normal, xr[node_list[5]]);
const auto x7 = symmetrize_coordinates(origin, normal, xr[node_list[4]]);
const CubeTransformation T{x0, x1, x2, x3, x4, x5, x6, x7};
const auto& quadrature =
QuadratureManager::instance().getCubeFormula(GaussLegendreQuadratureDescriptor{degree + 1});
_computeEjkMean(quadrature, T, Xj, Vi, degree, basis_dimension, inv_Vj_wq_detJ_ek, mean_of_ejk);
} else {
throw NotImplementedError("unexpected cell type: " + std::string{name(cell_type)});
}
}
size_t
PolynomialReconstruction::_getNumberOfColumns(
const std::vector<std::shared_ptr<const DiscreteFunctionVariant>>& discrete_function_variant_list) const
{
size_t number_of_columns = 0;
for (auto discrete_function_variant_p : discrete_function_variant_list) {
number_of_columns += std::visit(
[](auto&& discrete_function) -> size_t {
using DiscreteFunctionT = std::decay_t<decltype(discrete_function)>;
if constexpr (is_discrete_function_P0_v<DiscreteFunctionT>) {
using data_type = std::decay_t<typename DiscreteFunctionT::data_type>;
if constexpr (std::is_arithmetic_v<data_type>) {
return 1;
} else if constexpr (is_tiny_vector_v<data_type> or is_tiny_matrix_v<data_type>) {
return data_type::Dimension;
} else {
// LCOV_EXCL_START
throw UnexpectedError("unexpected data type " + demangle<data_type>());
// LCOV_EXCL_STOP
}
} else if constexpr (is_discrete_function_P0_vector_v<DiscreteFunctionT>) {
using data_type = std::decay_t<typename DiscreteFunctionT::data_type>;
if constexpr (std::is_arithmetic_v<data_type>) {
return discrete_function.size();
} else if constexpr (is_tiny_vector_v<data_type> or is_tiny_matrix_v<data_type>) {
return discrete_function.size() * data_type::Dimension;
} else {
// LCOV_EXCL_START
throw UnexpectedError("unexpected data type " + demangle<data_type>());
// LCOV_EXCL_STOP
}
} else {
// LCOV_EXCL_START
throw UnexpectedError("unexpected discrete function type");
// LCOV_EXCL_STOP
}
},
discrete_function_variant_p->discreteFunction());
}
return number_of_columns;
}
template <MeshConcept MeshType>
std::vector<PolynomialReconstruction::MutableDiscreteFunctionDPkVariant>
PolynomialReconstruction::_createMutableDiscreteFunctionDPKVariantList(
const std::shared_ptr<const MeshType>& p_mesh,
const std::vector<std::shared_ptr<const DiscreteFunctionVariant>>& discrete_function_variant_list) const{
std::vector<MutableDiscreteFunctionDPkVariant> mutable_discrete_function_dpk_variant_list;
for (size_t i_discrete_function_variant = 0; i_discrete_function_variant < discrete_function_variant_list.size();
++i_discrete_function_variant) {
auto discrete_function_variant = discrete_function_variant_list[i_discrete_function_variant];
std::visit(
[&](auto&& discrete_function) {
using DiscreteFunctionT = std::decay_t<decltype(discrete_function)>;
if constexpr (is_discrete_function_P0_v<DiscreteFunctionT>) {
using DataType = std::remove_const_t<std::decay_t<typename DiscreteFunctionT::data_type>>;
mutable_discrete_function_dpk_variant_list.push_back(
DiscreteFunctionDPk<MeshType::Dimension, DataType>(p_mesh, m_descriptor.degree()));
} else if constexpr (is_discrete_function_P0_vector_v<DiscreteFunctionT>) {
using DataType = std::remove_const_t<std::decay_t<typename DiscreteFunctionT::data_type>>;
mutable_discrete_function_dpk_variant_list.push_back(
DiscreteFunctionDPkVector<MeshType::Dimension, DataType>(p_mesh, m_descriptor.degree(),
discrete_function.size()));
} else {
// LCOV_EXCL_START
throw UnexpectedError("unexpected discrete function type");
// LCOV_EXCL_STOP
}
},
discrete_function_variant->discreteFunction());
}
return mutable_discrete_function_dpk_variant_list;
}
template <MeshConcept MeshType>
void
PolynomialReconstruction::_checkDataAndSymmetriesCompatibility(
