55 zero_indices(
unsigned int (&indices)[dim])
57 for (
unsigned int d = 0; d < dim; ++d)
68 increment_indices(
unsigned int (&indices)[dim],
const unsigned int dofs1d)
71 for (
unsigned int d = 0; d < dim - 1; ++d)
72 if (indices[d] == dofs1d)
88template <
int xdim,
int xspacedim>
95 template <
int spacedim>
104 template <
int spacedim>
109 const unsigned int dim = 2;
111 unsigned int q_deg = fe.
degree;
160 std::vector<
Point<dim - 1>> constraint_points;
162 constraint_points.emplace_back(0.5);
165 for (
unsigned int i = 1; i < q_deg; ++i)
166 constraint_points.push_back(
170 for (
unsigned int i = 1; i < q_deg; ++i)
171 constraint_points.push_back(
183 const std::vector<unsigned int> &index_map_inverse =
185 const std::vector<unsigned int> face_index_map =
192 for (
unsigned int i = 0; i < constraint_points.size(); ++i)
193 for (
unsigned int j = 0; j < q_deg + 1; ++j)
196 p[0] = constraint_points[i][0];
198 fe.
poly_space->compute_value(index_map_inverse[j], p);
210 template <
int spacedim>
215 const unsigned int dim = 3;
217 unsigned int q_deg = fe.
degree;
237 std::vector<
Point<dim - 1>> constraint_points;
240 constraint_points.emplace_back(0.5, 0.5);
243 constraint_points.emplace_back(0, 0.5);
244 constraint_points.emplace_back(1, 0.5);
245 constraint_points.emplace_back(0.5, 0);
246 constraint_points.emplace_back(0.5, 1);
250 const unsigned int n = q_deg - 1;
251 const double step = 1. / q_deg;
252 std::vector<Point<1>> line_support_points(n);
253 for (
unsigned int i = 0; i < n; ++i)
254 line_support_points[i][0] = (i + 1) * step;
258 auto get_points = [&](
const unsigned int face_no,
259 const unsigned int subface_no) {
261 ReferenceCells::get_hypercube<2>(),
284 for (
unsigned int face = 0;
287 for (
unsigned int subface = 0;
291 const auto p_line = get_points(face, subface);
292 constraint_points.insert(constraint_points.end(),
298 std::vector<
Point<dim - 1>> inner_points(n * n);
299 for (
unsigned int i = 0, iy = 1; iy <= n; ++iy)
300 for (
unsigned int ix = 1; ix <= n; ++ix)
304 for (
unsigned int child = 0;
307 for (
const auto &inner_point : inner_points)
308 constraint_points.push_back(
315 const unsigned int pnts = (q_deg + 1) * (q_deg + 1);
319 const std::vector<unsigned int> &index_map_inverse =
321 const std::vector<unsigned int> face_index_map =
331 for (
unsigned int i = 0; i < constraint_points.size(); ++i)
333 const double interval =
static_cast<double>(q_deg * 2);
334 bool mirror[dim - 1];
346 for (
unsigned int k = 0; k < dim - 1; ++k)
348 const int coord_int =
349 static_cast<int>(constraint_points[i][k] * interval + 0.25);
350 constraint_point[k] = 1. * coord_int / interval;
372 mirror[k] = (constraint_point[k] > 0.5);
374 constraint_point[k] = 1.0 - constraint_point[k];
377 for (
unsigned int j = 0; j < pnts; ++j)
379 unsigned int indices[2] = {j % (q_deg + 1), j / (q_deg + 1)};
381 for (
unsigned int k = 0; k < 2; ++k)
383 indices[k] = q_deg - indices[k];
385 const unsigned int new_index =
386 indices[1] * (q_deg + 1) + indices[0];
389 fe.
poly_space->compute_value(index_map_inverse[new_index],
406template <
int dim,
int spacedim>
410 const std::vector<bool> &restriction_is_additive_flags)
414 restriction_is_additive_flags,
417 &poly_space) != nullptr ?
