37 #include <boost/container/small_vector.hpp>
50 template <
int dim,
int spacedim>
52 const unsigned int polynomial_degree)
53 : polynomial_degree(polynomial_degree)
55 , line_support_points(
QGaussLobatto<1>(polynomial_degree + 1))
56 , tensor_product_quadrature(false)
57 , output_data(nullptr)
62 template <
int dim,
int spacedim>
80 template <
int dim,
int spacedim>
85 const unsigned int n_original_q_points)
89 this->update_each = update_flags;
91 const unsigned int n_q_points = quadrature.
size();
94 volume_elements.resize(n_original_q_points);
101 tensor_product_quadrature =
false;
107 if (tensor_product_quadrature)
109 const std::array<Quadrature<1>, dim> &quad_array =
111 for (
unsigned int i = 1; i < dim && tensor_product_quadrature; ++i)
113 if (quad_array[i - 1].size() != quad_array[i].size())
115 tensor_product_quadrature =
false;
120 const std::vector<Point<1>> &points_1 =
121 quad_array[i - 1].get_points();
122 const std::vector<Point<1>> &points_2 =
123 quad_array[i].get_points();
124 const std::vector<double> &weights_1 =
125 quad_array[i - 1].get_weights();
126 const std::vector<double> &weights_2 =
127 quad_array[i].get_weights();
128 for (
unsigned int j = 0; j < quad_array[i].size(); ++j)
130 if (std::abs(points_1[j][0] - points_2[j][0]) > 1.e-10 ||
131 std::abs(weights_1[j] - weights_2[j]) > 1.e-10)
133 tensor_product_quadrature =
false;
140 if (tensor_product_quadrature)
147 shape_info.lexicographic_numbering =
148 FETools::lexicographic_to_hierarchic_numbering<dim>(
150 shape_info.n_q_points = n_q_points;
151 shape_info.dofs_per_component_on_cell =
160 template <
int dim,
int spacedim>
165 const unsigned int n_original_q_points)
167 initialize(update_flags, quadrature, n_original_q_points);
171 if (dim > 1 && tensor_product_quadrature)
173 constexpr
unsigned int facedim = dim - 1;
176 shape_info.lexicographic_numbering =
177 FETools::lexicographic_to_hierarchic_numbering<facedim>(
179 shape_info.n_q_points = n_original_q_points;
180 shape_info.dofs_per_component_on_cell =
186 if (this->update_each &
190 aux[0].resize(n_original_q_points);
192 aux[1].resize(n_original_q_points);
197 unit_tangentials[i].resize(n_original_q_points);
198 std::fill(unit_tangentials[i].
begin(),
199 unit_tangentials[i].
end(),
204 .resize(n_original_q_points);
219 template <
int dim,
int spacedim>
242 ExcMessage(
"It only makes sense to create polynomial mappings "
243 "with a polynomial degree greater or equal to one."));
248 template <
int dim,
int spacedim>
255 template <
int dim,
int spacedim>
257 : polynomial_degree(mapping.polynomial_degree)
258 , line_support_points(mapping.line_support_points)
259 , polynomials_1d(mapping.polynomials_1d)
260 , renumber_lexicographic_to_hierarchic(
261 mapping.renumber_lexicographic_to_hierarchic)
262 , unit_cell_support_points(mapping.unit_cell_support_points)
263 , support_point_weights_perimeter_to_interior(
264 mapping.support_point_weights_perimeter_to_interior)
265 , support_point_weights_cell(mapping.support_point_weights_cell)
270 template <
int dim,
int spacedim>
271 std::unique_ptr<Mapping<dim, spacedim>>
274 return std::make_unique<MappingQ<dim, spacedim>>(*this);
279 template <
int dim,
int spacedim>
283 return polynomial_degree;
288 template <
int dim,
int spacedim>
296 this->compute_mapping_support_points(cell),
298 polynomials_1d.size() == 2,
299 renumber_lexicographic_to_hierarchic));
322 template <
int dim,
int spacedim>