const std::vector<std::shared_ptr<const DiscreteFunctionVariant>>& discrete_function_variant_list) const
{
for (auto&& discrete_function_variant : discrete_function_variant_list) {
std::visit(
[&](auto&& discrete_function) {
using DiscreteFunctionT = std::decay_t<decltype(discrete_function)>;
if constexpr (is_discrete_function_P0_v<DiscreteFunctionT> or
is_discrete_function_P0_vector_v<DiscreteFunctionT>) {
using DataType = std::decay_t<typename DiscreteFunctionT::data_type>;
if constexpr (is_tiny_vector_v<DataType>) {
if constexpr (DataType::Dimension != MeshType::Dimension) {
std::stringstream error_msg;
error_msg << "cannot symmetrize vectors of dimension " << DataType::Dimension
<< " using a mesh of dimension " << MeshType::Dimension;
throw NormalError(error_msg.str());
}
} else if constexpr (is_tiny_matrix_v<DataType>) {
if constexpr ((DataType::NumberOfRows != MeshType::Dimension) or
(DataType::NumberOfColumns != MeshType::Dimension)) {
std::stringstream error_msg;
error_msg << "cannot symmetrize matrices of dimensions " << DataType::NumberOfRows << 'x'
<< DataType::NumberOfColumns << " using a mesh of dimension " << MeshType::Dimension;
throw NormalError(error_msg.str());
}
}
} else {
// LCOV_EXCL_START
throw UnexpectedError("invalid discrete function type");
// LCOV_EXCL_STOP
}
},
discrete_function_variant->discreteFunction());
}
}
template <MeshConcept MeshType>
[[nodiscard]] std::vector<std::shared_ptr<const DiscreteFunctionDPkVariant>>PolynomialReconstruction::_build(
const std::shared_ptr<const MeshType>& p_mesh,
const std::vector<std::shared_ptr<const DiscreteFunctionVariant>>& discrete_function_variant_list) const
{
const MeshType& mesh = *p_mesh;
using Rd = TinyVector<MeshType::Dimension>;
if (m_descriptor.symmetryBoundaryDescriptorList().size() > 0) {
this->_checkDataAndSymmetriesCompatibility<MeshType>(discrete_function_variant_list);
}
const size_t number_of_columns = this->_getNumberOfColumns(discrete_function_variant_list);
const size_t basis_dimension =
DiscreteFunctionDPk<MeshType::Dimension, double>::BasisViewType::dimensionFromDegree(m_descriptor.degree());
const auto& stencil_array =
StencilManager::instance().getCellToCellStencilArray(mesh.connectivity(), m_descriptor.stencilDescriptor(),
m_descriptor.symmetryBoundaryDescriptorList());
auto xr = mesh.xr();
auto xj = MeshDataManager::instance().getMeshData(mesh).xj();
auto Vj = MeshDataManager::instance().getMeshData(mesh).Vj();
auto cell_is_owned = mesh.connectivity().cellIsOwned();
auto cell_type = mesh.connectivity().cellType();
auto cell_to_node_matrix = mesh.connectivity().cellToNodeMatrix();
auto cell_to_face_matrix = mesh.connectivity().cellToFaceMatrix();
auto full_stencil_size = [&](const CellId cell_id) {
auto stencil_cell_list = stencil_array[cell_id];
size_t stencil_size = stencil_cell_list.size();
for (size_t i = 0; i < m_descriptor.symmetryBoundaryDescriptorList().size(); ++i) {
auto& ghost_stencil = stencil_array.symmetryBoundaryStencilArrayList()[i].stencilArray();
stencil_size += ghost_stencil[cell_id].size();
}
return stencil_size;
};
const size_t max_stencil_size = [&]() {
size_t max_size = 0;
for (CellId cell_id = 0; cell_id < mesh.numberOfCells(); ++cell_id) {
const size_t stencil_size = full_stencil_size(cell_id);
if (cell_is_owned[cell_id] and stencil_size > max_size) {
max_size = stencil_size;
}
}
return max_size;
}();
SmallArray<const Rd> symmetry_normal_list = [&] {
SmallArray<Rd> normal_list(m_descriptor.symmetryBoundaryDescriptorList().size());
size_t i_symmetry_boundary = 0;
for (auto p_boundary_descriptor : m_descriptor.symmetryBoundaryDescriptorList()) {
const IBoundaryDescriptor& boundary_descriptor = *p_boundary_descriptor;
