Reference documentation for deal.II version 9.5.0

Namespaces  
namespace  internal 
Classes  
class  Cache 
struct  CellDataTransferBuffer 
class  MarchingCubeAlgorithm 
struct  OrientationLookupTable 
struct  OrientationLookupTable< 1 > 
struct  OrientationLookupTable< 2 > 
struct  OrientationLookupTable< 3 > 
struct  PeriodicFacePair 
Enumerations  
enum  CacheUpdateFlags { update_nothing = 0x000 , update_vertex_to_cell_map = 0x001 , update_vertex_to_cell_centers_directions , update_used_vertices = 0x008 , update_used_vertices_rtree = 0x010 , update_cell_bounding_boxes_rtree = 0x020 , update_covering_rtree = 0x040 , update_locally_owned_cell_bounding_boxes_rtree = 0x080 , update_vertex_to_neighbor_subdomain = 0x100 , update_vertex_with_ghost_neighbors = 0x200 , update_all = 0xFFF } 
Functions  
template<typename DataType , typename MeshType >  
void  exchange_cell_data_to_ghosts (const MeshType &mesh, const std::function< std_cxx17::optional< DataType >(const typename MeshType::active_cell_iterator &)> &pack, const std::function< void(const typename MeshType::active_cell_iterator &, const DataType &)> &unpack, const std::function< bool(const typename MeshType::active_cell_iterator &)> &cell_filter=always_return< typename MeshType::active_cell_iterator, bool >{true}) 
template<typename DataType , typename MeshType >  
void  exchange_cell_data_to_level_ghosts (const MeshType &mesh, const std::function< std_cxx17::optional< DataType >(const typename MeshType::level_cell_iterator &)> &pack, const std::function< void(const typename MeshType::level_cell_iterator &, const DataType &)> &unpack, const std::function< bool(const typename MeshType::level_cell_iterator &)> &cell_filter=always_return< typename MeshType::level_cell_iterator, bool >{ true}) 
template<int spacedim>  
std::vector< std::vector< BoundingBox< spacedim > > >  exchange_local_bounding_boxes (const std::vector< BoundingBox< spacedim > > &local_bboxes, const MPI_Comm mpi_communicator) 
template<int spacedim>  
RTree< std::pair< BoundingBox< spacedim >, unsigned int > >  build_global_description_tree (const std::vector< BoundingBox< spacedim > > &local_description, const MPI_Comm mpi_communicator) 
template<int dim, int spacedim>  
void  collect_coinciding_vertices (const Triangulation< dim, spacedim > &tria, std::map< unsigned int, std::vector< unsigned int > > &coinciding_vertex_groups, std::map< unsigned int, unsigned int > &vertex_to_coinciding_vertex_group) 
template<int dim, int spacedim>  
std::map< unsigned int, std::set<::types::subdomain_id > >  compute_vertices_with_ghost_neighbors (const Triangulation< dim, spacedim > &tria) 
template<class StreamType >  
StreamType &  operator<< (StreamType &s, const CacheUpdateFlags u) 
CacheUpdateFlags  operator (const CacheUpdateFlags f1, const CacheUpdateFlags f2) 
CacheUpdateFlags  operator~ (const CacheUpdateFlags f1) 
CacheUpdateFlags &  operator= (CacheUpdateFlags &f1, const CacheUpdateFlags f2) 
CacheUpdateFlags  operator& (const CacheUpdateFlags f1, const CacheUpdateFlags f2) 
CacheUpdateFlags &  operator&= (CacheUpdateFlags &f1, const CacheUpdateFlags f2) 
template<>  
void  rotate (const double angle, Triangulation< 1, 2 > &triangulation) 
template<>  
void  rotate (const double angle, Triangulation< 2, 2 > &triangulation) 
template<int dim>  
void  laplace_transform (const std::map< unsigned int, Point< dim > > &new_points, Triangulation< dim > &triangulation, const Function< dim > *coefficient, const bool solve_for_absolute_positions) 
template<typename CellIterator >  
void  match_periodic_face_pairs (std::set< std::pair< CellIterator, unsigned int > > &pairs1, std::set< std::pair< std_cxx20::type_identity_t< CellIterator >, unsigned int > > &pairs2, const unsigned int direction, std::vector< PeriodicFacePair< CellIterator > > &matched_pairs, const ::Tensor< 1, CellIterator::AccessorType::space_dimension > &offset, const FullMatrix< double > &matrix) 
template<typename MeshType >  
void  collect_periodic_faces (const MeshType &mesh, const types::boundary_id b_id, const unsigned int direction, std::vector< PeriodicFacePair< typename MeshType::cell_iterator > > &matched_pairs, const Tensor< 1, MeshType::space_dimension > &offset, const FullMatrix< double > &matrix) 
template<int spacedim>  
bool  orthogonal_equality (const Point< spacedim > &point1, const Point< spacedim > &point2, const unsigned int direction, const Tensor< 1, spacedim > &offset, const FullMatrix< double > &matrix) 
template<>  
double  cell_measure< 1 > (const std::vector< Point< 1 > > &all_vertices, const ArrayView< const unsigned int > &vertex_indices) 
template<>  
double  cell_measure< 2 > (const std::vector< Point< 2 > > &all_vertices, const ArrayView< const unsigned int > &vertex_indices) 
template<>  
double  cell_measure< 3 > (const std::vector< Point< 3 > > &all_vertices, const ArrayView< const unsigned int > &vertex_indices) 
Information about meshes and cells  
template<int dim, int spacedim>  
double  diameter (const Triangulation< dim, spacedim > &tria) 
template<int dim, int spacedim>  
double  volume (const Triangulation< dim, spacedim > &tria) 
template<int dim, int spacedim>  
double  volume (const Triangulation< dim, spacedim > &tria, const Mapping< dim, spacedim > &mapping) 
template<int dim, int spacedim>  
double  minimal_cell_diameter (const Triangulation< dim, spacedim > &triangulation, const Mapping< dim, spacedim > &mapping=(ReferenceCells::get_hypercube< dim >() .template get_default_linear_mapping< dim, spacedim >())) 
template<int dim, int spacedim>  
double  maximal_cell_diameter (const Triangulation< dim, spacedim > &triangulation, const Mapping< dim, spacedim > &mapping=(ReferenceCells::get_hypercube< dim >() .template get_default_linear_mapping< dim, spacedim >())) 
template<int dim>  
double  cell_measure (const std::vector< Point< dim > > &all_vertices, const unsigned int(&vertex_indices)[GeometryInfo< dim >::vertices_per_cell]) 
template<int dim>  
double  cell_measure (const std::vector< Point< dim > > &all_vertices, const ArrayView< const unsigned int > &vertex_indices) 
template<int dim, int spacedim>  
std::pair< DerivativeForm< 1, dim, spacedim >, Tensor< 1, spacedim > >  affine_cell_approximation (const ArrayView< const Point< spacedim > > &vertices) 
template<int dim>  
Vector< double >  compute_aspect_ratio_of_cells (const Mapping< dim > &mapping, const Triangulation< dim > &triangulation, const Quadrature< dim > &quadrature) 
template<int dim>  
double  compute_maximum_aspect_ratio (const Mapping< dim > &mapping, const Triangulation< dim > &triangulation, const Quadrature< dim > &quadrature) 
template<int dim, int spacedim>  
BoundingBox< spacedim >  compute_bounding_box (const Triangulation< dim, spacedim > &triangulation) 
template<typename Iterator >  
Point< Iterator::AccessorType::space_dimension >  project_to_object (const Iterator &object, const Point< Iterator::AccessorType::space_dimension > &trial_point) 
template<int dim, int spacedim>  
std::tuple< std::vector< Point< spacedim > >, std::vector< CellData< dim > >, SubCellData >  get_coarse_mesh_description (const Triangulation< dim, spacedim > &tria) 
Functions supporting the creation of meshes  
template<int dim, int spacedim>  
void  delete_unused_vertices (std::vector< Point< spacedim > > &vertices, std::vector< CellData< dim > > &cells, SubCellData &subcelldata) 
template<int dim, int spacedim>  
void  delete_duplicated_vertices (std::vector< Point< spacedim > > &all_vertices, std::vector< CellData< dim > > &cells, SubCellData &subcelldata, std::vector< unsigned int > &considered_vertices, const double tol=1e12) 
template<int dim>  
void  delete_duplicated_vertices (std::vector< Point< dim > > &vertices, const double tol=1e12) 
template<int dim, int spacedim>  
void  invert_all_negative_measure_cells (const std::vector< Point< spacedim > > &all_vertices, std::vector< CellData< dim > > &cells) 
template<int dim, int spacedim>  
std::size_t  invert_cells_with_negative_measure (const std::vector< Point< spacedim > > &all_vertices, std::vector< CellData< dim > > &cells) 
template<int dim>  
void  consistently_order_cells (std::vector< CellData< dim > > &cells) 
Rotating, stretching and otherwise transforming meshes  
template<int dim, typename Transformation , int spacedim>  
void  transform (const Transformation &transformation, Triangulation< dim, spacedim > &triangulation) 
template<int dim, int spacedim>  
void  shift (const Tensor< 1, spacedim > &shift_vector, Triangulation< dim, spacedim > &triangulation) 
template<int dim, int spacedim>  
void  rotate (const double angle, Triangulation< dim, spacedim > &triangulation) 
template<int dim>  
void  rotate (const Tensor< 1, 3, double > &axis, const double angle, Triangulation< dim, 3 > &triangulation) 
template<int dim>  
void  rotate (const double angle, const unsigned int axis, Triangulation< dim, 3 > &triangulation) 
template<int dim>  
void  laplace_transform (const std::map< unsigned int, Point< dim > > &new_points, Triangulation< dim > &tria, const Function< dim, double > *coefficient=nullptr, const bool solve_for_absolute_positions=false) 
template<int dim, int spacedim>  
std::map< unsigned int, Point< spacedim > >  get_all_vertices_at_boundary (const Triangulation< dim, spacedim > &tria) 
template<int dim, int spacedim>  
void  scale (const double scaling_factor, Triangulation< dim, spacedim > &triangulation) 
template<int dim, int spacedim>  
void  distort_random (const double factor, Triangulation< dim, spacedim > &triangulation, const bool keep_boundary=true, const unsigned int seed=boost::random::mt19937::default_seed) 
template<int dim, int spacedim>  
void  remove_hanging_nodes (Triangulation< dim, spacedim > &tria, const bool isotropic=false, const unsigned int max_iterations=100) 
template<int dim, int spacedim>  
void  remove_anisotropy (Triangulation< dim, spacedim > &tria, const double max_ratio=1.6180339887, const unsigned int max_iterations=5) 
template<int dim, int spacedim>  
void  regularize_corner_cells (Triangulation< dim, spacedim > &tria, const double limit_angle_fraction=.75) 
Finding cells and vertices of a triangulation  
template<int dim, int spacedim>  
return_type  compute_point_locations (const Cache< dim, spacedim > &cache, const std::vector< Point< spacedim > > &points, const typename Triangulation< dim, spacedim >::active_cell_iterator &cell_hint=typename Triangulation< dim, spacedim >::active_cell_iterator()) 
template<int dim, int spacedim>  
return_type  compute_point_locations_try_all (const Cache< dim, spacedim > &cache, const std::vector< Point< spacedim > > &points, const typename Triangulation< dim, spacedim >::active_cell_iterator &cell_hint=typename Triangulation< dim, spacedim >::active_cell_iterator()) 
template<int dim, int spacedim>  
return_type  distributed_compute_point_locations (const GridTools::Cache< dim, spacedim > &cache, const std::vector< Point< spacedim > > &local_points, const std::vector< std::vector< BoundingBox< spacedim > > > &global_bboxes, const double tolerance=1e10, const std::vector< bool > &marked_vertices={}, const bool enforce_unique_mapping=true) 
template<int dim, int spacedim>  
std::map< unsigned int, Point< spacedim > >  extract_used_vertices (const Triangulation< dim, spacedim > &container, const Mapping< dim, spacedim > &mapping=(ReferenceCells::get_hypercube< dim >() .template get_default_linear_mapping< dim, spacedim >())) 
template<int spacedim>  
unsigned int  find_closest_vertex (const std::map< unsigned int, Point< spacedim > > &vertices, const Point< spacedim > &p) 
template<int dim, template< int, int > class MeshType, int spacedim>  
unsigned int  find_closest_vertex (const MeshType< dim, spacedim > &mesh, const Point< spacedim > &p, const std::vector< bool > &marked_vertices={}) 
template<int dim, template< int, int > class MeshType, int spacedim>  
unsigned int  find_closest_vertex (const Mapping< dim, spacedim > &mapping, const MeshType< dim, spacedim > &mesh, const Point< spacedim > &p, const std::vector< bool > &marked_vertices={}) 
template<class MeshType >  
std::vector< typename MeshType::active_cell_iterator >  find_cells_adjacent_to_vertex (const MeshType &container, const unsigned int vertex_index) 
template<int dim, template< int, int > class MeshType, int spacedim>  
std::pair< typename MeshType< dim, spacedim >::active_cell_iterator, Point< dim > >  find_active_cell_around_point (const Mapping< dim, spacedim > &mapping, const MeshType< dim, spacedim > &mesh, const Point< spacedim > &p, const std::vector< bool > &marked_vertices={}, const double tolerance=1.e10) 
template<int dim, template< int, int > class MeshType, int spacedim>  
MeshType< dim, spacedim >::active_cell_iterator  find_active_cell_around_point (const MeshType< dim, spacedim > &mesh, const Point< spacedim > &p, const std::vector< bool > &marked_vertices={}, const double tolerance=1.e10) 
template<int dim, int spacedim>  
std::pair< typename DoFHandler< dim, spacedim >::active_cell_iterator, Point< dim > >  find_active_cell_around_point (const hp::MappingCollection< dim, spacedim > &mapping, const DoFHandler< dim, spacedim > &mesh, const Point< spacedim > &p, const double tolerance=1.e10) 
template<int dim, int spacedim>  
std::pair< typename Triangulation< dim, spacedim >::active_cell_iterator, Point< dim > >  find_active_cell_around_point (const Cache< dim, spacedim > &cache, const Point< spacedim > &p, const typename Triangulation< dim, spacedim >::active_cell_iterator &cell_hint=typename Triangulation< dim, spacedim >::active_cell_iterator(), const std::vector< bool > &marked_vertices={}, const double tolerance=1.e10) 