341 const Point<1> &initial_p_unit)
const
345 return internal::MappingQImplementation::
346 do_transform_real_to_unit_cell_internal<1>(
349 this->compute_mapping_support_points(cell),
351 renumber_lexicographic_to_hierarchic);
361 const Point<2> &initial_p_unit)
const
363 return internal::MappingQImplementation::
364 do_transform_real_to_unit_cell_internal<2>(
367 this->compute_mapping_support_points(cell),
369 renumber_lexicographic_to_hierarchic);
379 const Point<3> &initial_p_unit)
const
381 return internal::MappingQImplementation::
382 do_transform_real_to_unit_cell_internal<3>(
385 this->compute_mapping_support_points(cell),
387 renumber_lexicographic_to_hierarchic);
397 const Point<1> &initial_p_unit)
const
400 const int spacedim = 2;
407 auto mdata = Utilities::dynamic_unique_cast<InternalData>(
408 get_data(update_flags, point_quadrature));
410 mdata->mapping_support_points = this->compute_mapping_support_points(cell);
414 return internal::MappingQImplementation::
415 do_transform_real_to_unit_cell_internal_codim1<1>(
418 mdata->mapping_support_points,
420 renumber_lexicographic_to_hierarchic);
430 const Point<2> &initial_p_unit)
const
433 const int spacedim = 3;
440 auto mdata = Utilities::dynamic_unique_cast<InternalData>(
441 get_data(update_flags, point_quadrature));
443 mdata->mapping_support_points = this->compute_mapping_support_points(cell);
447 return internal::MappingQImplementation::
448 do_transform_real_to_unit_cell_internal_codim1<2>(
451 mdata->mapping_support_points,
453 renumber_lexicographic_to_hierarchic);
471 template <
int dim,
int spacedim>
479 if (this->preserves_vertex_locations() && (polynomial_degree == 1) &&
480 ((dim == 1) || ((dim == 2) && (dim == spacedim))))
503 const auto vertices_ = this->get_vertices(cell);
533 const double eps = 1
e-15;
566 if (this->preserves_vertex_locations())
568 initial_p_unit = cell->real_to_unit_cell_affine_approximation(p);
570 if (dim == 1 && polynomial_degree == 1)
571 return initial_p_unit;
576 for (
unsigned int d = 0;
d < dim; ++
d)
577 initial_p_unit[
d] = 0.5;
583 this->transform_real_to_unit_cell_internal(cell, p, initial_p_unit);
591 template <
int dim,
int spacedim>
609 const std::vector<Point<spacedim>> support_points =
610 this->compute_mapping_support_points(cell);
615 inverse_approximation(support_points, unit_cell_support_points);
617 const unsigned int n_points = real_points.size();
622 for (
unsigned int i = 0; i < n_points; i += n_lanes)
623 if (n_points - i > 1)
626 for (
unsigned int j = 0; j < n_lanes; ++j)
627 if (i + j < n_points)
628 for (
unsigned int d = 0;
d < spacedim; ++
d)
629 p_vec[
d][j] = real_points[i + j][
d];
631 for (
unsigned int d = 0;
d < spacedim; ++
d)
632 p_vec[
d][j] = real_points[i][
d];
635 internal::MappingQImplementation::
636 do_transform_real_to_unit_cell_internal<dim, spacedim>(
638 inverse_approximation.
compute(p_vec),
641 renumber_lexicographic_to_hierarchic);
648 for (
unsigned int j = 0; j < n_lanes && i + j < n_points; ++j)
650 for (
unsigned int d = 0;
d < dim; ++
d)
651 unit_points[i + j][
d] = unit_point[
d][j];
653 unit_points[i + j] = internal::MappingQImplementation::
654 do_transform_real_to_unit_cell_internal<dim, spacedim>(
656 inverse_approximation.
compute(real_points[i + j]),
659 renumber_lexicographic_to_hierarchic);
662 unit_points[i] = internal::MappingQImplementation::
663 do_transform_real_to_unit_cell_internal<dim, spacedim>(
665 inverse_approximation.