auto symmetry_boundary = getMeshFlatFaceBoundary(mesh, boundary_descriptor);
normal_list[i_symmetry_boundary++] = symmetry_boundary.outgoingNormal();
}
return normal_list;
}();
SmallArray<const Rd> symmetry_origin_list = [&] {
SmallArray<Rd> origin_list(m_descriptor.symmetryBoundaryDescriptorList().size());
size_t i_symmetry_boundary = 0;
for (auto p_boundary_descriptor : m_descriptor.symmetryBoundaryDescriptorList()) {
const IBoundaryDescriptor& boundary_descriptor = *p_boundary_descriptor;
auto symmetry_boundary = getMeshFlatFaceBoundary(mesh, boundary_descriptor);
origin_list[i_symmetry_boundary++] = symmetry_boundary.origin();
}
return origin_list;
}();
Kokkos::Experimental::UniqueToken<Kokkos::DefaultExecutionSpace::execution_space,
Kokkos::Experimental::UniqueTokenScope::Global>
tokens;
auto mutable_discrete_function_dpk_variant_list =
this->_createMutableDiscreteFunctionDPKVariantList(p_mesh, discrete_function_variant_list);
SmallArray<SmallMatrix<double>> A_pool(Kokkos::DefaultExecutionSpace::concurrency());
SmallArray<SmallMatrix<double>> B_pool(Kokkos::DefaultExecutionSpace::concurrency());
SmallArray<SmallVector<double>> G_pool(Kokkos::DefaultExecutionSpace::concurrency());
SmallArray<SmallMatrix<double>> X_pool(Kokkos::DefaultExecutionSpace::concurrency());
SmallArray<SmallArray<double>> inv_Vj_wq_detJ_ek_pool(Kokkos::DefaultExecutionSpace::concurrency());
SmallArray<SmallArray<double>> mean_j_of_ejk_pool(Kokkos::DefaultExecutionSpace::concurrency());
SmallArray<SmallArray<double>> mean_i_of_ejk_pool(Kokkos::DefaultExecutionSpace::concurrency());
SmallArray<SmallArray<double>> inv_Vj_alpha_p_1_wq_X_prime_orth_ek_pool(Kokkos::DefaultExecutionSpace::concurrency());
SmallArray<SmallArray<double>> mean_l_of_ejk_pool(Kokkos::DefaultExecutionSpace::concurrency());
for (size_t i = 0; i < A_pool.size(); ++i) {
A_pool[i] = SmallMatrix<double>(max_stencil_size, basis_dimension - 1);
B_pool[i] = SmallMatrix<double>(max_stencil_size, number_of_columns);
G_pool[i] = SmallVector<double>(basis_dimension - 1);
X_pool[i] = SmallMatrix<double>(basis_dimension - 1, number_of_columns);
inv_Vj_wq_detJ_ek_pool[i] = SmallArray<double>(basis_dimension);
mean_j_of_ejk_pool[i] = SmallArray<double>(basis_dimension - 1);
mean_i_of_ejk_pool[i] = SmallArray<double>(basis_dimension - 1);
inv_Vj_alpha_p_1_wq_X_prime_orth_ek_pool[i] = SmallArray<double>(basis_dimension);
}
parallel_for(
mesh.numberOfCells(), PUGS_CLASS_LAMBDA(const CellId cell_j_id) {
if (cell_is_owned[cell_j_id]) {
const int32_t t = tokens.acquire();
auto stencil_cell_list = stencil_array[cell_j_id];
ShrinkMatrixView B(B_pool[t], full_stencil_size(cell_j_id));
size_t column_begin = 0;
for (size_t i_discrete_function_variant = 0;
i_discrete_function_variant < discrete_function_variant_list.size(); ++i_discrete_function_variant) {
const auto& discrete_function_variant = discrete_function_variant_list[i_discrete_function_variant];
std::visit(
[&](auto&& discrete_function) {
using DiscreteFunctionT = std::decay_t<decltype(discrete_function)>;
if constexpr (is_discrete_function_P0_v<DiscreteFunctionT>) {
using DataType = std::decay_t<typename DiscreteFunctionT::data_type>;
const DataType& qj = discrete_function[cell_j_id];
size_t index = 0;
for (size_t i = 0; i < stencil_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = stencil_cell_list[i];
const DataType& qi_qj = discrete_function[cell_i_id] - qj;
if constexpr (std::is_arithmetic_v<DataType>) {
B(index, column_begin) = qi_qj;
} else if constexpr (is_tiny_vector_v<DataType>) {
for (size_t kB = column_begin, k = 0; k < DataType::Dimension; ++k, ++kB) {
B(index, kB) = qi_qj[k];
}
