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>
269 template <
int dim,
int spacedim>
270 std::unique_ptr<Mapping<dim, spacedim>>
273 return std::make_unique<MappingQ<dim, spacedim>>(*this);
278 template <
int dim,
int spacedim>
282 return polynomial_degree;
287 template <
int dim,
int spacedim>
295 this->compute_mapping_support_points(cell),
297 polynomials_1d.size() == 2,
298 renumber_lexicographic_to_hierarchic));
321 template <
int dim,
int spacedim>
340 const Point<1> & initial_p_unit)
const
344 return internal::MappingQImplementation::
345 do_transform_real_to_unit_cell_internal<1>(
348 this->compute_mapping_support_points(cell),
350 renumber_lexicographic_to_hierarchic);
360 const Point<2> & initial_p_unit)
const
362 return internal::MappingQImplementation::
363 do_transform_real_to_unit_cell_internal<2>(
366 this->compute_mapping_support_points(cell),
368 renumber_lexicographic_to_hierarchic);
378 const Point<3> & initial_p_unit)
const
380 return internal::MappingQImplementation::
381 do_transform_real_to_unit_cell_internal<3>(
384 this->compute_mapping_support_points(cell),
386 renumber_lexicographic_to_hierarchic);
396 const Point<1> & initial_p_unit)
const
399 const int spacedim = 2;
406 auto mdata = Utilities::dynamic_unique_cast<InternalData>(
407 get_data(update_flags, point_quadrature));
409 mdata->mapping_support_points = this->compute_mapping_support_points(cell);
413 return internal::MappingQImplementation::
414 do_transform_real_to_unit_cell_internal_codim1<1>(
417 mdata->mapping_support_points,
419 renumber_lexicographic_to_hierarchic);
429 const Point<2> & initial_p_unit)
const
432 const int spacedim = 3;
439 auto mdata = Utilities::dynamic_unique_cast<InternalData>(
440 get_data(update_flags, point_quadrature));
442 mdata->mapping_support_points = this->compute_mapping_support_points(cell);
446 return internal::MappingQImplementation::
447 do_transform_real_to_unit_cell_internal_codim1<2>(
450 mdata->mapping_support_points,
452 renumber_lexicographic_to_hierarchic);
470 template <
int dim,
int spacedim>
478 if (this->preserves_vertex_locations() && (polynomial_degree == 1) &&
479 ((dim == 1) || ((dim == 2) && (dim == spacedim))))
502 const auto vertices_ = this->get_vertices(cell);
506 for (
unsigned int i = 0; i <
vertices.size(); ++i)
532 const double eps = 1
e-15;
565 if (this->preserves_vertex_locations())
567 initial_p_unit = cell->real_to_unit_cell_affine_approximation(p);
569 if (dim == 1 && polynomial_degree == 1)
570 return initial_p_unit;
575 for (
unsigned int d = 0;
d < dim; ++
d)
576 initial_p_unit[
d] = 0.5;
582 this->transform_real_to_unit_cell_internal(cell, p, initial_p_unit);
590 template <
int dim,
int spacedim>
608 const std::vector<Point<spacedim>> support_points =
609 this->compute_mapping_support_points(cell);
614 inverse_approximation(support_points, unit_cell_support_points);
616 const unsigned int n_points = real_points.size();
621 for (
unsigned int i = 0; i < n_points; i += n_lanes)
622 if (n_points - i > 1)
625 for (
unsigned int j = 0; j < n_lanes; ++j)
626 if (i + j < n_points)
627 for (
unsigned int d = 0;
d < spacedim; ++
d)
628 p_vec[
d][j] = real_points[i + j][
d];
630 for (
unsigned int d = 0;
d < spacedim; ++
d)
631 p_vec[
d][j] = real_points[i][
d];
634 internal::MappingQImplementation::
635 do_transform_real_to_unit_cell_internal<dim, spacedim>(
637 inverse_approximation.