compute(real_points[i]),
668 renumber_lexicographic_to_hierarchic);
673 template <
int dim,
int spacedim>
684 for (
unsigned int i = 0; i < 5; ++i)
729 template <
int dim,
int spacedim>
730 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
734 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase> data_ptr =
735 std::make_unique<InternalData>(polynomial_degree);
737 data.
initialize(this->requires_update_flags(update_flags), q, q.
size());
744 template <
int dim,
int spacedim>
745 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
752 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase> data_ptr =
753 std::make_unique<InternalData>(polynomial_degree);
757 ReferenceCells::get_hypercube<dim>(), quadrature[0]),
758 quadrature[0].size());
765 template <
int dim,
int spacedim>
766 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
771 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase> data_ptr =
772 std::make_unique<InternalData>(polynomial_degree);
776 ReferenceCells::get_hypercube<dim>(), quadrature),
784 template <
int dim,
int spacedim>
800 const unsigned int n_q_points = quadrature.
size();
820 (polynomial_degree == 1 && this->preserves_vertex_locations() ?
826 internal::MappingQImplementation::
827 maybe_update_q_points_Jacobians_and_grads_tensor<dim, spacedim>(
828 computed_cell_similarity,
838 computed_cell_similarity,
842 renumber_lexicographic_to_hierarchic,
849 computed_cell_similarity,
853 renumber_lexicographic_to_hierarchic,
859 spacedim>(computed_cell_similarity,
863 renumber_lexicographic_to_hierarchic,
868 spacedim>(computed_cell_similarity,
872 renumber_lexicographic_to_hierarchic,
875 internal::MappingQImplementation::
876 maybe_update_jacobian_pushed_forward_2nd_derivatives<dim, spacedim>(
877 computed_cell_similarity,
881 renumber_lexicographic_to_hierarchic,
886 spacedim>(computed_cell_similarity,
890 renumber_lexicographic_to_hierarchic,
893 internal::MappingQImplementation::
894 maybe_update_jacobian_pushed_forward_3rd_derivatives<dim, spacedim>(
895 computed_cell_similarity,
899 renumber_lexicographic_to_hierarchic,
903 const std::vector<double> &weights = quadrature.
get_weights();
911 (output_data.
JxW_values.size() == n_q_points),
933 1
e-12 * Utilities::fixed_power<dim>(
934 cell->diameter() / std::sqrt(
double(dim))),
936 cell->center(), det,
point)));
946 for (
unsigned int i = 0; i < spacedim; ++i)
947 for (
unsigned int j = 0; j < dim; ++j)
951 for (
unsigned int i = 0; i < dim; ++i)
952 for (
unsigned int j = 0; j < dim; ++j)
953 G[i][j] = DX_t[i] * DX_t[j];
959 if (computed_cell_similarity ==
970 Assert(spacedim == dim + 1,
972 "There is no (unique) cell normal for " +
974 "-dimensional cells in " +
976 "-dimensional space. This only works if the "
977 "space dimension is one greater than the "
978 "dimensionality of the mesh cells."));
982 cross_product_2d(-DX_t[0]);
985 cross_product_3d(DX_t[0], DX_t[1]);
990 if (cell->direction_flag() ==
false)
998 return computed_cell_similarity;
1003 template <
int dim,
int spacedim>
1007 const unsigned int face_no,
1040 ReferenceCells::get_hypercube<dim>(),
1042 cell->face_orientation(face_no),
1043 cell->face_flip(face_no),
1044 cell->face_rotation(face_no),
1045 quadrature[0].
size()),
1049 renumber_lexicographic_to_hierarchic,
1055 template <
int dim,
int spacedim>
1059 const unsigned int face_no,
1060 const unsigned int subface_no,
1091 ReferenceCells::get_hypercube<dim>(),
1094 cell->face_orientation(face_no),
1095 cell->face_flip(face_no),
1096 cell->face_rotation(face_no),
1098 cell->subface_case(face_no)),
1102 renumber_lexicographic_to_hierarchic,
1108 template <
int dim,
int spacedim>
1125 const unsigned int n_q_points = quadrature.