template<int dim, template< int, int > class MeshType, int spacedim>  
std::pair< typename MeshType< dim, spacedim >::active_cell_iterator, Point< dim > >  find_active_cell_around_point (const Mapping< dim, spacedim > &mapping, const MeshType< dim, spacedim > &mesh, const Point< spacedim > &p, const std::vector< std::set< typename MeshType< dim, spacedim >::active_cell_iterator > > &vertex_to_cell_map, const std::vector< std::vector< Tensor< 1, spacedim > > > &vertex_to_cell_centers, const typename MeshType< dim, spacedim >::active_cell_iterator &cell_hint=typename MeshType< dim, spacedim >::active_cell_iterator(), const std::vector< bool > &marked_vertices={}, const RTree< std::pair< Point< spacedim >, unsigned int > > &used_vertices_rtree=RTree< std::pair< Point< spacedim >, unsigned int > >{}, const double tolerance=1.e10, const RTree< std::pair< BoundingBox< spacedim >, typename Triangulation< dim, spacedim >::active_cell_iterator > > *relevant_cell_bounding_boxes_rtree=nullptr) 
template<int dim, template< int, int > class MeshType, int spacedim>  
std::vector< std::pair< typename MeshType< dim, spacedim >::active_cell_iterator, Point< dim > > >  find_all_active_cells_around_point (const Mapping< dim, spacedim > &mapping, const MeshType< dim, spacedim > &mesh, const Point< spacedim > &p, const double tolerance, const std::pair< typename MeshType< dim, spacedim >::active_cell_iterator, Point< dim > > &first_cell) 
template<int dim, template< int, int > class MeshType, int spacedim>  
std::vector< std::pair< typename MeshType< dim, spacedim >::active_cell_iterator, Point< dim > > >  find_all_active_cells_around_point (const Mapping< dim, spacedim > &mapping, const MeshType< dim, spacedim > &mesh, const Point< spacedim > &p, const double tolerance=1e10, const std::vector< bool > &marked_vertices={}) 
template<class MeshType >  
std::vector< typename MeshType::active_cell_iterator >  get_active_child_cells (const typename MeshType::cell_iterator &cell) 
template<class MeshType >  
void  get_active_neighbors (const typename MeshType::active_cell_iterator &cell, std::vector< typename MeshType::active_cell_iterator > &active_neighbors) 
template<class MeshType >  
std::vector< typename MeshType::active_cell_iterator >  compute_active_cell_halo_layer (const MeshType &mesh, const std::function< bool(const typename MeshType::active_cell_iterator &)> &predicate) 
template<class MeshType >  
std::vector< typename MeshType::cell_iterator >  compute_cell_halo_layer_on_level (const MeshType &mesh, const std::function< bool(const typename MeshType::cell_iterator &)> &predicate, const unsigned int level) 
template<class MeshType >  
std::vector< typename MeshType::active_cell_iterator >  compute_ghost_cell_halo_layer (const MeshType &mesh) 
template<class MeshType >  
std::vector< typename MeshType::active_cell_iterator >  compute_active_cell_layer_within_distance (const MeshType &mesh, const std::function< bool(const typename MeshType::active_cell_iterator &)> &predicate, const double layer_thickness) 
template<class MeshType >  
std::vector< typename MeshType::active_cell_iterator >  compute_ghost_cell_layer_within_distance (const MeshType &mesh, const double layer_thickness) 
template<class MeshType >  
std::pair< Point< MeshType::space_dimension >, Point< MeshType::space_dimension > >  compute_bounding_box (const MeshType &mesh, const std::function< bool(const typename MeshType::active_cell_iterator &)> &predicate) 
template<class MeshType >  
std::vector< BoundingBox< MeshType::space_dimension > >  compute_mesh_predicate_bounding_box (const MeshType &mesh, const std::function< bool(const typename MeshType::active_cell_iterator &)> &predicate, const unsigned int refinement_level=0, const bool allow_merge=false, const unsigned int max_boxes=numbers::invalid_unsigned_int) 
template<int spacedim>  
return_type  guess_point_owner (const std::vector< std::vector< BoundingBox< spacedim > > > &global_bboxes, const std::vector< Point< spacedim > > &points) 
template<int spacedim>  
return_type  guess_point_owner (const RTree< std::pair< BoundingBox< spacedim >, unsigned int > > &covering_rtree, const std::vector< Point< spacedim > > &points) 
template<int dim, int spacedim>  
std::vector< std::set< typename Triangulation< dim, spacedim >::active_cell_iterator > >  vertex_to_cell_map (const Triangulation< dim, spacedim > &triangulation) 
template<int dim, int spacedim>  
std::vector< std::vector< Tensor< 1, spacedim > > >  vertex_to_cell_centers_directions (const Triangulation< dim, spacedim > &mesh, const std::vector< std::set< typename Triangulation< dim, spacedim >::active_cell_iterator > > &vertex_to_cells) 
template<int dim, int spacedim>  
unsigned int  find_closest_vertex_of_cell (const typename Triangulation< dim, spacedim >::active_cell_iterator &cell, const Point< spacedim > &position, const Mapping< dim, spacedim > &mapping=(ReferenceCells::get_hypercube< dim >() .template get_default_linear_mapping< dim, spacedim >())) 
template<int dim, int spacedim>  
std::map< unsigned int, types::global_vertex_index >  compute_local_to_global_vertex_index_map (const parallel::distributed::Triangulation< dim, spacedim > &triangulation) 
template<int dim, int spacedim>  
std::pair< unsigned int, double >  get_longest_direction (typename Triangulation< dim, spacedim >::active_cell_iterator cell) 
Partitions and subdomains of triangulations  
template<int dim, int spacedim>  
void  get_face_connectivity_of_cells (const Triangulation< dim, spacedim > &triangulation, DynamicSparsityPattern &connectivity) 
template<int dim, int spacedim>  
void  get_vertex_connectivity_of_cells (const Triangulation< dim, spacedim > &triangulation, DynamicSparsityPattern &connectivity) 
template<int dim, int spacedim>  
void  get_vertex_connectivity_of_cells_on_level (const Triangulation< dim, spacedim > &triangulation, const unsigned int level, DynamicSparsityPattern &connectivity) 
template<int dim, int spacedim>  
void  partition_triangulation (const unsigned int n_partitions, Triangulation< dim, spacedim > &triangulation, const SparsityTools::Partitioner partitioner=SparsityTools::Partitioner::metis) 
template<int dim, int spacedim>  
void  partition_triangulation (const unsigned int n_partitions, const std::vector< unsigned int > &cell_weights, Triangulation< dim, spacedim > &triangulation, const SparsityTools::Partitioner partitioner=SparsityTools::Partitioner::metis) 
template<int dim, int spacedim>  
void  partition_triangulation (const unsigned int n_partitions, const SparsityPattern &cell_connection_graph, Triangulation< dim, spacedim > &triangulation, const SparsityTools::Partitioner partitioner=SparsityTools::Partitioner::metis) 
template<int dim, int spacedim>  
void  partition_triangulation (const unsigned int n_partitions, const std::vector< unsigned int > &cell_weights, const SparsityPattern &cell_connection_graph, Triangulation< dim, spacedim > &triangulation, const SparsityTools::Partitioner partitioner=SparsityTools::Partitioner::metis) 
template<int dim, int spacedim>  
void  partition_triangulation_zorder (const unsigned int n_partitions, Triangulation< dim, spacedim > &triangulation, const bool group_siblings=true) 
template<int dim, int spacedim>  
void  partition_multigrid_levels (Triangulation< dim, spacedim > &triangulation) 
template<int dim, int spacedim>  
std::vector< types::subdomain_id >  get_subdomain_association (const Triangulation< dim, spacedim > &triangulation, const std::vector< CellId > &cell_ids) 
template<int dim, int spacedim>  
void  get_subdomain_association (const Triangulation< dim, spacedim > &triangulation, std::vector< types::subdomain_id > &subdomain) 
template<int dim, int spacedim>  
unsigned int  count_cells_with_subdomain_association (const Triangulation< dim, spacedim > &triangulation, const types::subdomain_id subdomain) 
template<int dim, int spacedim>  
std::vector< bool >  get_locally_owned_vertices (const Triangulation< dim, spacedim > &triangulation) 
Comparing different meshes  
template<typename MeshType >  
std::list< std::pair< typename MeshType::cell_iterator, typename MeshType::cell_iterator > >  get_finest_common_cells (const MeshType &mesh_1, const MeshType &mesh_2) 
template<int dim, int spacedim>  
bool  have_same_coarse_mesh (const Triangulation< dim, spacedim > &mesh_1, const Triangulation< dim, spacedim > &mesh_2) 
template<typename MeshType >  
bool  have_same_coarse_mesh (const MeshType &mesh_1, const MeshType &mesh_2) 
Dealing with distorted cells  
template<int dim, int spacedim>  
Triangulation< dim, spacedim >::DistortedCellList  fix_up_distorted_child_cells (const typename Triangulation< dim, spacedim >::DistortedCellList &distorted_cells, Triangulation< dim, spacedim > &triangulation) 
Extracting and creating patches of cells  
These functions extract and create patches of cells surrounding a single cell, and creating triangulation out of them.  
template<class MeshType >  
std::vector< typename MeshType::active_cell_iterator >  get_patch_around_cell (const typename MeshType::active_cell_iterator &cell) 
template<class Container >  
std::vector< typename Container::cell_iterator >  get_cells_at_coarsest_common_level (const std::vector< typename Container::active_cell_iterator > &patch_cells) 
template<class Container >  
void  build_triangulation_from_patch (const std::vector< typename Container::active_cell_iterator > &patch, Triangulation< Container::dimension, Container::space_dimension > &local_triangulation, std::map< typename Triangulation< Container::dimension, Container::space_dimension >::active_cell_iterator, typename Container::active_cell_iterator > &patch_to_global_tria_map) 
template<int dim, int spacedim>  
std::map< types::global_dof_index, std::vector< typename DoFHandler< dim, spacedim >::active_cell_iterator > >  get_dof_to_support_patch_map (DoFHandler< dim, spacedim > &dof_handler) 
Dealing with periodic domains  
template<typename FaceIterator >  
bool  orthogonal_equality (std::bitset< 3 > &orientation, const FaceIterator &face1, const FaceIterator &face2, const unsigned int direction, const Tensor< 1, FaceIterator::AccessorType::space_dimension > &offset=Tensor< 1, FaceIterator::AccessorType::space_dimension >(), const FullMatrix< double > &matrix=FullMatrix< double >()) 
template<typename FaceIterator >  
bool  orthogonal_equality (const FaceIterator &face1, const FaceIterator &face2, const unsigned int direction, const Tensor< 1, FaceIterator::AccessorType::space_dimension > &offset=Tensor< 1, FaceIterator::AccessorType::space_dimension >(), const FullMatrix< double > &matrix=FullMatrix< double >()) 
template<typename MeshType >  
void  collect_periodic_faces (const MeshType &mesh, const types::boundary_id b_id1, const types::boundary_id b_id2, const unsigned int direction, std::vector< PeriodicFacePair< typename MeshType::cell_iterator > > &matched_pairs, const Tensor< 1, MeshType::space_dimension > &offset=::Tensor< 1, MeshType::space_dimension >(), const FullMatrix< double > &matrix=FullMatrix< double >()) 
template<typename MeshType >  
void  collect_periodic_faces (const MeshType &mesh, const types::boundary_id b_id, const unsigned int direction, std::vector< PeriodicFacePair< typename MeshType::cell_iterator > > &matched_pairs, const ::Tensor< 1, MeshType::space_dimension > &offset=::Tensor< 1, MeshType::space_dimension >(), const FullMatrix< double > &matrix=FullMatrix< double >()) 
Dealing with boundary and manifold ids  
template<int dim, int spacedim>  
void  copy_boundary_to_manifold_id (Triangulation< dim, spacedim > &tria, const bool reset_boundary_ids=false) 
template<int dim, int spacedim>  
void  map_boundary_to_manifold_ids (const std::vector< types::boundary_id > &src_boundary_ids, const std::vector< types::manifold_id > &dst_manifold_ids, Triangulation< dim, spacedim > &tria, const std::vector< types::boundary_id > &reset_boundary_ids={}) 
template<int dim, int spacedim>  
void  copy_material_to_manifold_id (Triangulation< dim, spacedim > &tria, const bool compute_face_ids=false) 
template<int dim, int spacedim>  
void  assign_co_dimensional_manifold_indicators (Triangulation< dim, spacedim > &tria, const std::function< types::manifold_id(const std::set< types::manifold_id > &)> &disambiguation_function=[](const std::set< types::manifold_id > &manifold_ids) { if(manifold_ids.size()==1) return *manifold_ids.begin();else return numbers::flat_manifold_id;}, bool overwrite_only_flat_manifold_ids=true) 
Exceptions  
static ::ExceptionBase &  ExcInvalidNumberOfPartitions (int arg1) 
static ::ExceptionBase &  ExcNonExistentSubdomain (int arg1) 
static ::ExceptionBase &  ExcTriangulationHasBeenRefined () 
static ::ExceptionBase &  ExcScalingFactorNotPositive (double arg1) 
static ::ExceptionBase &  ExcVertexNotUsed (unsigned int arg1) 
This namespace is a collection of algorithms working on triangulations, such as shifting or rotating triangulations, but also finding a cell that contains a given point. See the descriptions of the individual functions for more information.
The enum type given to the Cache class to select what information to update.
You can select more than one flag by concatenation using the bitwise or operator(CacheUpdateFlags,CacheUpdateFlags)
.
Enumerator  