424template <
int dim,
int spacedim>
429 ExcMessage(
"The first support point has to be zero."));
430 Assert(points.back()[0] == 1,
431 ExcMessage(
"The last support point has to be one."));
436 const unsigned int q_dofs_per_cell =
437 Utilities::fixed_power<dim>(
q_degree + 1);
443 [
this, q_dofs_per_cell]() {
444 std::vector<unsigned int> renumber =
445 FETools::hierarchic_to_lexicographic_numbering<dim>(
q_degree);
446 for (
unsigned int i = q_dofs_per_cell; i < this->
n_dofs_per_cell(); ++i)
447 renumber.push_back(i);
448 auto *tensor_poly_space_ptr =
450 if (tensor_poly_space_ptr !=
nullptr)
455 auto *tensor_piecewise_poly_space_ptr =
dynamic_cast<
458 if (tensor_piecewise_poly_space_ptr !=
nullptr)
463 auto *tensor_bubbles_poly_space_ptr =
466 if (tensor_bubbles_poly_space_ptr !=
nullptr)
471 auto *tensor_const_poly_space_ptr =
474 if (tensor_const_poly_space_ptr !=
nullptr)
500template <
int dim,
int spacedim>
511 Assert(interpolation_matrix.
m() == this->n_dofs_per_cell(),
513 this->n_dofs_per_cell()));
519 const unsigned int q_dofs_per_cell =
520 Utilities::fixed_power<dim>(
q_degree + 1);
521 const unsigned int source_q_dofs_per_cell =
522 Utilities::fixed_power<dim>(source_fe->degree + 1);
528 for (
unsigned int j = 0; j < q_dofs_per_cell; ++j)
538 for (
unsigned int i = 0; i < source_q_dofs_per_cell; ++i)
539 interpolation_matrix(j, i) =
540 source_fe->poly_space->compute_value(i, p);
547 source_fe->n_dofs_per_cell());
548 for (
unsigned int i = 0; i < source_q_dofs_per_cell; ++i)
549 interpolation_matrix(q_dofs_per_cell, i) = 0.;
550 for (
unsigned int j = 0; j < q_dofs_per_cell; ++j)
551 interpolation_matrix(j, source_q_dofs_per_cell) = 0.;
552 interpolation_matrix(q_dofs_per_cell, source_q_dofs_per_cell) = 1.;
558 for (
unsigned int j = 0; j < source_fe->n_dofs_per_cell(); ++j)
559 if (std::fabs(interpolation_matrix(i, j)) <
eps)
560 interpolation_matrix(i, j) = 0.;
569 for (
unsigned int j = 0; j < source_fe->n_dofs_per_cell(); ++j)
570 sum += interpolation_matrix(i, j);
601template <
int dim,
int spacedim>
606 const unsigned int face_no)
const
610 interpolation_matrix,
616template <
int dim,
int spacedim>
620 const unsigned int subface,
622 const unsigned int face_no)
const
636 Assert(interpolation_matrix.
n() == this->n_dofs_per_face(face_no),
638 this->n_dofs_per_face(face_no)));
684 double matrix_entry =
690 if (std::fabs(matrix_entry - 1.0) < eps)
692 if (std::fabs(matrix_entry) < eps)
695 interpolation_matrix(i, j) = matrix_entry;
708 sum += interpolation_matrix(j, i);
727template <
int dim,
int spacedim>
736template <
int dim,
int spacedim>
737std::vector<std::pair<unsigned int, unsigned int>>
789template <
int dim,
int spacedim>
790std::vector<std::pair<unsigned int, unsigned int>>
807 const unsigned int p = this->
degree;
808 const unsigned int q = fe_q_other->degree;
810 std::vector<std::pair<unsigned int, unsigned int>> identities;
812 const std::vector<unsigned int> &index_map_inverse =
814 const std::vector<unsigned int> &index_map_inverse_other =
815 fe_q_other->get_poly_space_numbering_inverse();
817 for (
unsigned int i = 0; i < p - 1; ++i)
818 for (
unsigned int j = 0; j < q - 1; ++j)
821 fe_q_other->unit_support_points[index_map_inverse_other[j + 1]]
823 identities.emplace_back(i, j);
844 const std::vector<unsigned int> &index_map_inverse_q =