} else if constexpr (is_tiny_matrix_v<DataType>) {
for (size_t k = 0; k < DataType::NumberOfRows; ++k) { for (size_t l = 0; l < DataType::NumberOfColumns; ++l) {
B(index, column_begin + k * DataType::NumberOfColumns + l) = qi_qj(k, l);
}
}
}
}
for (size_t i_symmetry = 0; i_symmetry < stencil_array.symmetryBoundaryStencilArrayList().size();
++i_symmetry) {
auto& ghost_stencil = stencil_array.symmetryBoundaryStencilArrayList()[i_symmetry].stencilArray();
auto ghost_cell_list = ghost_stencil[cell_j_id];
for (size_t i = 0; i < ghost_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = ghost_cell_list[i];
if constexpr (std::is_arithmetic_v<DataType>) {
const DataType& qi_qj = discrete_function[cell_i_id] - qj;
B(index, column_begin) = qi_qj;
} else if constexpr (is_tiny_vector_v<DataType>) {
if constexpr (DataType::Dimension == MeshType::Dimension) {
const Rd& normal = symmetry_normal_list[i_symmetry];
const DataType& qi = discrete_function[cell_i_id];
const DataType& qi_qj = symmetrize_vector(normal, qi) - qj;
for (size_t kB = column_begin, k = 0; k < DataType::Dimension; ++k, ++kB) {
B(index, kB) = qi_qj[k];
}
} else {
// LCOV_EXCL_START
std::stringstream error_msg;
error_msg << "cannot symmetrize vectors of dimension " << DataType::Dimension
<< " using a mesh of dimension " << MeshType::Dimension;
throw UnexpectedError(error_msg.str());
// LCOV_EXCL_STOP
}
} else if constexpr (is_tiny_matrix_v<DataType>) {
if constexpr ((DataType::NumberOfColumns == DataType::NumberOfRows) and
(DataType::NumberOfColumns == MeshType::Dimension)) {
const Rd& normal = symmetry_normal_list[i_symmetry];
const DataType& qi = discrete_function[cell_i_id];
const DataType& qi_qj = symmetrize_matrix(normal, qi) - qj;
for (size_t k = 0; k < DataType::NumberOfRows; ++k) {
for (size_t l = 0; l < DataType::NumberOfColumns; ++l) {
B(index, column_begin + k * DataType::NumberOfColumns + l) = qi_qj(k, l);
}
}
} else {
// LCOV_EXCL_START
std::stringstream error_msg;
error_msg << "cannot symmetrize matrices of dimensions " << DataType::NumberOfRows << 'x'
<< DataType::NumberOfColumns << " using a mesh of dimension " << MeshType::Dimension;
throw UnexpectedError(error_msg.str());
// LCOV_EXCL_STOP
}
}
}
}
if constexpr (std::is_arithmetic_v<DataType>) {
++column_begin;
} else if constexpr (is_tiny_vector_v<DataType> or is_tiny_matrix_v<DataType>) {
column_begin += DataType::Dimension;
}
} else if constexpr (is_discrete_function_P0_vector_v<DiscreteFunctionT>) {
using DataType = std::decay_t<typename DiscreteFunctionT::data_type>;
const auto qj_vector = discrete_function[cell_j_id];
if constexpr (std::is_arithmetic_v<DataType>) {
size_t index = 0;
for (size_t i = 0; i < stencil_cell_list.size(); ++i, ++index) { const CellId cell_i_id = stencil_cell_list[i];
for (size_t l = 0; l < qj_vector.size(); ++l) {
const DataType& qj = qj_vector[l];
const DataType& qi_qj = discrete_function[cell_i_id][l] - qj;
B(index, column_begin + l) = qi_qj;
}
}
for (size_t i_symmetry = 0; i_symmetry < stencil_array.symmetryBoundaryStencilArrayList().size();
++i_symmetry) {
auto& ghost_stencil = stencil_array.symmetryBoundaryStencilArrayList()[i_symmetry].stencilArray();
auto ghost_cell_list = ghost_stencil[cell_j_id];
for (size_t i = 0; i < ghost_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = ghost_cell_list[i];
for (size_t l = 0; l < qj_vector.size(); ++l) {
const DataType& qj = qj_vector[l];
const DataType& qi_qj = discrete_function[cell_i_id][l] - qj;
B(index, column_begin + l) = qi_qj;
}
}
}
} else if constexpr (is_tiny_vector_v<DataType>) {
size_t index = 0;
for (size_t i = 0; i < stencil_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = stencil_cell_list[i];