size();
1135 renumber_lexicographic_to_hierarchic,
1140 internal::MappingQImplementation::maybe_update_jacobian_grads<dim, spacedim>(
1145 renumber_lexicographic_to_hierarchic,
1154 renumber_lexicographic_to_hierarchic,
1163 renumber_lexicographic_to_hierarchic,
1166 internal::MappingQImplementation::
1167 maybe_update_jacobian_pushed_forward_2nd_derivatives<dim, spacedim>(
1172 renumber_lexicographic_to_hierarchic,
1181 renumber_lexicographic_to_hierarchic,
1184 internal::MappingQImplementation::
1185 maybe_update_jacobian_pushed_forward_3rd_derivatives<dim, spacedim>(
1190 renumber_lexicographic_to_hierarchic,
1193 const UpdateFlags update_flags = data.update_each;
1194 const std::vector<double> &weights = quadrature.
get_weights();
1215 Assert(det > 1
e-12 * Utilities::fixed_power<dim>(
1216 cell->diameter() / std::sqrt(
double(dim))),
1218 cell->center(), det,
point)));
1222 for (
unsigned int d = 0;
d < spacedim;
d++)
1230 normal /= normal.
norm();
1239 template <
int dim,
int spacedim>
1256 output_data.
initialize(unit_points.size(), update_flags);
1258 auto internal_data =
1259 this->get_data(update_flags,
1261 unit_points.end())));
1271 renumber_lexicographic_to_hierarchic,
1279 template <
int dim,
int spacedim>
1283 const unsigned int face_no,
1309 renumber_lexicographic_to_hierarchic,
1315 template <
int dim,
int spacedim>
1331 template <
int dim,
int spacedim>
1347 template <
int dim,
int spacedim>
1355 switch (mapping_kind)
1379 template <
int dim,
int spacedim>
1391 &data = *
static_cast<const InternalData &
>(mapping_data).output_data;
1393 switch (mapping_kind)
1399 "update_covariant_transformation"));
1401 for (
unsigned int q = 0; q < output.size(); ++q)
1402 for (
unsigned int i = 0; i < spacedim; ++i)
1403 for (
unsigned int j = 0; j < spacedim; ++j)
1408 for (
unsigned int K = 0;
K < dim; ++
K)
1410 tmp[
K] = covariant[j][0] * input[q][i][0][
K];
1411 for (
unsigned int J = 1; J < dim; ++J)
1412 tmp[
K] += covariant[j][J] * input[q][i][J][
K];
1414 for (
unsigned int k = 0; k < spacedim; ++k)
1416 output[q][i][j][k] = covariant[k][0] * tmp[0];
1417 for (
unsigned int K = 1;
K < dim; ++
K)
1418 output[q][i][j][k] += covariant[k][
K] * tmp[
K];
1431 template <
int dim,
int spacedim>
1439 switch (mapping_kind)
1456 template <
int dim,
int spacedim>
1463 if (this->polynomial_degree == 2)
1465 for (
unsigned int line_no = 0;
1466 line_no < GeometryInfo<dim>::lines_per_cell;
1473 cell->line(line_no));
1487 std::vector<Point<spacedim>> tmp_points;
1488 for (
unsigned int line_no = 0;
1489 line_no < GeometryInfo<dim>::lines_per_cell;
1496 cell->line(line_no));
1504 const auto reference_cell = ReferenceCells::get_hypercube<dim>();
1505 const std::array<Point<spacedim>, 2>
vertices{
1507 cell->vertex(
reference_cell.line_to_cell_vertices(line_no, 1))}};
1509 const std::size_t n_rows =
1510 support_point_weights_perimeter_to_interior[0].size(0);
1511 a.resize(a.size() + n_rows);
1515 support_point_weights_perimeter_to_interior[0],
1532 std::vector<Point<3>> tmp_points;
1535 for (
unsigned int face_no = 0; face_no < faces_per_cell; ++face_no)
1540 const bool face_orientation = cell->face_orientation(face_no),
1541 face_flip = cell->face_flip(face_no),
1542 face_rotation = cell->face_rotation(face_no);
1547 for (
unsigned int i = 0; i < vertices_per_face; ++i)
1548 Assert(face->vertex_index(i) ==
1550 face_no, i, face_orientation, face_flip, face_rotation)),
1555 for (
unsigned int i = 0; i < lines_per_face; ++i)
1558 face_no, i, face_orientation, face_flip, face_rotation)),
1564 boost::container::small_vector<Point<3>, 200> tmp_points(
1569 if (polynomial_degree > 1)
1570 for (
unsigned int line = 0; line < GeometryInfo<2>::lines_per_cell;
1572 for (
unsigned int i = 0; i < polynomial_degree - 1; ++i)
1573 tmp_points[4 + line * (polynomial_degree - 1) + i] =
1575 (polynomial_degree - 1) *
1579 const std::size_t n_rows =
1580 support_point_weights_perimeter_to_interior[1].size(0);
1581 a.resize(a.size() + n_rows);
1583 face->get_manifold().get_new_points(