847 std::vector<std::pair<unsigned int, unsigned int>> identities;
849 for (
unsigned int i = 0; i < this->
degree - 1; ++i)
850 for (
unsigned int j = 0; j < fe_p_other->degree - 1; ++j)
853 fe_p_other->get_unit_support_points()[j + 3][0]) < 1e-14)
854 identities.emplace_back(i, j);
884template <
int dim,
int spacedim>
885std::vector<std::pair<unsigned int, unsigned int>>
888 const unsigned int)
const
900 const unsigned int p = this->
degree;
901 const unsigned int q = fe_q_other->degree;
903 std::vector<std::pair<unsigned int, unsigned int>> identities;
905 const std::vector<unsigned int> &index_map_inverse =
907 const std::vector<unsigned int> &index_map_inverse_other =
908 fe_q_other->get_poly_space_numbering_inverse();
910 for (
unsigned int i1 = 0; i1 < p - 1; ++i1)
911 for (
unsigned int i2 = 0; i2 < p - 1; ++i2)
912 for (
unsigned int j1 = 0; j1 < q - 1; ++j1)
913 for (
unsigned int j2 = 0; j2 < q - 1; ++j2)
924 identities.emplace_back(i1 * (p - 1) + i2, j1 * (q - 1) + j2);
932 return std::vector<std::pair<unsigned int, unsigned int>>();
943 return std::vector<std::pair<unsigned int, unsigned int>>();
948 return std::vector<std::pair<unsigned int, unsigned int>>();
960template <
int dim,
int spacedim>
963 const std::vector<
Point<1>> &points)
965 const std::vector<unsigned int> &index_map_inverse =
978 for (
unsigned int k = 0; k < support_quadrature.size(); ++k)
980 support_quadrature.point(k);
985template <
int dim,
int spacedim>
988 const std::vector<
Point<1>> &points)
993 const unsigned int face_no = 0;
996 Utilities::fixed_power<dim - 1>(
q_degree + 1));
1004 const std::vector<unsigned int> face_index_map =
1012 const Quadrature<dim - 1> support_quadrature(support_1d);
1017 for (
unsigned int k = 0; k < support_quadrature.size(); ++k)
1019 support_quadrature.point(k);
1024template <
int dim,
int spacedim>
1040 const unsigned int face_no = 0;
1048 const unsigned int n =
q_degree - 1;
1069 for (
unsigned int local = 0; local < this->
n_dofs_per_quad(face_no); ++local)
1073 unsigned int i = local % n, j = local / n;
1082 i + (n - 1 - j) * n - local;
1086 (n - 1 - j) + (n - 1 - i) * n - local;
1090 (n - 1 - i) + j * n - local;
1097 j + (n - 1 - i) * n - local;
1101 (n - 1 - i) + (n - 1 - j) * n - local;
1105 (n - 1 - j) + i * n - local;
1111template <
int dim,
int spacedim>
1114 const unsigned int face_index,
1115 const unsigned int face,
1129 const unsigned int dof_index_on_vertex =
1135 face, face_vertex, combined_orientation) *
1137 dof_index_on_vertex;
1144 const unsigned int index =
1152 unsigned int adjusted_dof_index_on_line = 0;
1161 adjusted_dof_index_on_line = dof_index_on_line;
1163 adjusted_dof_index_on_line =
1176 combined_orientation ==
1179 adjusted_dof_index_on_line = dof_index_on_line;
1189 combined_orientation) *
1191 adjusted_dof_index_on_line);
1199 const unsigned int index =
1214template <
int dim,
int spacedim>
1215std::vector<unsigned int>
1220 std::vector<unsigned int> dpo(dim + 1, 1U);
1221 for (
unsigned int i = 1; i < dpo.size(); ++i)
1222 dpo[i] = dpo[i - 1] * (
degree - 1);
1228template <
int dim,
int spacedim>
1231 const std::vector<
Point<1>> &points)
1238template <
int dim,
int spacedim>
1241 const unsigned int child,
1248 "Prolongation matrices are only available for refined cells!"));
1250 child, this->
reference_cell().