for (size_t l = 0; l < qj_vector.size(); ++l) {
const DataType& qj = qj_vector[l];
const DataType& qi_qj = discrete_function[cell_i_id][l] - qj;
for (size_t kB = column_begin + l * DataType::Dimension, k = 0; k < DataType::Dimension;
++k, ++kB) {
B(index, kB) = qi_qj[k];
}
}
}
for (size_t i_symmetry = 0; i_symmetry < stencil_array.symmetryBoundaryStencilArrayList().size();
++i_symmetry) {
if constexpr (DataType::Dimension == MeshType::Dimension) {
auto& ghost_stencil = stencil_array.symmetryBoundaryStencilArrayList()[i_symmetry].stencilArray();
auto ghost_cell_list = ghost_stencil[cell_j_id];
const Rd& normal = symmetry_normal_list[i_symmetry];
for (size_t i = 0; i < ghost_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = ghost_cell_list[i];
for (size_t l = 0; l < qj_vector.size(); ++l) {
const DataType& qj = qj_vector[l];
const DataType& qi = discrete_function[cell_i_id][l];
const DataType& qi_qj = symmetrize_vector(normal, qi) - qj;
for (size_t kB = column_begin + l * DataType::Dimension, k = 0; k < DataType::Dimension;
++k, ++kB) {
B(index, kB) = qi_qj[k];
}
}
}
} else {
// LCOV_EXCL_START
std::stringstream error_msg;
error_msg << "cannot symmetrize vectors of dimension " << DataType::Dimension
<< " using a mesh of dimension " << MeshType::Dimension;
throw UnexpectedError(error_msg.str());
// LCOV_EXCL_STOP
}
}
} else if constexpr (is_tiny_matrix_v<DataType>) {
for (size_t i_symmetry = 0; i_symmetry < stencil_array.symmetryBoundaryStencilArrayList().size();
++i_symmetry) {
auto& ghost_stencil = stencil_array.symmetryBoundaryStencilArrayList()[i_symmetry].stencilArray();
auto ghost_cell_list = ghost_stencil[cell_j_id]; if (ghost_cell_list.size() > 0) {
throw NotImplementedError("TinyMatrix symmetries for reconstruction of DiscreteFunctionP0Vector");
}
}
}
if constexpr (std::is_arithmetic_v<DataType>) {
column_begin += qj_vector.size();
} else if constexpr (is_tiny_vector_v<DataType> or is_tiny_matrix_v<DataType>) {
column_begin += qj_vector.size() * DataType::Dimension;
}
} else {
// LCOV_EXCL_START
throw UnexpectedError("invalid discrete function type");
// LCOV_EXCL_STOP
}
},
discrete_function_variant->discreteFunction());
}
ShrinkMatrixView A(A_pool[t], full_stencil_size(cell_j_id));
if ((m_descriptor.degree() == 1) and
(m_descriptor.integrationMethodType() == IntegrationMethodType::cell_center)) {
const Rd& Xj = xj[cell_j_id];
size_t index = 0;
for (size_t i = 0; i < stencil_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = stencil_cell_list[i];
const Rd Xi_Xj = xj[cell_i_id] - Xj;
for (size_t l = 0; l < basis_dimension - 1; ++l) {
A(index, l) = Xi_Xj[l];
}
}
for (size_t i_symmetry = 0; i_symmetry < stencil_array.symmetryBoundaryStencilArrayList().size();
++i_symmetry) {
auto& ghost_stencil = stencil_array.symmetryBoundaryStencilArrayList()[i_symmetry].stencilArray();
auto ghost_cell_list = ghost_stencil[cell_j_id];
const Rd& origin = symmetry_origin_list[i_symmetry];
const Rd& normal = symmetry_normal_list[i_symmetry];
for (size_t i = 0; i < ghost_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = ghost_cell_list[i];
const Rd Xi_Xj = symmetrize_coordinates(origin, normal, xj[cell_i_id]) - Xj;
for (size_t l = 0; l < basis_dimension - 1; ++l) {
A(index, l) = Xi_Xj[l];
}
}
}
} else if ((m_descriptor.integrationMethodType() == IntegrationMethodType::element) or
(m_descriptor.integrationMethodType() == IntegrationMethodType::boundary)) {
if ((m_descriptor.integrationMethodType() == IntegrationMethodType::boundary) and
(MeshType::Dimension == 2)) {
if constexpr (MeshType::Dimension == 2) {
SmallArray<double>& inv_Vj_alpha_p_1_wq_X_prime_orth_ek = inv_Vj_alpha_p_1_wq_X_prime_orth_ek_pool[t];
SmallArray<double>& mean_j_of_ejk = mean_j_of_ejk_pool[t];