compute(p_vec),
640 renumber_lexicographic_to_hierarchic);
647 for (
unsigned int j = 0; j < n_lanes && i + j < n_points; ++j)
649 for (
unsigned int d = 0;
d < dim; ++
d)
650 unit_points[i + j][
d] = unit_point[
d][j];
652 unit_points[i + j] = internal::MappingQImplementation::
653 do_transform_real_to_unit_cell_internal<dim, spacedim>(
655 inverse_approximation.
compute(real_points[i + j]),
658 renumber_lexicographic_to_hierarchic);
661 unit_points[i] = internal::MappingQImplementation::
662 do_transform_real_to_unit_cell_internal<dim, spacedim>(
664 inverse_approximation.
compute(real_points[i]),
667 renumber_lexicographic_to_hierarchic);
672 template <
int dim,
int spacedim>
683 for (
unsigned int i = 0; i < 5; ++i)
728 template <
int dim,
int spacedim>
729 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
733 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase> data_ptr =
734 std::make_unique<InternalData>(polynomial_degree);
736 data.
initialize(this->requires_update_flags(update_flags), q, q.
size());
743 template <
int dim,
int spacedim>
744 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
751 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase> data_ptr =
752 std::make_unique<InternalData>(polynomial_degree);
756 ReferenceCells::get_hypercube<dim>(), quadrature[0]),
757 quadrature[0].size());
764 template <
int dim,
int spacedim>
765 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
770 std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase> data_ptr =
771 std::make_unique<InternalData>(polynomial_degree);
775 ReferenceCells::get_hypercube<dim>(), quadrature),
783 template <
int dim,
int spacedim>
799 const unsigned int n_q_points = quadrature.
size();
819 (polynomial_degree == 1 && this->preserves_vertex_locations() ?
825 internal::MappingQImplementation::
826 maybe_update_q_points_Jacobians_and_grads_tensor<dim, spacedim>(
827 computed_cell_similarity,
837 computed_cell_similarity,
841 renumber_lexicographic_to_hierarchic,
848 computed_cell_similarity,
852 renumber_lexicographic_to_hierarchic,
858 spacedim>(computed_cell_similarity,
862 renumber_lexicographic_to_hierarchic,
867 spacedim>(computed_cell_similarity,
871 renumber_lexicographic_to_hierarchic,
874 internal::MappingQImplementation::
875 maybe_update_jacobian_pushed_forward_2nd_derivatives<dim, spacedim>(
876 computed_cell_similarity,
880 renumber_lexicographic_to_hierarchic,
885 spacedim>(computed_cell_similarity,
889 renumber_lexicographic_to_hierarchic,
892 internal::MappingQImplementation::
893 maybe_update_jacobian_pushed_forward_3rd_derivatives<dim, spacedim>(
894 computed_cell_similarity,
898 renumber_lexicographic_to_hierarchic,
902 const std::vector<double> &weights = quadrature.
get_weights();
930 1
e-12 * Utilities::fixed_power<dim>(
931 cell->diameter() / std::sqrt(
double(dim))),
933 cell->center(), det,
point)));
943 for (
unsigned int i = 0; i < spacedim; ++i)
944 for (
unsigned int j = 0; j < dim; ++j)
948 for (
unsigned int i = 0; i < dim; ++i)
949 for (
unsigned int j = 0; j < dim; ++j)
950 G[i][j] = DX_t[i] * DX_t[j];
955 if (computed_cell_similarity ==
966 Assert(spacedim == dim + 1,
968 "There is no (unique) cell normal for " +
970 "-dimensional cells in " +
972 "-dimensional space. This only works if the "
973 "space dimension is one greater than the "
974 "dimensionality of the mesh cells."));
978 cross_product_2d(-DX_t[0]);
981 cross_product_3d(DX_t[0], DX_t[1]);
986 if (cell->direction_flag() ==
false)
994 return computed_cell_similarity;
999 template <
int dim,
int spacedim>
1003 const unsigned int face_no,
1036 ReferenceCells::get_hypercube<dim>(),
1038 cell->face_orientation(face_no),
1039 cell->face_flip(face_no),
1040 cell->face_rotation(face_no),
1041 quadrature[0].