update_nothing  Update Nothing. 
update_vertex_to_cell_map  Update vertex_to_cell_map, as returned by GridTools::vertex_to_cell_map(). 
update_vertex_to_cell_centers_directions  Update vertex_to_cell_centers_directions, as returned by GridTools::vertex_to_cell_centers_directions() 
update_used_vertices  Update a mapping of used vertices. 
update_used_vertices_rtree  Update an RTree of the used vertices. 
update_cell_bounding_boxes_rtree  Update an RTree of the cell bounding boxes. 
update_covering_rtree  Update the covering rtree object, initialized with pairs of a bounding box and an unsigned int. The bounding boxes are used to describe approximately which portion of the mesh contains locally owned cells by the process of rank the second element of the pair. 
update_locally_owned_cell_bounding_boxes_rtree  Update an RTree of locally owned cell bounding boxes. 
update_vertex_to_neighbor_subdomain  Update vertex to neighbor subdomain 
update_vertex_with_ghost_neighbors  Update the information about which subdomains are connected to each vertex. 
update_all  Update all objects. 
Definition at line 33 of file grid_tools_cache_update_flags.h.
double GridTools::diameter  (  const Triangulation< dim, spacedim > &  tria  ) 
Return the diameter of a triangulation. The diameter is computed using only the vertices, i.e. if the diameter should be larger than the maximal distance between boundary vertices due to a higher order mapping, then this function will not catch this.
Definition at line 88 of file grid_tools.cc.
double GridTools::volume  (  const Triangulation< dim, spacedim > &  tria  ) 
Compute the volume (i.e. the dimdimensional measure) of the triangulation. We compute the measure using the integral \(\sum_K \int_K 1 \; dx\) where \(K\) are the cells of the given triangulation. The integral is approximated via quadrature. This version of the function uses a linear mapping to compute the JxW values on each cell.
If the triangulation is a dimdimensional one embedded in a higher dimensional space of dimension spacedim, then the value returned is the dimdimensional measure. For example, for a twodimensional triangulation in threedimensional space, the value returned is the area of the surface so described. (This obviously makes sense since the spacedimdimensional measure of a dimdimensional triangulation would always be zero if dim < spacedim).
This function also works for objects of type parallel::distributed::Triangulation, in which case the function is a collective operation.
tria  The triangulation. 
Definition at line 144 of file grid_tools.cc.
double GridTools::volume  (  const Triangulation< dim, spacedim > &  tria, 
const Mapping< dim, spacedim > &  mapping  
) 
Compute the volume (i.e. the dimdimensional measure) of the triangulation. We compute the measure using the integral \(\sum_K \int_K 1 \; dx\) where \(K\) are the cells of the given triangulation. The integral is approximated via quadrature for which we use the mapping argument.
If the triangulation is a dimdimensional one embedded in a higher dimensional space of dimension spacedim, then the value returned is the dimdimensional measure. For example, for a twodimensional triangulation in threedimensional space, the value returned is the area of the surface so described. (This obviously makes sense since the spacedimdimensional measure of a dimdimensional triangulation would always be zero if dim < spacedim.
This function also works for objects of type parallel::distributed::Triangulation, in which case the function is a collective operation.
tria  The triangulation. 
mapping  The Mapping which computes the Jacobians used to approximate the volume via quadrature. Explicitly using a higherorder Mapping (i.e., instead of using the other version of this function) will result in a more accurate approximation of the volume on Triangulations with curvature described by Manifold objects. 
Definition at line 158 of file grid_tools.cc.
double GridTools::minimal_cell_diameter  (  const Triangulation< dim, spacedim > &  triangulation, 
const Mapping< dim, spacedim > &  mapping = (ReferenceCells::get_hypercube<dim>() .template get_default_linear_mapping<dim, spacedim>() ) 