SmallArray<double>& mean_i_of_ejk = mean_i_of_ejk_pool[t];
auto face_to_node_matrix = p_mesh->connectivity().faceToNodeMatrix();
auto cell_face_is_reversed = p_mesh->connectivity().cellFaceIsReversed();
const Rd& Xj = xj[cell_j_id];
_computeEjkMeanByBoundary(*p_mesh, Xj, cell_j_id, cell_to_face_matrix, face_to_node_matrix,
cell_face_is_reversed, Vj, m_descriptor.degree(), basis_dimension,
inv_Vj_alpha_p_1_wq_X_prime_orth_ek, mean_j_of_ejk);
size_t index = 0;
for (size_t i = 0; i < stencil_cell_list.size(); ++i, ++index) { const CellId cell_i_id = stencil_cell_list[i];
_computeEjkMeanByBoundary(*p_mesh, Xj, cell_i_id, cell_to_face_matrix, face_to_node_matrix,
cell_face_is_reversed, Vj, m_descriptor.degree(), basis_dimension,
inv_Vj_alpha_p_1_wq_X_prime_orth_ek, mean_i_of_ejk);
for (size_t l = 0; l < basis_dimension - 1; ++l) {
A(index, l) = mean_i_of_ejk[l] - mean_j_of_ejk[l];
}
}
for (size_t i_symmetry = 0; i_symmetry < stencil_array.symmetryBoundaryStencilArrayList().size();
++i_symmetry) {
auto& ghost_stencil = stencil_array.symmetryBoundaryStencilArrayList()[i_symmetry].stencilArray();
auto ghost_cell_list = ghost_stencil[cell_j_id];
const Rd& origin = symmetry_origin_list[i_symmetry];
const Rd& normal = symmetry_normal_list[i_symmetry];
for (size_t i = 0; i < ghost_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = ghost_cell_list[i];
_computeEjkMeanByBoundaryInSymmetricCell(origin, normal, //
Xj, cell_i_id, xr, cell_to_face_matrix, face_to_node_matrix,
cell_face_is_reversed, Vj, m_descriptor.degree(),
basis_dimension, inv_Vj_alpha_p_1_wq_X_prime_orth_ek,
mean_i_of_ejk);
for (size_t l = 0; l < basis_dimension - 1; ++l) {
A(index, l) = mean_i_of_ejk[l] - mean_j_of_ejk[l];
}
}
}
} else {
throw UnexpectedError("invalid mesh dimension");
}
} else {
SmallArray<double>& inv_Vj_wq_detJ_ek = inv_Vj_wq_detJ_ek_pool[t];
SmallArray<double>& mean_j_of_ejk = mean_j_of_ejk_pool[t];
SmallArray<double>& mean_i_of_ejk = mean_i_of_ejk_pool[t];
const Rd& Xj = xj[cell_j_id];
_computeEjkMean(Xj, xr, cell_to_node_matrix[cell_j_id], cell_type[cell_j_id], Vj[cell_j_id],
m_descriptor.degree(), basis_dimension, inv_Vj_wq_detJ_ek, mean_j_of_ejk);
size_t index = 0;
for (size_t i = 0; i < stencil_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = stencil_cell_list[i];
_computeEjkMean(Xj, xr, cell_to_node_matrix[cell_i_id], cell_type[cell_i_id], Vj[cell_i_id],
m_descriptor.degree(), basis_dimension, inv_Vj_wq_detJ_ek, mean_i_of_ejk);
for (size_t l = 0; l < basis_dimension - 1; ++l) {
A(index, l) = mean_i_of_ejk[l] - mean_j_of_ejk[l];
}
}
for (size_t i_symmetry = 0; i_symmetry < stencil_array.symmetryBoundaryStencilArrayList().size();
++i_symmetry) {
auto& ghost_stencil = stencil_array.symmetryBoundaryStencilArrayList()[i_symmetry].stencilArray();
auto ghost_cell_list = ghost_stencil[cell_j_id];
const Rd& origin = symmetry_origin_list[i_symmetry];
const Rd& normal = symmetry_normal_list[i_symmetry];
for (size_t i = 0; i < ghost_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = ghost_cell_list[i];
_computeEjkMeanInSymmetricCell(origin, normal, //
Xj, xr, cell_to_node_matrix[cell_i_id], cell_type[cell_i_id],
Vj[cell_i_id], m_descriptor.degree(), basis_dimension, inv_Vj_wq_detJ_ek, mean_i_of_ejk);
for (size_t l = 0; l < basis_dimension - 1; ++l) {
A(index, l) = mean_i_of_ejk[l] - mean_j_of_ejk[l];
}
}
}
}
} else {
throw UnexpectedError("invalid integration strategy");
}
if (m_descriptor.rowWeighting()) {
// Add row weighting (give more importance to cells that are
// closer to j)
const Rd& Xj = xj[cell_j_id];
size_t index = 0;
for (size_t i = 0; i < stencil_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = stencil_cell_list[i];