size()),
1045 renumber_lexicographic_to_hierarchic,
1051 template <
int dim,
int spacedim>
1055 const unsigned int face_no,
1056 const unsigned int subface_no,
1087 ReferenceCells::get_hypercube<dim>(),
1090 cell->face_orientation(face_no),
1091 cell->face_flip(face_no),
1092 cell->face_rotation(face_no),
1094 cell->subface_case(face_no)),
1098 renumber_lexicographic_to_hierarchic,
1104 template <
int dim,
int spacedim>
1121 const unsigned int n_q_points = quadrature.
size();
1131 renumber_lexicographic_to_hierarchic,
1136 internal::MappingQImplementation::maybe_update_jacobian_grads<dim, spacedim>(
1141 renumber_lexicographic_to_hierarchic,
1150 renumber_lexicographic_to_hierarchic,
1159 renumber_lexicographic_to_hierarchic,
1162 internal::MappingQImplementation::
1163 maybe_update_jacobian_pushed_forward_2nd_derivatives<dim, spacedim>(
1168 renumber_lexicographic_to_hierarchic,
1177 renumber_lexicographic_to_hierarchic,
1180 internal::MappingQImplementation::
1181 maybe_update_jacobian_pushed_forward_3rd_derivatives<dim, spacedim>(
1186 renumber_lexicographic_to_hierarchic,
1189 const UpdateFlags update_flags = data.update_each;
1190 const std::vector<double> &weights = quadrature.
get_weights();
1211 Assert(det > 1
e-12 * Utilities::fixed_power<dim>(
1212 cell->diameter() / std::sqrt(
double(dim))),
1214 cell->center(), det,
point)));
1218 for (
unsigned int d = 0;
d < spacedim;
d++)
1226 normal /= normal.
norm();
1235 template <
int dim,
int spacedim>
1252 output_data.
initialize(unit_points.size(), update_flags);
1254 auto internal_data =
1255 this->get_data(update_flags,
1257 unit_points.end())));
1267 renumber_lexicographic_to_hierarchic,
1275 template <
int dim,
int spacedim>
1279 const unsigned int face_no,
1305 renumber_lexicographic_to_hierarchic,
1311 template <
int dim,
int spacedim>
1327 template <
int dim,
int spacedim>
1343 template <
int dim,
int spacedim>
1351 switch (mapping_kind)
1375 template <
int dim,
int spacedim>
1387 &data = *
static_cast<const InternalData &
>(mapping_data).output_data;
1389 switch (mapping_kind)
1395 "update_covariant_transformation"));
1397 for (
unsigned int q = 0; q < output.size(); ++q)
1398 for (
unsigned int i = 0; i < spacedim; ++i)
1399 for (
unsigned int j = 0; j < spacedim; ++j)
1404 for (
unsigned int K = 0;
K < dim; ++
K)
1406 tmp[
K] = covariant[j][0] * input[q][i][0][
K];
1407 for (
unsigned int J = 1; J < dim; ++J)
1408 tmp[
K] += covariant[j][J] * input[q][i][J][
K];
1410 for (
unsigned int k = 0; k < spacedim; ++k)
1412 output[q][i][j][k] = covariant[k][0] * tmp[0];
1413 for (
unsigned int K = 1;
K < dim; ++
K)
1414 output[q][i][j][k] += covariant[k][
K] * tmp[
K];
1427 template <
int dim,
int spacedim>
1435 switch (mapping_kind)
1452 template <
int dim,
int spacedim>
1459 if (this->polynomial_degree == 2)
1461 for (
unsigned int line_no = 0;
1462 line_no < GeometryInfo<dim>::lines_per_cell;
1469 cell->line(line_no));
1483 std::vector<Point<spacedim>> tmp_points;
1484 for (
unsigned int line_no = 0;
1485 line_no < GeometryInfo<dim>::lines_per_cell;
1492 cell->line(line_no));
1500 const auto reference_cell = ReferenceCells::get_hypercube<dim>();
1501 const std::array<Point<spacedim>, 2>
vertices{
1503 cell->vertex(