1585 support_point_weights_perimeter_to_interior[1],
1604 for (
unsigned int q = 0, q2 = 0; q2 < polynomial_degree - 1; ++q2)
1605 for (
unsigned int q1 = 0; q1 < polynomial_degree - 1; ++q1, ++q)
1608 line_support_points[q2 + 1][0]);
1613 const std::size_t n_rows = weights.size(0);
1614 a.resize(a.size() + n_rows);
1616 cell->get_manifold().get_new_points(
1622 template <
int dim,
int spacedim>
1633 template <
int dim,
int spacedim>
1634 std::vector<Point<spacedim>>
1639 std::vector<Point<spacedim>> a;
1640 a.reserve(Utilities::fixed_power<dim>(polynomial_degree + 1));
1642 a.push_back(cell->vertex(i));
1644 if (this->polynomial_degree > 1)
1651 bool all_manifold_ids_are_equal = (dim == spacedim);
1652 if (all_manifold_ids_are_equal &&
1658 all_manifold_ids_are_equal =
false;
1661 for (
unsigned int l = 0; l < GeometryInfo<dim>::lines_per_cell; ++
l)
1663 all_manifold_ids_are_equal =
false;
1666 if (all_manifold_ids_are_equal)
1668 const std::size_t n_rows = support_point_weights_cell.size(0);
1669 a.resize(a.size() + n_rows);
1673 support_point_weights_cell,
1680 add_line_support_points(cell, a);
1685 add_line_support_points(cell, a);
1688 if (dim != spacedim)
1689 add_quad_support_points(cell, a);
1692 const std::size_t n_rows =
1693 support_point_weights_perimeter_to_interior[1].size(0);
1694 a.resize(a.size() + n_rows);
1698 support_point_weights_perimeter_to_interior[1],
1705 add_line_support_points(cell, a);
1706 add_quad_support_points(cell, a);
1710 const std::size_t n_rows =
1711 support_point_weights_perimeter_to_interior[2].size(0);
1712 a.resize(a.size() + n_rows);
1716 support_point_weights_perimeter_to_interior[2],
1732 template <
int dim,
int spacedim>
1742 template <
int dim,
int spacedim>
1748 ExcMessage(
"The dimension of your mapping (" +
1750 ") and the reference cell cell_type (" +
1752 " ) do not agree."));
1760 #include "mapping_q.inst"
ArrayView< typename std::remove_reference< typename std::iterator_traits< Iterator >::reference >::type, MemorySpaceType > make_array_view(const Iterator begin, const Iterator end)
virtual void get_new_points(const ArrayView< const Point< spacedim >> &surrounding_points, const Table< 2, double > &weights, ArrayView< Point< spacedim >> new_points) const
virtual Point< spacedim > get_new_point_on_line(const typename Triangulation< dim, spacedim >::line_iterator &line) const
Triangulation< dim, spacedim >::cell_iterator cell_of_current_support_points
virtual std::size_t memory_consumption() const override
std::vector< Point< spacedim > > mapping_support_points
bool tensor_product_quadrature
internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > * output_data
void initialize_face(const UpdateFlags update_flags, const Quadrature< dim > &quadrature, const unsigned int n_original_q_points)
InternalData(const unsigned int polynomial_degree)
AlignedVector< double > volume_elements
void initialize(const UpdateFlags update_flags, const Quadrature< dim > &quadrature, const unsigned int n_original_q_points)
virtual void add_line_support_points(const typename Triangulation< dim, spacedim >::cell_iterator &cell, std::vector< Point< spacedim >> &a) const
const std::vector< unsigned int > renumber_lexicographic_to_hierarchic
const Table< 2, double > support_point_weights_cell
virtual std::vector< Point< spacedim > > compute_mapping_support_points(const typename Triangulation< dim, spacedim >::cell_iterator &cell) const
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > get_data(const UpdateFlags, const Quadrature< dim > &quadrature) const override
void fill_mapping_data_for_generic_points(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const ArrayView< const Point< dim >> &unit_points, const UpdateFlags update_flags, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const
void fill_mapping_data_for_face_quadrature(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_number, const Quadrature< dim - 1 > &face_quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const