template n_children<dim>(refinement_case));
1253 if (this->
prolongation[refinement_case - 1][child].n() == 0)
1258 if (this->
prolongation[refinement_case - 1][child].n() ==
1263 const unsigned int q_dofs_per_cell =
1264 Utilities::fixed_power<dim>(
q_degree + 1);
1278 for (
unsigned int i = 0; i < q_dofs_per_cell; ++i)
1281 i, this->unit_support_points[i])) < eps,
1283 "The Lagrange polynomial does not evaluate "
1284 "to one or zero in a nodal point. "
1285 "This typically indicates that the "
1286 "polynomial interpolation is "
1287 "ill-conditioned such that round-off "
1288 "prevents the sum to be one."));
1289 for (
unsigned int j = 0; j < q_dofs_per_cell; ++j)
1292 i, this->unit_support_points[j])) < eps,
1294 "The Lagrange polynomial does not evaluate "
1295 "to one or zero in a nodal point. "
1296 "This typically indicates that the "
1297 "polynomial interpolation is "
1298 "ill-conditioned such that round-off "
1299 "prevents the sum to be one."));
1307 const unsigned int dofs1d =
q_degree + 1;
1308 std::vector<Table<2, double>> subcell_evaluations(
1311 const std::vector<unsigned int> &index_map_inverse =
1316 unsigned int step_size_diag = 0;
1318 unsigned int factor = 1;
1319 for (
unsigned int d = 0;
d < dim; ++
d)
1321 step_size_diag += factor;
1331 for (
unsigned int j = 0; j < dofs1d; ++j)
1333 const unsigned int diag_comp = index_map_inverse[j * step_size_diag];
1339 for (
unsigned int i = 0; i < dofs1d; ++i)
1340 for (
unsigned int d = 0;
d < dim; ++
d)
1345 const double cell_value =
1346 this->
poly_space->compute_value(index_map_inverse[i], point);
1365 if (std::fabs(cell_value) < eps)
1366 subcell_evaluations[
d](j, i) = 0;
1368 subcell_evaluations[
d](j, i) = cell_value;
1374 unsigned int j_indices[dim];
1375 internal::FE_Q_Base::zero_indices<dim>(j_indices);
1376 for (
unsigned int j = 0; j < q_dofs_per_cell; j += dofs1d)
1378 unsigned int i_indices[dim];
1379 internal::FE_Q_Base::zero_indices<dim>(i_indices);
1380 for (
unsigned int i = 0; i < q_dofs_per_cell; i += dofs1d)
1382 double val_extra_dim = 1.;
1383 for (
unsigned int d = 1;
d < dim; ++
d)
1385 subcell_evaluations[d](j_indices[d - 1], i_indices[d - 1]);
1389 for (
unsigned int jj = 0; jj < dofs1d; ++jj)
1391 const unsigned int j_ind = index_map_inverse[j + jj];
1392 for (
unsigned int ii = 0; ii < dofs1d; ++ii)
1393 prolongate(j_ind, index_map_inverse[i + ii]) =
1394 val_extra_dim * subcell_evaluations[0](jj, ii);
1399 internal::FE_Q_Base::increment_indices<dim>(i_indices, dofs1d);
1402 internal::FE_Q_Base::increment_indices<dim>(j_indices, dofs1d);
1408 prolongate(q_dofs_per_cell, q_dofs_per_cell) = 1.;
1418 sum += prolongate(row, col);
1419 Assert(std::fabs(sum - 1.) <
1423 "prolongation matrix do not add to one. "
1424 "This typically indicates that the "
1425 "polynomial interpolation is "
1426 "ill-conditioned such that round-off "
1427 "prevents the sum to be one."));
1433 this->
prolongation[refinement_case - 1][child]) = std::move(prolongate);
1442template <
int dim,
int spacedim>
1445 const unsigned int child,
1452 "Restriction matrices are only available for refined cells!"));
1454 child, this->
reference_cell().
template n_children<dim>(refinement_case));
1457 if (this->
restriction[refinement_case - 1][child].n() == 0)
1462 if (this->
restriction[refinement_case - 1][child].n() ==
1464 return this->
restriction[refinement_case - 1][child];
1469 const unsigned int q_dofs_per_cell =
1470 Utilities::fixed_power<dim>(
q_degree + 1);
1491 const std::vector<unsigned int> &index_map_inverse =
1494 const unsigned int dofs1d =
q_degree + 1;
1495 std::vector<Tensor<1, dim>> evaluations1d(dofs1d);
1499 for (
unsigned int i = 0; i < q_dofs_per_cell; ++i)
1501 unsigned int mother_dof = index_map_inverse[i];
1516 for (
unsigned int j = 0; j < dofs1d; ++j)
1517 for (
unsigned int d = 0;
d < dim; ++
d)
1521 evaluations1d[j][
d] =
1522 this->
poly_space->compute_value(index_map_inverse[j],
1525 unsigned int j_indices[dim];
1526 internal::FE_Q_Base::zero_indices<dim>(j_indices);
1527 double sum_check = 0;
1528 for (
unsigned int j = 0; j < q_dofs_per_cell; j += dofs1d)
1530 double val_extra_dim = 1.;
1531 for (
unsigned int d = 1;
d < dim; ++
d)
1532 val_extra_dim *= evaluations1d[j_indices[d - 1]][d];
1533 for (
unsigned int jj = 0; jj < dofs1d; ++jj)
1541 const double val = val_extra_dim * evaluations1d[jj][0];
1542 const unsigned int child_dof = index_map_inverse[j + jj];
1543 if (std::fabs(val - 1.) < eps)
1544 my_restriction(mother_dof, child_dof) = 1.;
1545 else if (std::fabs(val) > eps)
1546 my_restriction(mother_dof, child_dof) = val;
1549 internal::FE_Q_Base::increment_indices<dim>(j_indices,
1553 Assert(std::fabs(sum_check - 1.0) <
1557 "restriction matrix do not add to one. "
1558 "This typically indicates that the "
1559 "polynomial interpolation is "
1560 "ill-conditioned such that round-off "
1561 "prevents the sum to be one."));
1575 std::move(my_restriction);
1578 return this->
restriction[refinement_case - 1][child];
1588template <
int dim,