reference_cell.line_to_cell_vertices(line_no, 1))}};
1505 const std::size_t n_rows =
1506 support_point_weights_perimeter_to_interior[0].size(0);
1507 a.resize(a.size() + n_rows);
1511 support_point_weights_perimeter_to_interior[0],
1528 std::vector<Point<3>> tmp_points;
1531 for (
unsigned int face_no = 0; face_no < faces_per_cell; ++face_no)
1536 const bool face_orientation = cell->face_orientation(face_no),
1537 face_flip = cell->face_flip(face_no),
1538 face_rotation = cell->face_rotation(face_no);
1543 for (
unsigned int i = 0; i < vertices_per_face; ++i)
1544 Assert(face->vertex_index(i) ==
1546 face_no, i, face_orientation, face_flip, face_rotation)),
1551 for (
unsigned int i = 0; i < lines_per_face; ++i)
1554 face_no, i, face_orientation, face_flip, face_rotation)),
1560 boost::container::small_vector<Point<3>, 200> tmp_points(
1565 if (polynomial_degree > 1)
1566 for (
unsigned int line = 0; line < GeometryInfo<2>::lines_per_cell;
1568 for (
unsigned int i = 0; i < polynomial_degree - 1; ++i)
1569 tmp_points[4 + line * (polynomial_degree - 1) + i] =
1571 (polynomial_degree - 1) *
1575 const std::size_t n_rows =
1576 support_point_weights_perimeter_to_interior[1].size(0);
1577 a.resize(a.size() + n_rows);
1579 face->get_manifold().get_new_points(
1581 support_point_weights_perimeter_to_interior[1],
1600 for (
unsigned int q = 0, q2 = 0; q2 < polynomial_degree - 1; ++q2)
1601 for (
unsigned int q1 = 0; q1 < polynomial_degree - 1; ++q1, ++q)
1604 line_support_points[q2 + 1][0]);
1609 const std::size_t n_rows = weights.size(0);
1610 a.resize(a.size() + n_rows);
1612 cell->get_manifold().get_new_points(
1618 template <
int dim,
int spacedim>
1629 template <
int dim,
int spacedim>
1630 std::vector<Point<spacedim>>
1635 std::vector<Point<spacedim>> a;
1636 a.reserve(Utilities::fixed_power<dim>(polynomial_degree + 1));
1638 a.push_back(cell->vertex(i));
1640 if (this->polynomial_degree > 1)
1647 bool all_manifold_ids_are_equal = (dim == spacedim);
1648 if (all_manifold_ids_are_equal &&
1654 all_manifold_ids_are_equal =
false;
1657 for (
unsigned int l = 0; l < GeometryInfo<dim>::lines_per_cell; ++
l)
1659 all_manifold_ids_are_equal =
false;
1662 if (all_manifold_ids_are_equal)
1664 const std::size_t n_rows = support_point_weights_cell.size(0);
1665 a.resize(a.size() + n_rows);
1669 support_point_weights_cell,
1676 add_line_support_points(cell, a);
1681 add_line_support_points(cell, a);
1684 if (dim != spacedim)
1685 add_quad_support_points(cell, a);
1688 const std::size_t n_rows =
1689 support_point_weights_perimeter_to_interior[1].size(0);
1690 a.resize(a.size() + n_rows);
1694 support_point_weights_perimeter_to_interior[1],
1701 add_line_support_points(cell, a);
1702 add_quad_support_points(cell, a);
1706 const std::size_t n_rows =
1707 support_point_weights_perimeter_to_interior[2].size(0);
1708 a.resize(a.size() + n_rows);
1712 support_point_weights_perimeter_to_interior[2],
1728 template <
int dim,
int spacedim>
1738 template <
int dim,
int spacedim>
1744 ExcMessage(
"The dimension of your mapping (" +
1746 ") and the reference cell cell_type (" +
1748 " ) do not agree."));
1756 #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< T >::value, 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)