virtual BoundingBox< spacedim > get_bounding_box(const typename Triangulation< dim, spacedim >::cell_iterator &cell) const override
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > get_subface_data(const UpdateFlags flags, const Quadrature< dim - 1 > &quadrature) const override
virtual void fill_fe_subface_values(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int subface_no, const Quadrature< dim - 1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
virtual CellSimilarity::Similarity fill_fe_values(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
virtual void fill_fe_immersed_surface_values(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const NonMatching::ImmersedSurfaceQuadrature< dim > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
const unsigned int polynomial_degree
virtual void transform(const ArrayView< const Tensor< 1, dim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 1, spacedim >> &output) const override
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > get_face_data(const UpdateFlags flags, const hp::QCollection< dim - 1 > &quadrature) const override
Point< dim > transform_real_to_unit_cell_internal(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p, const Point< dim > &initial_p_unit) const
const std::vector< Table< 2, double > > support_point_weights_perimeter_to_interior
const std::vector< Point< 1 > > line_support_points
virtual Point< spacedim > transform_unit_to_real_cell(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< dim > &p) const override
const std::vector< Polynomials::Polynomial< double > > polynomials_1d
virtual std::unique_ptr< Mapping< dim, spacedim > > clone() const override
const std::vector< Point< dim > > unit_cell_support_points
virtual void transform_points_real_to_unit_cell(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const ArrayView< const Point< spacedim >> &real_points, const ArrayView< Point< dim >> &unit_points) const override
virtual Point< dim > transform_real_to_unit_cell(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p) const override
MappingQ(const unsigned int polynomial_degree)
virtual UpdateFlags requires_update_flags(const UpdateFlags update_flags) const override
virtual void fill_fe_face_values(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const hp::QCollection< dim - 1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
virtual bool is_compatible_with(const ReferenceCell &reference_cell) const override
virtual void add_quad_support_points(const typename Triangulation< dim, spacedim >::cell_iterator &cell, std::vector< Point< spacedim >> &a) const
unsigned int get_degree() const
Abstract base class for mapping classes.
virtual void transform_points_real_to_unit_cell(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const ArrayView< const Point< spacedim >> &real_points, const ArrayView< Point< dim >> &unit_points) const
const Tensor< 1, spacedim > & normal_vector(const unsigned int i) const
const std::vector< Point< dim > > & get_points() const
bool is_tensor_product() const
const std::vector< double > & get_weights() const
const std::array< Quadrature< 1 >, dim > & get_tensor_basis() const
unsigned int size() const
constexpr DEAL_II_HOST Number determinant(const SymmetricTensor< 2, dim, Number > &)
numbers::NumberTraits< Number >::real_type norm() const
Triangulation< dim, spacedim > & get_triangulation()
static constexpr std::size_t size()
unsigned int size() const
Point< dim, Number > compute(const Point< spacedim, Number > &p) const
#define DEAL_II_NAMESPACE_OPEN
#define DEAL_II_NAMESPACE_CLOSE
static ::ExceptionBase & ExcInternalError()
static ::ExceptionBase & ExcDimensionMismatch(std::size_t arg1, std::size_t arg2)
#define Assert(cond, exc)
static ::ExceptionBase & ExcNotImplemented()
static ::ExceptionBase & ExcImpossibleInDim(int arg1)
#define AssertDimension(dim1, dim2)
static ::ExceptionBase & ExcMessage(std::string arg1)
#define AssertThrow(cond, exc)
@ update_jacobian_pushed_forward_2nd_derivatives
@ update_volume_elements
Determinant of the Jacobian.