) 
Return an approximation of the diameter of the smallest active cell of a triangulation. See step24 for an example of use of this function.
Notice that, even if you pass a nontrivial mapping, the returned value is computed only using information on the vertices of the triangulation, possibly transformed by the mapping. While this is accurate most of the times, it may fail to give the correct result when the triangulation contains very distorted cells.
Definition at line 4454 of file grid_tools.cc.
double GridTools::maximal_cell_diameter  (  const Triangulation< dim, spacedim > &  triangulation, 
const Mapping< dim, spacedim > &  mapping = (ReferenceCells::get_hypercube<dim>() .template get_default_linear_mapping<dim, spacedim>() ) 

) 
Return an approximation of the diameter of the largest active cell of a triangulation.
Notice that, even if you pass a nontrivial mapping to this function, the returned value is computed only using information on the vertices of the triangulation, possibly transformed by the mapping. While this is accurate most of the times, it may fail to give the correct result when the triangulation contains very distorted cells.
Definition at line 4481 of file grid_tools.cc.
double GridTools::cell_measure  (  const std::vector< Point< dim > > &  all_vertices, 
const unsigned int(&)  vertex_indices[GeometryInfo< dim >::vertices_per_cell]  
) 
Given a list of vertices (typically obtained using Triangulation::get_vertices) as the first, and a list of vertex indices that characterize a single cell as the second argument, return the measure (area, volume) of this cell. If this is a real cell, then you can get the same result using cell>measure()
, but this function also works for cells that do not exist except that you make it up by naming its vertices from the list.
double GridTools::cell_measure  (  const std::vector< Point< dim > > &  all_vertices, 
const ArrayView< const unsigned int > &  vertex_indices  
) 
Given a list of vertices (typically obtained using Triangulation::get_vertices()) as the first, and a list of vertex indices that characterize a single cell as the second argument, return the measure (area, volume) of this cell. If this is a real cell, then you can get the same result using cell>measure()
, but this function also works for cells that do not exist except that you make it up by naming its vertices from the list.
The size of vertex_indices
, combined with dim
, implicitly encodes the ReferenceCell type of the provided cell. For example, if dim == 2
and vertex_indices.size() == 3
then the cell is a triangle, but if dim == 2
and vertex_indices.size() == 4
then the cell is a quadrilateral. A std::vector is implicitly convertible to an ArrayView, so it can be passed directly to this function. See the ArrayView class for more information.
std::pair< DerivativeForm< 1, dim, spacedim >, Tensor< 1, spacedim > > GridTools::affine_cell_approximation  (  const ArrayView< const Point< spacedim > > &  vertices  ) 
This function computes an affine approximation of the map from the unit coordinates to the real coordinates of the form \(p_\text{real} = A
p_\text{unit} + b \) by a least squares fit of this affine function to the \(2^\text{dim}\) vertices representing a quadrilateral or hexahedral cell in spacedim
dimensions. The result is returned as a pair with the matrix A as the first argument and the vector b describing distance of the plane to the origin.
For any valid mesh cell whose geometry is not degenerate, this operation results in a unique affine mapping, even in cases where the actual transformation by a bi/trilinear or higher order mapping might be singular. The result is exact in case the transformation from the unit to the real cell is indeed affine, such as in one dimension or for Cartesian and affine (parallelogram) meshes in 2d/3d.
This approximation is underlying the function TriaAccessor::real_to_unit_cell_affine_approximation() function.
For exact transformations to the unit cell, use Mapping::transform_real_to_unit_cell().
Definition at line 309 of file grid_tools.cc.
Vector< double > GridTools::compute_aspect_ratio_of_cells  (  const Mapping< dim > &  mapping, 
const Triangulation< dim > &  triangulation,  
const Quadrature< dim > &  quadrature  
) 
Computes an aspect ratio measure for all locallyowned active cells and fills a vector with one entry per cell, given a triangulation
and mapping
. The size of the vector that is returned equals the number of active cells. The vector contains zero for non locallyowned cells. The aspect ratio of a cell is defined as the ratio of the maximum to minimum singular value of the Jacobian, taking the maximum over all quadrature points of a quadrature rule specified via quadrature
. For example, for the special case of rectangular elements in 2d with dimensions \(a\) and \(b\) ( \(a \geq b\)), this function returns the usual aspect ratio definition \(a/b\). The above definition using singular values is a generalization to arbitrarily deformed elements. This function is intended to be used for \(d=2,3\) space dimensions, but it can also be used for \(d=1\) returning a value of 1.
Definition at line 333 of file grid_tools.cc.
double GridTools::compute_maximum_aspect_ratio  (  const Mapping< dim > &  mapping, 
const Triangulation< dim > &  triangulation,  
const Quadrature< dim > &  quadrature  
) 
Computes the maximum aspect ratio by taking the maximum over all cells.
Definition at line 399 of file grid_tools.cc.
BoundingBox< spacedim > GridTools::compute_bounding_box  (  const Triangulation< dim, spacedim > &  triangulation  ) 
Compute the smallest box containing the entire triangulation.
If the input triangulation is a parallel::distributed::Triangulation
, then each processor will compute a bounding box enclosing all locally owned, ghost, and artificial cells. In the case of a domain without curved boundaries, these bounding boxes will all agree between processors because the union of the areas occupied by artificial and ghost cells equals the union of the areas occupied by the cells that other processors own. However, if the domain has curved boundaries, this is no longer the case. The bounding box returned may be appropriate for the current processor, but different from the bounding boxes computed on other processors.
Definition at line 415 of file grid_tools.cc.
Point< Iterator::AccessorType::space_dimension > GridTools::project_to_object  (  const Iterator &  object, 
const Point< Iterator::AccessorType::space_dimension > &  trial_point  
) 
Return the point on the geometrical object object
closest to the given point trial_point
. For example, if object
is a onedimensional line or edge, then the returned point will be a point on the geodesic that connects the vertices as the manifold associated with the object sees it (i.e., the geometric line may be curved if it lives in a higher dimensional space). If the iterator points to a quadrilateral in a higher dimensional space, then the returned point lies within the convex hull of the vertices of the quad as seen by the associated manifold.
object
) but may only provide a few correct digits if the object has high curvature. If your manifold supports it then the specialized function Manifold::project_to_manifold() may perform better. std::tuple< std::vector< Point< spacedim > >, std::vector< CellData< dim > >, SubCellData > GridTools::get_coarse_mesh_description  (  const Triangulation< dim, spacedim > &  tria  ) 
Return the arrays that define the coarse mesh of a Triangulation. This function is the inverse of Triangulation::create_triangulation().
The return value is a tuple with the vector of vertices, the vector of cells, and a SubCellData structure. The latter contains additional information about faces and lines.
This function is useful in cases where one needs to deconstruct a Triangulation or manipulate the numbering of the vertices in some way: an example is GridGenerator::merge_triangulations().
Definition at line 555 of file grid_tools.cc.
void GridTools::delete_unused_vertices  (  std::vector< Point< spacedim > > &  vertices, 
std::vector< CellData< dim > > &  cells,  
SubCellData &  subcelldata  
) 
Remove vertices that are not referenced by any of the cells. This function is called by all GridIn::read_*
functions to eliminate vertices that are listed in the input files but are not used by the cells in the input file. While these vertices should not be in the input from the beginning, they sometimes are, most often when some cells have been removed by hand without wanting to update the vertex lists, as they might be lengthy.
This function is called by all GridIn::read_*
functions as the triangulation class requires them to be called with used vertices only. This is so, since the vertices are copied verbatim by that class, so we have to eliminate unused vertices beforehand.
Not implemented for the codimension one case.
Definition at line 656 of file grid_tools.cc.
void GridTools::delete_duplicated_vertices  (  std::vector< Point< spacedim > > &  all_vertices, 
std::vector< CellData< dim > > &  cells,  
SubCellData &  subcelldata,  
std::vector< unsigned int > &  considered_vertices,  
const double  tol = 1e12 

) 
Remove vertices that are duplicated, due to the input of a structured grid, for example. If these vertices are not removed, the faces bounded by these vertices become part of the boundary, even if they are in the interior of the mesh.
This function is called by some GridIn::read_*
functions. Only the vertices with indices in considered_vertices
are tested for equality. This speeds up the algorithm, which is, for worstcase hyper cube geometries \(O(N^{3/2})\) in 2d and \(O(N^{5/3})\) in 3d: quite slow. However, if you wish to consider all vertices, simply pass an empty vector. In that case, the function fills considered_vertices
with all vertices.
Two vertices are considered equal if their difference in each coordinate direction is less than tol
. This implies that nothing happens if the tolerance is set to zero.
Definition at line 761 of file grid_tools.cc.
void GridTools::delete_duplicated_vertices  (  std::vector< Point< dim > > &  vertices, 
const double  tol = 1e12 