const double weight = 1. / l2Norm(xj[cell_i_id] - Xj);
for (size_t l = 0; l < basis_dimension - 1; ++l) {
A(index, l) *= weight;
}
for (size_t l = 0; l < number_of_columns; ++l) {
B(index, l) *= weight;
}
}
for (size_t i_symmetry = 0; i_symmetry < stencil_array.symmetryBoundaryStencilArrayList().size();
++i_symmetry) {
auto& ghost_stencil = stencil_array.symmetryBoundaryStencilArrayList()[i_symmetry].stencilArray();
auto ghost_cell_list = ghost_stencil[cell_j_id];
const Rd& origin = symmetry_origin_list[i_symmetry];
const Rd& normal = symmetry_normal_list[i_symmetry];
for (size_t i = 0; i < ghost_cell_list.size(); ++i, ++index) {
const CellId cell_i_id = ghost_cell_list[i];
const double weight = 1. / l2Norm(symmetrize_coordinates(origin, normal, xj[cell_i_id]) - Xj);
for (size_t l = 0; l < basis_dimension - 1; ++l) {
A(index, l) *= weight;
}
for (size_t l = 0; l < number_of_columns; ++l) {
B(index, l) *= weight;
}
}
}
}
const SmallMatrix<double>& X = X_pool[t];
if (m_descriptor.preconditioning()) {
// Add column weighting preconditioning (increase the presition)
SmallVector<double>& G = G_pool[t];
for (size_t l = 0; l < A.numberOfColumns(); ++l) {
double g = 0;
for (size_t i = 0; i < A.numberOfRows(); ++i) {
const double Ail = A(i, l);
g += Ail * Ail;
}
G[l] = std::sqrt(g);
}
for (size_t l = 0; l < A.numberOfColumns(); ++l) {
const double Gl = G[l];
for (size_t i = 0; i < A.numberOfRows(); ++i) {
A(i, l) *= Gl;
} }
Givens::solveCollectionInPlace(A, X, B);
for (size_t l = 0; l < X.numberOfRows(); ++l) {
const double Gl = G[l];
for (size_t i = 0; i < X.numberOfColumns(); ++i) {
X(l, i) *= Gl;
}
}
} else {
Givens::solveCollectionInPlace(A, X, B);
}
column_begin = 0;
for (size_t i_dpk_variant = 0; i_dpk_variant < mutable_discrete_function_dpk_variant_list.size();
++i_dpk_variant) {
const auto& dpk_variant = mutable_discrete_function_dpk_variant_list[i_dpk_variant];
const auto& discrete_function_variant = discrete_function_variant_list[i_dpk_variant];
std::visit(
[&](auto&& dpk_function, auto&& p0_function) {
using DPkFunctionT = std::decay_t<decltype(dpk_function)>;
using P0FunctionT = std::decay_t<decltype(p0_function)>;
using DataType = std::remove_const_t<std::decay_t<typename DPkFunctionT::data_type>>;
using P0DataType = std::remove_const_t<std::decay_t<typename P0FunctionT::data_type>>;
if constexpr (std::is_same_v<DataType, P0DataType>) {
if constexpr (is_discrete_function_P0_v<P0FunctionT>) {
if constexpr (is_discrete_function_dpk_scalar_v<DPkFunctionT>) {
auto dpk_j = dpk_function.coefficients(cell_j_id);
dpk_j[0] = p0_function[cell_j_id];
if constexpr (std::is_arithmetic_v<DataType>) {
if (m_descriptor.degree() > 1) {
auto& mean_j_of_ejk = mean_j_of_ejk_pool[t];
for (size_t i = 0; i < basis_dimension - 1; ++i) {
dpk_j[0] -= X(i, column_begin) * mean_j_of_ejk[i];
}
}
for (size_t i = 0; i < basis_dimension - 1; ++i) {
auto& dpk_j_ip1 = dpk_j[i + 1];
dpk_j_ip1 = X(i, column_begin);
}
++column_begin;
} else if constexpr (is_tiny_vector_v<DataType>) {
if (m_descriptor.degree() > 1) {
auto& mean_j_of_ejk = mean_j_of_ejk_pool[t];
for (size_t i = 0; i < basis_dimension - 1; ++i) {
auto& dpk_j_0 = dpk_j[0];
for (size_t k = 0; k < DataType::Dimension; ++k) {
dpk_j_0[k] -= X(i, column_begin + k) * mean_j_of_ejk[i];
}
}
}
for (size_t i = 0; i < basis_dimension - 1; ++i) {
auto& dpk_j_ip1 = dpk_j[i + 1];
for (size_t k = 0; k < DataType::Dimension; ++k) {
dpk_j_ip1[k] = X(i, column_begin + k);
}
}
column_begin += DataType::Dimension;
} else if constexpr (is_tiny_matrix_v<DataType>) {
if (m_descriptor.degree() > 1) {
auto& mean_j_of_ejk = mean_j_of_ejk_pool[t];
for (size_t i = 0; i < basis_dimension - 1; ++i) {