@ update_contravariant_transformation
Contravariant transformation.
@ update_jacobian_pushed_forward_grads
@ update_jacobian_grads
Gradient of volume element.
@ update_normal_vectors
Normal vectors.
@ update_JxW_values
Transformed quadrature weights.
@ update_covariant_transformation
Covariant transformation.
@ update_jacobians
Volume element.
@ update_inverse_jacobians
Volume element.
@ update_quadrature_points
Transformed quadrature points.
@ update_default
No update.
@ update_jacobian_pushed_forward_3rd_derivatives
@ update_boundary_forms
Outer normal vector, not normalized.
const Manifold< dim, spacedim > & get_manifold(const types::manifold_id number) const
@ mapping_covariant_gradient
@ mapping_contravariant_hessian
@ mapping_covariant_hessian
@ mapping_contravariant_gradient
CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt K
void reference_cell(Triangulation< dim, spacedim > &tria, const ReferenceCell &reference_cell)
std::enable_if_t< std::is_fundamental_v< T >, std::size_t > memory_consumption(const T &t)
Point< spacedim > point(const gp_Pnt &p, const double tolerance=1e-10)
void quadrature_points(const Triangulation< dim, spacedim > &triangulation, const Quadrature< dim > &quadrature, const std::vector< std::vector< BoundingBox< spacedim >>> &global_bounding_boxes, ParticleHandler< dim, spacedim > &particle_handler, const Mapping< dim, spacedim > &mapping=(ReferenceCells::get_hypercube< dim >() .template get_default_linear_mapping< dim, spacedim >()), const std::vector< std::vector< double >> &properties={})
SymmetricTensor< 2, dim, Number > d(const Tensor< 2, dim, Number > &F, const Tensor< 2, dim, Number > &dF_dt)
SymmetricTensor< 2, dim, Number > e(const Tensor< 2, dim, Number > &F)
Tensor< 2, dim, Number > l(const Tensor< 2, dim, Number > &F, const Tensor< 2, dim, Number > &dF_dt)
std::vector< Polynomial< double > > generate_complete_Lagrange_basis(const std::vector< Point< 1 >> &points)
VectorType::value_type * begin(VectorType &V)
VectorType::value_type * end(VectorType &V)
constexpr T pow(const T base, const int iexp)
std::string to_string(const number value, const unsigned int digits=numbers::invalid_unsigned_int)
std::string int_to_string(const unsigned int value, const unsigned int digits=numbers::invalid_unsigned_int)
Point< 1 > transform_real_to_unit_cell(const std::array< Point< spacedim >, GeometryInfo< 1 >::vertices_per_cell > &vertices, const Point< spacedim > &p)
void transform_gradients(const ArrayView< const Tensor< rank, dim >> &input, const MappingKind mapping_kind, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, const ArrayView< Tensor< rank, spacedim >> &output)
void do_fill_fe_face_values(const ::MappingQ< dim, spacedim > &mapping, const typename ::Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int subface_no, const typename QProjector< dim >::DataSetDescriptor data_set, const Quadrature< dim - 1 > &quadrature, const typename ::MappingQ< dim, spacedim >::InternalData &data, const std::vector< Polynomials::Polynomial< double >> &polynomials_1d, const std::vector< unsigned int > &renumber_lexicographic_to_hierarchic, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data)
std::vector< Point< dim > > unit_support_points(const std::vector< Point< 1 >> &line_support_points, const std::vector< unsigned int > &renumbering)
void maybe_update_jacobian_3rd_derivatives(const CellSimilarity::Similarity cell_similarity, const typename ::MappingQ< dim, spacedim >::InternalData &data, const ArrayView< const Point< dim >> &unit_points, const std::vector< Polynomials::Polynomial< double >> &polynomials_1d, const std::vector< unsigned int > &renumber_lexicographic_to_hierarchic, std::vector< DerivativeForm< 4, dim, spacedim >> &jacobian_3rd_derivatives)