) 
Remove vertices that are duplicated.
Two vertices are considered equal if their difference in each coordinate direction is less than tol
. This implies that nothing happens if the tolerance is set to zero.
Definition at line 892 of file grid_tools.cc.
void GridTools::invert_all_negative_measure_cells  (  const std::vector< Point< spacedim > > &  all_vertices, 
std::vector< CellData< dim > > &  cells  
) 
Grids generated by grid generators may have an orientation of cells which is the inverse of the orientation required by deal.II.
In 2d and 3d this function checks whether all cells have negative or positive measure/volume. In the former case, all cells are inverted. It does nothing in 1d.
The inversion of cells might also work when only a subset of all cells have negative volume. However, grids consisting of a mixture of negative and positively oriented cells are very likely to be broken. Therefore, an exception is thrown, in case cells are not uniformly oriented.
all_vertices  The vertices of the mesh. 
cells  The array of CellData objects that describe the mesh's topology. 
Definition at line 1003 of file grid_tools.cc.
std::size_t GridTools::invert_cells_with_negative_measure  (  const std::vector< Point< spacedim > > &  all_vertices, 
std::vector< CellData< dim > > &  cells  
) 
Check the given cells and inverts any cell that is considered to have negative measure/volume in the orientation required by deal.II.
This function is identical to invert_all_negative_measure_cells() except it does not throw an error if only some of the cells are inverted. Instead, this function returns how many cells were inverted. Additionally, it will always throw an exception outside of codimension 0.
Definition at line 923 of file grid_tools.cc.
void GridTools::consistently_order_cells  (  std::vector< CellData< dim > > &  cells  ) 
Given a vector of CellData objects describing a mesh, reorder their vertices so that all lines are consistently oriented.
The expectations on orientation and a discussion of this function are available in the reordering module.
cells  The array of CellData objects that describe the mesh's topology. 
Definition at line 2026 of file grid_tools.cc.
void GridTools::transform  (  const Transformation &  transformation, 
Triangulation< dim, spacedim > &  triangulation  
) 
Transform the vertices of the given triangulation by applying the function object provided as first argument to all its vertices.
The transformation given as argument is used to transform each vertex. Its respective type has to offer a functionlike syntax, i.e. the predicate is either an object of a type that has an operator()
, or it is a pointer to a nonmember function, or it is a lambda function object. In either case, argument and return value have to be of type Point<spacedim>. An example – a simple transformation that moves the object two units to the right in the \(x_1\) direction – could look like as follows:
Here, the transformation is provided by a lambda function that takes a Point<dim>
as input and returns a Point<dim>
as output.
This function is used in the "Possibilities for extensions" section of step38. It is also used in step49 and step53.
void GridTools::shift  (  const Tensor< 1, spacedim > &  shift_vector, 
Triangulation< dim, spacedim > &  triangulation  
) 
Shift each vertex of the triangulation by the given shift vector. This function uses the transform() function above, so the requirements on the triangulation stated there hold for this function as well; in particular, this is true about the discussion about manifolds.
Definition at line 2136 of file grid_tools.cc.
void GridTools::rotate  (  const double  angle, 
Triangulation< dim, spacedim > &  triangulation  
) 
Rotate all vertices of the given twodimensional triangulation in counterclockwise sense around the origin of the coordinate system by the given angle (given in radians, rather than degrees). This function uses the transform() function above, so the requirements on the triangulation stated there hold for this function as well; in particular, this is true about the discussion about manifolds.
Definition at line 2146 of file grid_tools.cc.
void GridTools::rotate  (  const Tensor< 1, 3, double > &  axis, 
const double  angle,  
Triangulation< dim, 3 > &  triangulation  
) 
Rotate all vertices of the given triangulation
in counterclockwise direction around the axis
described by a unit vector. Otherwise like the function above; in particular, this function calls the transform() function and so the discussion about manifolds there also applies here.
[in]  angle  Angle in radians to rotate the Triangulation by. 
[in]  axis  A unit vector that defines the axis of rotation. 
[in,out]  triangulation  The Triangulation object to rotate. 
Definition at line 2177 of file grid_tools.cc.
void GridTools::rotate  (  const double  angle, 
const unsigned int  axis,  
Triangulation< dim, 3 > &  triangulation  
) 
Rotate all vertices of the given triangulation
in counterclockwise direction around the axis with the given index. Otherwise like the function above; in particular, this function calls the transform() function and so the discussion about manifolds there also applies here.
[in]  angle  Angle in radians to rotate the Triangulation by. 
[in]  axis  Index of the coordinate axis to rotate around, keeping that coordinate fixed (0=x axis, 1=y axis, 2=z axis). 
[in,out]  triangulation  The Triangulation object to rotate. 
Definition at line 2187 of file grid_tools.cc.
void GridTools::laplace_transform  (  const std::map< unsigned int, Point< dim > > &  new_points, 
Triangulation< dim > &  tria,  
const Function< dim, double > *  coefficient = nullptr , 

const bool  solve_for_absolute_positions = false 

) 
Transform the given triangulation smoothly to a different domain where, typically, each of the vertices at the boundary of the triangulation is mapped to the corresponding points in the new_points
map.
The unknown displacement field \(u_d(\mathbf x)\) in direction \(d\) is obtained from the minimization problem
\[ \min\, \int \frac{1}{2} c(\mathbf x) \mathbf \nabla u_d(\mathbf x) \cdot \mathbf \nabla u_d(\mathbf x) \,\rm d x \]
subject to prescribed constraints. The minimizer is obtained by solving the Laplace equation of the dim components of a displacement field that maps the current domain into one described by new_points
. Linear finite elements with four Gaussian quadrature points in each direction are used. The difference between the vertex positions specified in new_points
and their current value in tria
therefore represents the prescribed values of this displacement field at the boundary of the domain, or more precisely at all of those locations for which new_points
provides values (which may be at part of the boundary, or even in the interior of the domain). The function then evaluates this displacement field at each unconstrained vertex and uses it to place the mapped vertex where the displacement field locates it. Because the solution of the Laplace equation is smooth, this guarantees a smooth mapping from the old domain to the new one.
[in]  new_points  The locations where a subset of the existing vertices are to be placed. Typically, this would be a map from the vertex indices of all nodes on the boundary to their new locations, thus completely specifying the geometry of the mapped domain. However, it may also include interior points if necessary and it does not need to include all boundary vertices (although you then lose control over the exact shape of the mapped domain). 
[in,out]  tria  The Triangulation object. This object is changed in place, i.e., the previous locations of vertices are overwritten. 
[in]  coefficient  An optional coefficient for the Laplace problem. Larger values make cells less prone to deformation (effectively increasing their stiffness). The coefficient is evaluated in the coordinate system of the old, undeformed configuration of the triangulation as input, i.e., before the transformation is applied. Should this function be provided, sensible results can only be expected if all coefficients are positive. 
[in]  solve_for_absolute_positions  If set to true , the minimization problem is formulated with respect to the final vertex positions as opposed to their displacement. The two formulations are equivalent for the homogeneous problem (default value of coefficient ), but they result in very different mesh motion otherwise. Since in most cases one will be using a nonconstant coefficient in displacement formulation, the default value of this parameter is false . 
std::map< unsigned int, Point< spacedim > > GridTools::get_all_vertices_at_boundary  (  const Triangulation< dim, spacedim > &  tria  ) 
Return a std::map with all vertices of faces located in the boundary
[in]  tria  The Triangulation object. 
Definition at line 2352 of file grid_tools.cc.
void GridTools::scale  (  const double  scaling_factor, 
Triangulation< dim, spacedim > &  triangulation  
) 
Scale the entire triangulation by the given factor. To preserve the orientation of the triangulation, the factor must be positive.
This function uses the transform() function above, so the requirements on the triangulation stated there hold for this function as well.
Definition at line 2202 of file grid_tools.cc.
void GridTools::distort_random  (  const double  factor, 
Triangulation< dim, spacedim > &  triangulation,  
const bool  keep_boundary = true , 

const unsigned int  seed = boost::random::mt19937::default_seed 

) 
Distort the given triangulation by randomly moving around all the vertices of the grid. The direction of movement of each vertex is random, while the length of the shift vector has a value of factor
times the minimal length of the active edges adjacent to this vertex. Note that factor
should obviously be well below 0.5
.
If keep_boundary
is set to true
(which is the default), then boundary vertices are not moved.
seed
is used for the initialization of the random engine. Its default value initializes the engine with the same state as in previous versions of deal.II.
Distort a triangulation in some random way.
Definition at line 2384 of file grid_tools.cc.
void GridTools::remove_hanging_nodes  (  Triangulation< dim, spacedim > &  tria, 
const bool  isotropic = false , 

const unsigned int  max_iterations = 100 

) 
Remove hanging nodes from a grid. If the isotropic
parameter is set to false
(default) this function detects cells with hanging nodes and refines the neighbours in the direction that removes hanging nodes. If the isotropic
parameter is set to true
, the neighbours refinement is made in each directions. In order to remove all hanging nodes this procedure has to be repeated: this could require a large number of iterations. To avoid this a max number (max_iterations
) of iteration is provided.
Consider the following grid:
isotropic
== false
would return:
isotropic
== true
would return:
[in,out]  tria  Triangulation to refine. 
[in]  isotropic  If true refine cells in each directions, otherwise (default value) refine the cell in the direction that removes hanging node. 
[in]  max_iterations  At each step only closest cells to hanging nodes are refined. The code may require a lot of iterations to remove all hanging nodes. max_iterations is the maximum number of iteration allowed. If max_iterations == numbers::invalid_unsigned_int this function continues refining until there are no hanging nodes. 
Definition at line 5229 of file grid_tools.cc.
void GridTools::remove_anisotropy  (  Triangulation< dim, spacedim > &  tria, 
const double  max_ratio = 1.6180339887 , 

const unsigned int  max_iterations = 5 

) 
Refine a mesh anisotropically such that the resulting mesh is composed by cells with maximum ratio between dimensions less than max_ratio
. This procedure requires an algorithm that may not terminate. Consequently, it is possible to set a maximum number of iterations through the max_iterations
parameter.
Starting from a cell like this:
This function would return:
[in,out]  tria  Triangulation to refine. 
[in]  max_ratio  Maximum value allowed among the ratio between the dimensions of each cell. 
[in]  max_iterations  Maximum number of iterations allowed. 
Definition at line 5262 of file grid_tools.cc.
void GridTools::regularize_corner_cells  (  Triangulation< dim, spacedim > &  tria, 
const double  limit_angle_fraction = .75 