int spacedim>
1591 const unsigned int shape_index,
1592 const unsigned int face_index)
const
1601 return (((shape_index == 0) && (face_index == 0)) ||
1602 ((shape_index == 1) && (face_index == 1)));
1617 const unsigned int vertex_no = shape_index;
1621 for (
unsigned int v = 0; v < GeometryInfo<dim>::vertices_per_face; ++v)
1631 const unsigned int line_index =
1637 if constexpr (dim == 2)
1638 return (line_index == face_index);
1639 else if constexpr (dim == 3)
1642 for (
unsigned int l = 0; l < GeometryInfo<3>::lines_per_face; ++
l)
1655 const unsigned int quad_index =
1666 return (quad_index == face_index);
1685template <
int dim,
int spacedim>
1686std::pair<Table<2, bool>, std::vector<unsigned int>>
1694 for (
unsigned int i = 0; i < Utilities::fixed_power<dim>(
q_degree + 1); ++i)
1695 constant_modes(0, i) =
true;
1696 return std::pair<Table<2, bool>, std::vector<unsigned int>>(
1697 constant_modes, std::vector<unsigned int>(1, 0));
1703#include "fe/fe_q_base.inst"
std::vector< unsigned int > get_poly_space_numbering_inverse() const
const ScalarPolynomialsBase< dim > & get_poly_space() const
virtual double shape_value(const unsigned int i, const Point< dim > &p) const override
const std::unique_ptr< ScalarPolynomialsBase< dim > > poly_space
Threads::Mutex prolongation_matrix_mutex
void initialize_unit_face_support_points(const std::vector< Point< 1 > > &points)
virtual bool hp_constraints_are_implemented() const override
virtual std::vector< std::pair< unsigned int, unsigned int > > hp_line_dof_identities(const FiniteElement< dim, spacedim > &fe_other) const override
virtual void get_interpolation_matrix(const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const override
Threads::Mutex restriction_matrix_mutex
virtual std::vector< std::pair< unsigned int, unsigned int > > hp_quad_dof_identities(const FiniteElement< dim, spacedim > &fe_other, const unsigned int face_no=0) const override
const unsigned int q_degree
virtual std::pair< Table< 2, bool >, std::vector< unsigned int > > get_constant_modes() const override
void initialize(const std::vector< Point< 1 > > &support_points_1d)
void initialize_unit_support_points(const std::vector< Point< 1 > > &points)
virtual void get_subface_interpolation_matrix(const FiniteElement< dim, spacedim > &source, const unsigned int subface, FullMatrix< double > &matrix, const unsigned int face_no=0) const override
virtual void get_face_interpolation_matrix(const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix, const unsigned int face_no=0) const override
static std::vector< unsigned int > get_dpo_vector(const unsigned int degree)
void initialize_constraints(const std::vector< Point< 1 > > &points)
void initialize_dof_index_permutations()
virtual const FullMatrix< double > & get_restriction_matrix(const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const override
virtual const FullMatrix< double > & get_prolongation_matrix(const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const override
virtual bool has_support_on_face(const unsigned int shape_index, const unsigned int face_index) const override
virtual unsigned int face_to_cell_index(const unsigned int face_dof_index, const unsigned int face, const types::geometric_orientation combined_orientation=numbers::default_geometric_orientation) const override
virtual std::vector< std::pair< unsigned int, unsigned int > > hp_vertex_dof_identities(const FiniteElement< dim, spacedim > &fe_other) const override
FE_Q_Base(const ScalarPolynomialsBase< dim > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags)
unsigned int get_first_line_index() const
unsigned int n_dofs_per_vertex() const
const unsigned int degree
unsigned int n_dofs_per_cell() const
unsigned int n_dofs_per_line() const
unsigned int get_first_quad_index(const unsigned int quad_no=0) const
unsigned int n_dofs_per_face(unsigned int face_no=0, unsigned int child=0) const
unsigned int n_components() const
ReferenceCell reference_cell() const
unsigned int get_first_face_line_index(const unsigned int face_no=0) const
unsigned int get_first_face_quad_index(const unsigned int face_no=0) const
unsigned int n_unique_faces() const
unsigned int n_dofs_per_quad(unsigned int face_no=0) const
unsigned int get_first_hex_index() const
std::vector< std::vector< Point< dim - 1 > > > unit_face_support_points
bool has_face_support_points(const unsigned int face_no=0) const
std::vector< std::vector< FullMatrix< double > > > restriction
std::vector< Table< 2, int > > adjust_quad_dof_index_for_face_orientation_table
const std::vector< Point< dim - 1 > > & get_unit_face_support_points(const unsigned int face_no=0) const
std::vector< int > adjust_line_dof_index_for_line_orientation_table
TableIndices< 2 > interface_constraints_size() const
std::vector< Point< dim > > unit_support_points
FullMatrix< double > interface_constraints
std::vector< std::vector< FullMatrix< double > > > prolongation
Class which transforms dim - 1-dimensional quadrature rules to dim-dimensional face quadratures.