auto& dpk_j_0 = dpk_j[0]; for (size_t k = 0; k < DataType::NumberOfRows; ++k) {
for (size_t l = 0; l < DataType::NumberOfColumns; ++l) {
dpk_j_0(k, l) -=
X(i, column_begin + k * DataType::NumberOfColumns + l) * mean_j_of_ejk[i];
}
}
}
}
for (size_t i = 0; i < basis_dimension - 1; ++i) {
auto& dpk_j_ip1 = dpk_j[i + 1];
for (size_t k = 0; k < DataType::NumberOfRows; ++k) {
for (size_t l = 0; l < DataType::NumberOfColumns; ++l) {
dpk_j_ip1(k, l) = X(i, column_begin + k * DataType::NumberOfColumns + l);
}
}
}
column_begin += DataType::Dimension;
} else {
// LCOV_EXCL_START
throw UnexpectedError("unexpected data type");
// LCOV_EXCL_STOP
}
} else {
// LCOV_EXCL_START
throw UnexpectedError("unexpected discrete dpk function type");
// LCOV_EXCL_STOP
}
} else if constexpr (is_discrete_function_P0_vector_v<P0FunctionT>) {
if constexpr (is_discrete_function_dpk_vector_v<DPkFunctionT>) {
auto dpk_j = dpk_function.coefficients(cell_j_id);
auto cell_vector = p0_function[cell_j_id];
const size_t size = basis_dimension;
for (size_t l = 0; l < cell_vector.size(); ++l) {
const size_t component_begin = l * size;
dpk_j[component_begin] = cell_vector[l];
if constexpr (std::is_arithmetic_v<DataType>) {
if (m_descriptor.degree() > 1) {
auto& mean_j_of_ejk = mean_j_of_ejk_pool[t];
for (size_t i = 0; i < basis_dimension - 1; ++i) {
dpk_j[component_begin] -= X(i, column_begin) * mean_j_of_ejk[i];
}
}
for (size_t i = 0; i < basis_dimension - 1; ++i) {
auto& dpk_j_ip1 = dpk_j[component_begin + i + 1];
dpk_j_ip1 = X(i, column_begin);
}
++column_begin;
} else if constexpr (is_tiny_vector_v<DataType>) {
if (m_descriptor.degree() > 1) {
auto& mean_j_of_ejk = mean_j_of_ejk_pool[t];
for (size_t i = 0; i < basis_dimension - 1; ++i) {
auto& dpk_j_0 = dpk_j[0];
for (size_t k = 0; k < DataType::Dimension; ++k) {
dpk_j_0[k] -= X(i, column_begin + k) * mean_j_of_ejk[i];
}
}
}
for (size_t i = 0; i < basis_dimension - 1; ++i) {
auto& dpk_j_ip1 = dpk_j[component_begin + i + 1];
for (size_t k = 0; k < DataType::Dimension; ++k) {
dpk_j_ip1[k] = X(i, column_begin + k);
}
}
column_begin += DataType::Dimension;
} else {
// LCOV_EXCL_START throw UnexpectedError("unexpected data type");
// LCOV_EXCL_STOP
}
}
} else {
// LCOV_EXCL_START
throw UnexpectedError("unexpected discrete dpk function type");
// LCOV_EXCL_STOP
}
} else {
// LCOV_EXCL_START
throw UnexpectedError("unexpected discrete function type");
// LCOV_EXCL_STOP
}
} else {
// LCOV_EXCL_START
throw UnexpectedError("incompatible data types");
// LCOV_EXCL_STOP
}
},
dpk_variant.mutableDiscreteFunctionDPk(), discrete_function_variant->discreteFunction());
}
tokens.release(t);
}
});
std::vector<std::shared_ptr<const DiscreteFunctionDPkVariant>> discrete_function_dpk_variant_list;
for (auto discrete_function_dpk_variant_p : mutable_discrete_function_dpk_variant_list) {
std::visit(
[&](auto&& mutable_function_dpk) {
synchronize(mutable_function_dpk.cellArrays());
discrete_function_dpk_variant_list.push_back(
std::make_shared<DiscreteFunctionDPkVariant>(mutable_function_dpk));
},
discrete_function_dpk_variant_p.mutableDiscreteFunctionDPk());
}
return discrete_function_dpk_variant_list;
}
std::vector<std::shared_ptr<const DiscreteFunctionDPkVariant>>
PolynomialReconstruction::build(
const std::vector<std::shared_ptr<const DiscreteFunctionVariant>>& discrete_function_variant_list) const
{
if (not hasSameMesh(discrete_function_variant_list)) {
throw NormalError("cannot reconstruct functions living of different meshes simultaneously");
}
auto mesh_v = getCommonMesh(discrete_function_variant_list);
return std::visit([&](auto&& p_mesh) { return this->_build(p_mesh, discrete_function_variant_list); },
mesh_v->variant());
}