) 
Analyze the boundary cells of a mesh, and if one cell is found at a corner position (with dim adjacent faces on the boundary), and its dimdimensional angle fraction exceeds limit_angle_fraction
, refine globally once, and replace the children of such cell with children where the corner is no longer offending the given angle fraction.
If no boundary cells exist with two adjacent faces on the boundary, then the triangulation is left untouched. If instead we do have cells with dim adjacent faces on the boundary, then the fraction between the dimdimensional solid angle and dim*pi/2 is checked against the parameter limit_angle_fraction
. If it is higher, the grid is refined once, and the children of the offending cell are replaced with some cells that instead respect the limit. After this process the triangulation is flattened, and all Manifold objects are restored as they were in the original triangulation.
An example is given by the following mesh, obtained by attaching a SphericalManifold to a mesh generated using GridGenerator::hyper_cube:
The four cells that were originally the corners of a square will give you some troubles during computations, as the jacobian of the transformation from the reference cell to those cells will go to zero, affecting the error constants of the finite element estimates.
Those cells have a corner with an angle that is very close to 180 degrees, i.e., an angle fraction very close to one.
The same code, adding a call to regularize_corner_cells:
generates a mesh that has a much better behavior w.r.t. the jacobian of the Mapping:
This mesh is very similar to the one obtained by GridGenerator::hyper_ball. However, using GridTools::regularize_corner_cells one has the freedom to choose when to apply the regularization, i.e., one could in principle first refine a few times, and then call the regularize_corner_cells function:
This generates the following mesh:
The function is currently implemented only for dim = 2 and will throw an exception if called with dim = 3.
[in,out]  tria  Triangulation to regularize. 
[in]  limit_angle_fraction  Maximum ratio of angle or solid angle that is allowed for a corner element in the mesh. 
Definition at line 5291 of file grid_tools.cc.
return_type GridTools::compute_point_locations  (  const Cache< dim, spacedim > &  cache, 
const std::vector< Point< spacedim > > &  points,  
const typename Triangulation< dim, spacedim >::active_cell_iterator &  cell_hint = typename Triangulation<dim, spacedim>::active_cell_iterator() 

) 
Given a Triangulation's cache
and a list of points
, call find_active_cell_around_point() on each element of points
, and return cells
, reference positions qpoints
, and a mapping maps
from local to global indices into points
.
[in]  cache  The triangulation's GridTools::Cache . 
[in]  points  A vector of points. 
[in]  cell_hint  (optional) A cell iterator for a cell which likely contains the first point of points . 
cells
: A vector of all the cells containing at least one of the points
.qpoints
: A vector of vectors of points. qpoints
[i] contains the reference positions of all points that fall within the cell cells
[i] .indices
: A vector of vectors of integers, containing the mapping between local numbering the cells
array (the first component of the returned tuple), and global index in the input array points
. In other words, the indices stored in the array indices[c]
correspond to those points of the input argument points
that are located on cells[c]
.If points
[a] and points
[b] are the only two points that fall in cells
[c], then qpoints
[c][0] and qpoints
[c][1] are the reference positions of points
[a] and points
[b] in cells
[c], and indices
[c][0] = a, indices
[c][1] = b. The function Mapping::transform_unit_to_real(qpoints[c][0]) returns points
[a].
The algorithm builds an rtree of points
to sort them spatially, before attempting to call find_active_cell_around_point().
spacedim != dim
).return_type
, is Definition at line 5607 of file grid_tools.cc.
return_type GridTools::compute_point_locations_try_all  (  const Cache< dim, spacedim > &  cache, 
const std::vector< Point< spacedim > > &  points,  
const typename Triangulation< dim, spacedim >::active_cell_iterator &  cell_hint = typename Triangulation<dim, spacedim>::active_cell_iterator() 

) 
This function is similar to GridTools::compute_point_locations(), but while compute_point_locations() silently ignores all points for which find_active_cell_around_point() fails, this function also returns a vector containing the indices of the points for which find_active_cell_around_point() failed.
return_type
contains the indices of points which are neither found inside the mesh nor lie in artificial cells. The return_type
equals the following tuple type: spacedim != dim
).For a more detailed documentation see GridTools::compute_point_locations().
Definition at line 5636 of file grid_tools.cc.
return_type GridTools::distributed_compute_point_locations  (  const GridTools::Cache< dim, spacedim > &  cache, 
const std::vector< Point< spacedim > > &  local_points,  
const std::vector< std::vector< BoundingBox< spacedim > > > &  global_bboxes,  
const double  tolerance = 1e10 , 

const std::vector< bool > &  marked_vertices = {} , 

const bool  enforce_unique_mapping = true 

) 
Given a cache
and a list of local_points
for each process, find the points lying on the locally owned part of the mesh and compute the quadrature rules for them. Distributed compute point locations is a function similar to GridTools::compute_point_locations but working for parallel::TriangulationBase objects and, unlike its serial version, also for a distributed triangulation (see parallel::distributed::Triangulation).
[in]  cache  a GridTools::Cache object 
[in]  local_points  the array of points owned by the current process. Every process can have a different array of points which can be empty and not contained within the locally owned part of the triangulation 
[in]  global_bboxes  a vector of vectors of bounding boxes; it describes the locally owned part of the mesh for each process. The bounding boxes describing which part of the mesh is locally owned by process with rank rk are contained in global_bboxes[rk]. The local description can be obtained from GridTools::compute_mesh_predicate_bounding_box; then the global one can be obtained using either GridTools::exchange_local_bounding_boxes or Utilities::MPI::all_gather 
[in]  tolerance  Tolerance in terms of unit cell coordinates. Depending on the problem, it might be necessary to adjust the tolerance in order to be able to identify a cell. Floating point arithmetic implies that a point will, in general, not lie exactly on a vertex, edge, or face. In either case, it is not predictable which of the cells adjacent to a vertex or an edge/face this function returns. Consequently, algorithms that call this function need to take into account that the returned cell will only contain the point approximately. 
[in]  enforce_unique_mapping  Enforce a one to one mapping between points in real and reference space. 
[in]  marked_vertices  An array of bools indicating which vertices of mesh will be considered within the search as the potentially closest vertex. On receiving a nonempty marked_vertices , the function will only search among marked_vertices for the closest vertex, otherwise on all vertices in the mesh. 
The elements of the output tuple are:
qpoints
[i] the reference positions of all points that fall within the cell cells
[i] .points
[i][j] is the point in the real space corresponding. to qpoints
[i][j] . Notice points
are the points lying on the locally owned part of the mesh; thus these can be either copies of local_points
or points received from other processes i.e. local_points for other processesowners
[i][j] contains the rank of the process owning the point[i][j] (previous element of the tuple).The function uses the triangulation's mpi communicator: for this reason it throws an assert error if the Triangulation is not derived from parallel::TriangulationBase .
In a serial execution the first three elements of the tuple are the same as in GridTools::compute_point_locations .
Note: this function is a collective operation.
return_type
, is Definition at line 5806 of file grid_tools.cc.
std::map< unsigned int, Point< spacedim > > GridTools::extract_used_vertices  (  const Triangulation< dim, spacedim > &  container, 
const Mapping< dim, spacedim > &  mapping = (ReferenceCells::get_hypercube<dim>() .template get_default_linear_mapping<dim, spacedim>() ) 

) 
Return a map vertex index > Point<spacedim>
containing the used vertices of the given container
. The key of the returned map (i.e., the first element of the pair above) is the global index in the triangulation, whereas the value of each pair is the physical location of the corresponding vertex. The used vertices are obtained by looping over all cells, and querying for each cell where its vertices are through the (optional) mapping
argument.
In serial Triangulation objects and parallel::shared::Triangulation objects, the size of the returned map equals Triangulation::n_used_vertices() (not Triangulation::n_vertices()). Note that in parallel::distributed::Triangulation objects, only vertices in locally owned cells and ghost cells are returned, as for all other vertices their real location might not be known (e.g. for distributed computations using MappingQEulerian).
If you use the default mapping
, the returned map satisfies the following equality:
Notice that the above is not satisfied for mappings that change the location of vertices, like MappingQEulerian.
container  The container to extract vertices from. 
mapping  The mapping to use to compute the points locations. 
Definition at line 6811 of file grid_tools.cc.
unsigned int GridTools::find_closest_vertex  (  const std::map< unsigned int, Point< spacedim > > &  vertices, 
const Point< spacedim > &  p  
) 
Find and return the index of the closest vertex to a given point in the map of vertices passed as the first argument.
vertices  A map of index>vertex, as returned by GridTools::extract_used_vertices(). 
p  The target point. 
p
. Definition at line 6830 of file grid_tools.cc.
unsigned int GridTools::find_closest_vertex  (  const MeshType< dim, spacedim > &  mesh, 
const Point< spacedim > &  p,  
const std::vector< bool > &  marked_vertices = {} 

) 
Find and return the index of the used vertex (or marked vertex) in a given mesh that is located closest to a given point.
This function uses the locations of vertices as stored in the triangulation. This is usually sufficient, unless you are using a Mapping that moves the vertices around (for example, MappingQEulerian). In this case, you should call the function with the same name and with an additional Mapping argument.
mesh  A variable of a type that satisfies the requirements of the MeshType concept. 
p  The point for which we want to find the closest vertex. 
marked_vertices  An array of bools indicating which vertices of mesh will be considered within the search as the potentially closest vertex. On receiving a nonempty marked_vertices , the function will only search among marked_vertices for the closest vertex. The size of this array should be equal to the value returned by Triangulation::n_vertices() for the triangulation underlying the given mesh (as opposed to the value returned by Triangulation::n_used_vertices()). 
Definition at line 2608 of file grid_tools.cc.
unsigned int GridTools::find_closest_vertex  (  const Mapping< dim, spacedim > &  mapping, 
const MeshType< dim, spacedim > &  mesh,  
const Point< spacedim > &  p,  
const std::vector< bool > &  marked_vertices = {} 