void transform_differential_forms(const ArrayView< const DerivativeForm< rank, dim, spacedim >> &input, const MappingKind mapping_kind, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, const ArrayView< Tensor< rank+1, spacedim >> &output)
void maybe_update_jacobian_grads(const CellSimilarity::Similarity cell_similarity, const typename ::MappingQ< dim, spacedim >::InternalData &data, const ArrayView< const Point< dim >> &unit_points, const std::vector< Polynomials::Polynomial< double >> &polynomials_1d, const std::vector< unsigned int > &renumber_lexicographic_to_hierarchic, std::vector< DerivativeForm< 2, dim, spacedim >> &jacobian_grads)
void maybe_update_jacobian_pushed_forward_grads(const CellSimilarity::Similarity cell_similarity, const typename ::MappingQ< dim, spacedim >::InternalData &data, const ArrayView< const Point< dim >> &unit_points, const std::vector< Polynomials::Polynomial< double >> &polynomials_1d, const std::vector< unsigned int > &renumber_lexicographic_to_hierarchic, std::vector< Tensor< 3, spacedim >> &jacobian_pushed_forward_grads)
void maybe_update_jacobian_2nd_derivatives(const CellSimilarity::Similarity cell_similarity, const typename ::MappingQ< dim, spacedim >::InternalData &data, const ArrayView< const Point< dim >> &unit_points, const std::vector< Polynomials::Polynomial< double >> &polynomials_1d, const std::vector< unsigned int > &renumber_lexicographic_to_hierarchic, std::vector< DerivativeForm< 3, dim, spacedim >> &jacobian_2nd_derivatives)
void maybe_update_q_points_Jacobians_generic(const CellSimilarity::Similarity cell_similarity, const typename ::MappingQ< dim, spacedim >::InternalData &data, const ArrayView< const Point< dim >> &unit_points, const std::vector< Polynomials::Polynomial< double >> &polynomials_1d, const std::vector< unsigned int > &renumber_lexicographic_to_hierarchic, std::vector< Point< spacedim >> &quadrature_points, std::vector< DerivativeForm< 1, dim, spacedim >> &jacobians, std::vector< DerivativeForm< 1, spacedim, dim >> &inverse_jacobians)
inline ::Table< 2, double > compute_support_point_weights_cell(const unsigned int polynomial_degree)
std::vector<::Table< 2, double > > compute_support_point_weights_perimeter_to_interior(const unsigned int polynomial_degree, const unsigned int dim)
void transform_hessians(const ArrayView< const Tensor< 3, dim >> &input, const MappingKind mapping_kind, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, const ArrayView< Tensor< 3, spacedim >> &output)
void transform_fields(const ArrayView< const Tensor< rank, dim >> &input, const MappingKind mapping_kind, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, const ArrayView< Tensor< rank, spacedim >> &output)
ProductTypeNoPoint< Number, Number2 >::type evaluate_tensor_product_value(const std::vector< Polynomials::Polynomial< double >> &poly, const std::vector< Number > &values, const Point< dim, Number2 > &p, const bool d_linear=false, const std::vector< unsigned int > &renumber={})
static const unsigned int invalid_unsigned_int
const types::manifold_id flat_manifold_id
bool is_finite(const double x)
static unsigned int face_to_cell_vertices(const unsigned int face, const unsigned int vertex, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false)
static double d_linear_shape_function(const Point< dim > &xi, const unsigned int i)