static void project_to_subface(const ReferenceCell &reference_cell, const SubQuadrature &quadrature, const unsigned int face_no, const unsigned int subface_no, std::vector< Point< dim > > &q_points, const RefinementCase< dim - 1 > &ref_case=RefinementCase< dim - 1 >::isotropic_refinement)
static void project_to_face(const ReferenceCell &reference_cell, const SubQuadrature &quadrature, const unsigned int face_no, std::vector< Point< dim > > &q_points)
const Point< dim > & point(const unsigned int i) const
unsigned int face_to_cell_vertices(const unsigned int face, const unsigned int vertex, const types::geometric_orientation face_orientation) const
void set_numbering(const std::vector< unsigned int > &renumber)
void set_numbering(const std::vector< unsigned int > &renumber)
void set_numbering(const std::vector< unsigned int > &renumber)
#define DEAL_II_NAMESPACE_OPEN
constexpr bool running_in_debug_mode()
#define DEAL_II_NAMESPACE_CLOSE
#define DEAL_II_ASSERT_UNREACHABLE()
#define DEAL_II_NOT_IMPLEMENTED()
static ::ExceptionBase & ExcNotImplemented()
#define Assert(cond, exc)
#define AssertDimension(dim1, dim2)
#define AssertIndexRange(index, range)
static ::ExceptionBase & ExcInternalError()
static ::ExceptionBase & ExcDimensionMismatch(std::size_t arg1, std::size_t arg2)
static ::ExceptionBase & ExcInterpolationNotImplemented()
static ::ExceptionBase & ExcMessage(std::string arg1)
#define AssertThrow(cond, exc)
Task< RT > new_task(const std::function< RT()> &function)
Point< spacedim > point(const gp_Pnt &p, const double tolerance=1e-10)
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)
SymmetricTensor< 2, dim, Number > d(const Tensor< 2, dim, Number > &F, const Tensor< 2, dim, Number > &dF_dt)
T sum(const T &t, const MPI_Comm mpi_communicator)
types::geometric_orientation combined_face_orientation(const bool face_orientation, const bool face_rotation, const bool face_flip)
constexpr unsigned int invalid_unsigned_int
constexpr types::geometric_orientation default_geometric_orientation
::VectorizedArray< Number, width > max(const ::VectorizedArray< Number, width > &, const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > sqrt(const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > abs(const ::VectorizedArray< Number, width > &)
unsigned char geometric_orientation
static void initialize_constraints(const std::vector< Point< 1 > > &, FE_Q_Base< 3, spacedim > &fe)
static void initialize_constraints(const std::vector< Point< 1 > > &, FE_Q_Base< 1, spacedim > &)
static void initialize_constraints(const std::vector< Point< 1 > > &, FE_Q_Base< 2, spacedim > &fe)
static Point< dim > cell_to_child_coordinates(const Point< dim > &p, const unsigned int child_index, const RefinementCase< dim > refine_case=RefinementCase< dim >::isotropic_refinement)
static Point< dim > child_to_cell_coordinates(const Point< dim > &p, const unsigned int child_index, const RefinementCase< dim > refine_case=RefinementCase< dim >::isotropic_refinement)