) 
Find and return the index of the used vertex (or marked vertex) in a given mesh that is located closest to a given point. Use the given mapping to compute the actual location of the vertices.
If the Mapping does not modify the position of the mesh vertices (like, for example, MappingQEulerian does), then this function is equivalent to the one with the same name, and without the mapping
argument.
mapping  A mapping used to compute the vertex locations 
mesh  A variable of a type that satisfies the requirements of the MeshType concept. 
p  The point for which we want to find the closest vertex. 
marked_vertices  An array of bools indicating which vertices of mesh will be considered within the search as the potentially closest vertex. On receiving a nonempty marked_vertices , the function will only search among marked_vertices for the closest vertex. The size of this array should be equal to the value returned by Triangulation::n_vertices() for the triangulation underlying the given mesh (as opposed to the value returned by Triangulation::n_used_vertices()). 
Definition at line 2675 of file grid_tools.cc.
std::vector< typename MeshType::active_cell_iterator > GridTools::find_cells_adjacent_to_vertex  (  const MeshType &  container, 
const unsigned int  vertex_index  
) 
Find and return a vector of iterators to active cells that surround a given vertex with index vertex_index
.
For locally refined grids, the vertex itself might not be a vertex of all adjacent cells that are returned. However, it will always be either a vertex of a cell or be a hanging node located on a face or an edge of it.
container  A variable of a type that satisfies the requirements of the MeshType concept. 
vertex_index  The index of the vertex for which we try to find adjacent cells. 
Definition at line 202 of file grid_tools_dof_handlers.cc.
std::pair< typename MeshType< dim, spacedim >::active_cell_iterator, Point< dim > > GridTools::find_active_cell_around_point  (  const Mapping< dim, spacedim > &  mapping, 
const MeshType< dim, spacedim > &  mesh,  
const Point< spacedim > &  p,  
const std::vector< bool > &  marked_vertices = {} , 

const double  tolerance = 1.e10 

) 
Find an active nonartificial cell that surrounds a given point p
. The return type is a pair of an iterator to the active cell along with the unit cell coordinates of the point.
The algorithm used in this function proceeds by first looking for the vertex located closest to the given point, see GridTools::find_closest_vertex(). Secondly, all adjacent cells to this vertex are found in the mesh, see GridTools::find_cells_adjacent_to_vertex(). Lastly, for each of these cells, the function tests whether the point is inside. This check is performed using the given mapping
argument to determine whether cells have straight or curved boundaries.
If a point lies on the boundary of two or more cells, then the algorithm tries to identify the cell that is of highest refinement level.
If the point requested does not lie in a locallyowned or ghost cell, then this function will return the (invalid) MeshType<dim, spacedim>::end() iterator. This case can be handled similarly to the various std::find()
and std::lower_bound()
functions.
mapping  The mapping used to determine whether the given point is inside a given cell. 
mesh  A variable of a type that satisfies the requirements of the MeshType concept. 
p  The point for which we want to find the surrounding cell. 
marked_vertices  An array of bool s indicating whether an entry in the vertex array should be considered (and the others must be ignored) as the potentially closest vertex to the specified point. On specifying a nondefault marked_vertices , find_closest_vertex() would only search among marked_vertices for the closest vertex. The size of this array should be equal to n_vertices() of the triangulation (as opposed to n_used_vertices() ). The motivation of using marked_vertices is to cut down the search space of vertices if one has a priori knowledge of a collection of vertices that the point of interest may be close to. 
tolerance  Tolerance in terms of unit cell coordinates. Depending on the problem, it might be necessary to adjust the tolerance in order to be able to identify a cell. Floating point arithmetic implies that a point will, in general, not lie exactly on a vertex, edge, or face. In either case, it is not predictable which of the cells adjacent to a vertex or an edge/face this function returns. Consequently, algorithms that call this function need to take into account that the returned cell will only contain the point approximately. 
Definition at line 440 of file grid_tools_dof_handlers.cc.
MeshType< dim, spacedim >::active_cell_iterator GridTools::find_active_cell_around_point  (  const MeshType< dim, spacedim > &  mesh, 
const Point< spacedim > &  p,  
const std::vector< bool > &  marked_vertices = {} , 

const double  tolerance = 1.e10 

) 
A version of the above function that assumes straight boundaries and as a consequence simply calls the above function using MappingQ1 for the mapping argument.
Definition at line 414 of file grid_tools_dof_handlers.cc.
std::pair< typename DoFHandler< dim, spacedim >::active_cell_iterator, Point< dim > > GridTools::find_active_cell_around_point  (  const hp::MappingCollection< dim, spacedim > &  mapping, 
const DoFHandler< dim, spacedim > &  mesh,  
const Point< spacedim > &  p,  
const double  tolerance = 1.e10 

) 
Another version where we use that mapping on a given cell that corresponds to the active finite element index of that cell. This is obviously only useful for hpproblems, since the active finite element index for all other DoF handlers is always zero.
Definition at line 1303 of file grid_tools_dof_handlers.cc.
std::pair< typename Triangulation< dim, spacedim >::active_cell_iterator, Point< dim > > GridTools::find_active_cell_around_point  (  const Cache< dim, spacedim > &  cache, 
const Point< spacedim > &  p,  
const typename Triangulation< dim, spacedim >::active_cell_iterator &  cell_hint = typename Triangulation<dim, spacedim>::active_cell_iterator() , 

const std::vector< bool > &  marked_vertices = {} , 

const double  tolerance = 1.e10 

) 
Finding an active nonartificial cell around a point can be very expensive in terms of computational costs. This function aims at providing a fast version of the above functions by using a spacetree to speed up the geometry search.
cache  Object with information about the spacetree of a triangulation, see GridTools::Cache. 
p  The point for which we want to find the surrounding cell. 
cell_hint  Gives a hint for the geometry search, which is beneficial if apriori knowledge is available regarding the cell on which the point may likely be located. A typical use case would be that this search has to be done for an array of points that are close to each other and where the adjacent cell of the previous point is a good hint for the next point in the array. 
marked_vertices  See above. 
tolerance  See above. 
The following code example shows how to use this function:
Definition at line 6847 of file grid_tools.cc.
std::pair< typename MeshType< dim, spacedim >::active_cell_iterator, Point< dim > > GridTools::find_active_cell_around_point  (  const Mapping< dim, spacedim > &  mapping, 
const MeshType< dim, spacedim > &  mesh,  
const Point< spacedim > &  p,  
const std::vector< std::set< typename MeshType< dim, spacedim >::active_cell_iterator > > &  vertex_to_cell_map,  
const std::vector< std::vector< Tensor< 1, spacedim > > > &  vertex_to_cell_centers,  
const typename MeshType< dim, spacedim >::active_cell_iterator &  cell_hint = typename MeshType<dim, spacedim>::active_cell_iterator() , 

const std::vector< bool > &  marked_vertices = {} , 

const RTree< std::pair< Point< spacedim >, unsigned int > > &  used_vertices_rtree = RTree<std::pair<Point<spacedim>, unsigned int>>{} , 

const double  tolerance = 1.e10 , 

const RTree< std::pair< BoundingBox< spacedim >, typename Triangulation< dim, spacedim >::active_cell_iterator > > *  relevant_cell_bounding_boxes_rtree = nullptr 

) 
A version of the previous function that exploits an already existing map between vertices and cells (constructed using the function GridTools::vertex_to_cell_map()), a map of vertex_to_cell_centers (obtained through GridTools::vertex_to_cell_centers_directions()), and optionally an RTree constructed from the used vertices of the Triangulation.
cache
in this case.Definition at line 2796 of file grid_tools.cc.
std::vector< std::pair< typename MeshType< dim, spacedim >::active_cell_iterator, Point< dim > > > GridTools::find_all_active_cells_around_point  (  const Mapping< dim, spacedim > &  mapping, 
const MeshType< dim, spacedim > &  mesh,  
const Point< spacedim > &  p,  
const double  tolerance,  
const std::pair< typename MeshType< dim, spacedim >::active_cell_iterator, Point< dim > > &  first_cell  
) 
As compared to the functions above, this function identifies all active nonartificial cells around a point for a given tolerance level tolerance
in terms of unit coordinates. Given a first cell with reference coordinates as parameter first_cell
, e.g. obtained by one of the functions above, all corresponding neighboring cells with points in unit coordinates are also identified.
This function is useful e.g. for discontinuous function spaces where, for the case the given point p
lies on a vertex, edge or face, several cells might hold independent values of the solution that get combined in some way in a user code.
This function is used as follows
Definition at line 613 of file grid_tools_dof_handlers.cc.
std::vector< std::pair< typename MeshType< dim, spacedim >::active_cell_iterator, Point< dim > > > GridTools::find_all_active_cells_around_point  (  const Mapping< dim, spacedim > &  mapping, 
const MeshType< dim, spacedim > &  mesh,  
const Point< spacedim > &  p,  
const double  tolerance = 1e10 , 

const std::vector< bool > &  marked_vertices = {} 

) 
A variant of the previous function that internally calls one of the functions find_active_cell_around_point() to obtain a first cell, and subsequently adds all other active nonartificial cells by calling the function find_all_active_cells_around_point() above.
Definition at line 583 of file grid_tools_dof_handlers.cc.
std::vector< typename MeshType::active_cell_iterator > GridTools::get_active_child_cells  (  const typename MeshType::cell_iterator &  cell  ) 
Return a list of all descendants of the given cell that are active. For example, if the current cell is once refined but none of its children are any further refined, then the returned list will contain all its children.
If the current cell is already active, then the returned list is empty (because the cell has no children that may be active).
MeshType  A type that satisfies the requirements of the MeshType concept. 
cell  An iterator pointing to a cell of the mesh. 
void GridTools::get_active_neighbors  (  const typename MeshType::active_cell_iterator &  cell, 
std::vector< typename MeshType::active_cell_iterator > &  active_neighbors  
) 
Extract the active cells around a given cell cell
and return them in the vector active_neighbors
. These neighbors are specifically the face neighbors of a cell or, if that neighbor is further refined, its active children that border on that face. On the other hand, the neighbors returned do not include cells that lie, for example, diagonally opposite to a vertex but are not face neighbors themselves. (In 3d, it also does not include cells that are adjacent to one of the edges of the current cell, but are not face neighbors.)
MeshType  A type that satisfies the requirements of the MeshType concept. 
[in]  cell  An iterator pointing to a cell of the mesh. 
[out]  active_neighbors  A list of active descendants of the given cell 
std::vector< typename MeshType::active_cell_iterator > GridTools::compute_active_cell_halo_layer  (  const MeshType &  mesh, 
const std::function< bool(const typename MeshType::active_cell_iterator &)> &  predicate  
) 
Extract and return the active cell layer around a subdomain (set of active cells) in the mesh
(i.e. those that share a common set of vertices with the subdomain but are not a part of it). Here, the "subdomain" consists of exactly all of those cells for which the predicate
returns true
.
An example of a custom predicate is one that checks for a given material id
and we can then extract the layer of cells around this material with the following call:
Predicates that are frequently useful can be found in namespace IteratorFilters. For example, it is possible to extract a layer of cells around all of those cells with a given material id,
or around all cells with one of a set of active FE indices for a DoFHandler with hpcapabilities
Note that in the last two examples we ensure that the predicate returns true only for locally owned cells. This means that the halo layer will not contain any artificial cells.
MeshType  A type that satisfies the requirements of the MeshType concept. 
[in]  mesh  A mesh (i.e. objects of type Triangulation or DoFHandler). 
[in]  predicate  A function (or object of a type with an operator()) defining the subdomain around which the halo layer is to be extracted. It is a function that takes in an active cell and returns a boolean. 
Definition at line 767 of file grid_tools_dof_handlers.cc.
std::vector< typename MeshType::cell_iterator > GridTools::compute_cell_halo_layer_on_level  (  const MeshType &  mesh, 
const std::function< bool(const typename MeshType::cell_iterator &)> &  predicate,  
const unsigned int  level  
) 
Extract and return the cell layer around a subdomain (set of cells) on a specified level of the mesh
(i.e. those cells on that level that share a common set of vertices with the subdomain but are not a part of it). Here, the "subdomain" consists of exactly all of those cells for which the predicate
returns true
.
Definition at line 805 of file grid_tools_dof_handlers.cc.
std::vector< typename MeshType::active_cell_iterator > GridTools::compute_ghost_cell_halo_layer  (  const MeshType &  mesh  ) 
Extract and return ghost cells which are the active cell layer around all locally owned cells. This is most relevant for parallel::shared::Triangulation where it will return a subset of all ghost cells on a processor, but for parallel::distributed::Triangulation this will return all the ghost cells.
MeshType  A type that satisfies the requirements of the MeshType concept. 
[in]  mesh  A mesh (i.e. objects of type Triangulation or DoFHandler). 
Definition at line 888 of file grid_tools_dof_handlers.cc.
std::vector< typename MeshType::active_cell_iterator > GridTools::compute_active_cell_layer_within_distance  (  const MeshType &  mesh, 
const std::function< bool(const typename MeshType::active_cell_iterator &)> &  predicate,  
const double  layer_thickness  
) 
Extract and return the set of active cells within a geometric distance of layer_thickness
around a subdomain (set of active cells) in the mesh
. Here, the "subdomain" consists of exactly all of those cells for which the predicate
returns true
.
The function first computes the cells that form the 'surface' of the subdomain that consists of all of the active cells for which the predicate is true. Using compute_bounding_box(), a bounding box is computed for this subdomain and extended by layer_thickness
. These cells are called interior subdomain boundary cells. The active cells with all of their vertices outside the extended bounding box are ignored. The cells that are inside the extended bounding box are then checked for their proximity to the interior subdomain boundary cells. This implies checking the distance between a pair of arbitrarily oriented cells, which is not trivial in general. To simplify this, the algorithm checks the distance between the two enclosing spheres of the cells. This will definitely result in slightly more cells being marked but also greatly simplifies the arithmetic complexity of the algorithm.
The image shows a mesh generated by subdivided_hyper_rectangle(). The cells are marked using three different colors. If the grey colored cells in the image are the cells for which the predicate is true, then the function compute_active_cell_layer_within_distance() will return a set of cell iterators corresponding to the cells colored in red. The red colored cells are the active cells that are within a given distance to the grey colored cells.
MeshType  A type that satisfies the requirements of the MeshType concept. 
mesh  A mesh (i.e. objects of type Triangulation or DoFHandler). 
predicate  A function (or object of a type with an operator()) defining the subdomain around which the halo layer is to be extracted. It is a function that takes in an active cell and returns a boolean. 
layer_thickness  specifies the geometric distance within which the function searches for active cells from the predicate domain. If the minimal distance between the enclosing sphere of the an active cell and the enclosing sphere of any of the cells for which the predicate returns true is less than layer_thickness , then the active cell is an active_cell_within_distance. 
layer_thickness
from the set of active cells for which the predicate
returns true
.See compute_active_cell_halo_layer().
Definition at line 911 of file grid_tools_dof_handlers.cc.
std::vector< typename MeshType::active_cell_iterator > GridTools::compute_ghost_cell_layer_within_distance  (  const MeshType &  mesh, 
const double  layer_thickness  
) 
Extract and return a set of ghost cells which are within a layer_thickness
around all locally owned cells. This is most relevant for parallel::shared::Triangulation where it will return a subset of all ghost cells on a process, but for parallel::distributed::Triangulation this will return all the ghost cells. All the cells for the parallel::shared::Triangulation class that are not owned by the current processor can be considered as ghost cells; in particular, they do not only form a single layer of cells around the locally owned ones.
MeshType  A type that satisfies the requirements of the MeshType concept. 
mesh  A mesh (i.e. objects of type Triangulation or DoFHandler). 
layer_thickness  specifies the geometric distance within which the function searches for active cells from the locally owned cells. 
layer_thickness
from the locally owned cells of a current process.Also see compute_ghost_cell_halo_layer() and compute_active_cell_layer_within_distance().
Definition at line 1057 of file grid_tools_dof_handlers.cc.
std::pair< Point< MeshType::space_dimension >, Point< MeshType::space_dimension > > GridTools::compute_bounding_box  (  const MeshType &  mesh, 
const std::function< bool(const typename MeshType::active_cell_iterator &)> &  predicate  
) 
Compute and return a bounding box, defined through a pair of points bottom left and top right, that surrounds a subdomain of the mesh
. Here, the "subdomain" consists of exactly all of those active cells for which the predicate
returns true
.
For a description of how predicate
works, see compute_active_cell_halo_layer().
Definition at line 1098 of file grid_tools_dof_handlers.cc.
std::vector< BoundingBox< MeshType::space_dimension > > GridTools::compute_mesh_predicate_bounding_box  (  const MeshType &  mesh, 
const std::function< bool(const typename MeshType::active_cell_iterator &)> &  predicate,  
const unsigned int  refinement_level = 0 , 

const bool  allow_merge = false , 

const unsigned int  max_boxes = numbers::invalid_unsigned_int 

) 
Compute a collection of bounding boxes so that all active cells for which the given predicate is true, are completely enclosed in at least one of the bounding boxes. Notice the cover is only guaranteed to contain all these active cells but it's not necessarily exact i.e. it can include a bigger area than their union. (This is of course unavoidable in any case if cells are not rectangular or brickshaped, but it is also true if cells are since it is inefficient to create as many bounding boxes as there are cells; rather, the algorithm here tries to combine the bounding boxes of multiple cells into a cheaper representation, at the cost of a set of bounding boxes that may be larger than the union of the cells – see the description of the relevant function arguments below.)
For each cell at a given refinement level containing active cells for which predicate
is true, the function creates a bounding box of its children for which predicate
is true.
This results in a cover of all active cells for which predicate
is true; the parameters allow_merge
and max_boxes
are used to reduce the number of cells at a computational cost and covering a bigger ndimensional volume.
[in]  mesh  The mesh object this function is to work on. This is generally either a triangulation of some kind, or a DoFHandler object. 
[in]  predicate  A functionlike object that returns true or false depending on whether the property of the cells to enclose is satisfied. An example is IteratorFilters::LocallyOwnedCell, but it can also be a lambda function or anything else that can be called with a cell as argument. This predicate is tested only on active cells. 
[in]  refinement_level  Defines the level at which the initial bounding boxes are created. The refinement should be set to a coarse refinement level. A bounding box is created for each active cell at a coarser level than refinement_level ; if refinement_level is higher than the number of levels of the triangulation an exception is thrown. 
[in]  allow_merge  This flag allows for box merging and, by default, is false. The algorithm has a cost of O(N^2) where N is the number of the bounding boxes created from the refinement level; for this reason, if the flag is set to true, make sure to choose wisely a coarse enough refinement_level . 
[in]  max_boxes  The maximum number of bounding boxes to compute. If more are created the smaller ones are merged with neighbors. By default after merging the boxes which can be expressed as a single one no more boxes are merged. See the BoundingBox::get_neighbor_type () function for details. Notice only neighboring cells are merged (see the get_neighbor_type function in bounding box class): if the target number of bounding boxes max_boxes can't be reached by merging neighbors an exception is thrown. 
The following image describes an example of the algorithm with refinement_level
= 2, allow_merge
= true and max_boxes
=
allow_merge
= true the number of bounding boxes is reduced while not changing the cover. If max_boxes
was left as default or bigger than 1 these two boxes would be returned.max_boxes
= 1 the smallest bounding box is merged to the bigger one. Notice it is important to choose the parameters wisely. For instance, allow_merge
= false and refinement_level
= 1 returns the very same bounding box but with a fraction of the computational cost.This function does not take into account the curvature of cells and thus it is not suited for handling curved geometry: the mapping is assumed to be linear.
Definition at line 3147 of file grid_tools.cc.
return_type GridTools::guess_point_owner  (  const std::vector< std::vector< BoundingBox< spacedim > > > &  global_bboxes, 
const std::vector< Point< spacedim > > &  points  
) 
Given an array of points, use the global bounding box description obtained using GridTools::compute_mesh_predicate_bounding_box to guess, for each of them, which process might own it.
[in]  global_bboxes  Vector of bounding boxes describing the portion of mesh with a property for each process. 
[in]  points  Array of points to test. 
unsigned int
of the point in points
to the rank of the owner.unsigned int
of the point in points
to the ranks of the guessed owners.return_type
, is Definition at line 3294 of file grid_tools.cc.
return_type GridTools::guess_point_owner  (  const RTree< std::pair< BoundingBox< spacedim >, unsigned int > > &  covering_rtree, 
const std::vector< Point< spacedim > > &  points  
) 
Given a covering rtree (see GridTools::Cache::get_covering_rtree()), and an array of points, find a superset of processes which, individually, may own the cell containing the points.
For further details see GridTools::guess_point_owner; here only different input/output types are reported:
[in]  covering_rtree  RTRee which enables us to identify which process(es) in a parallel computation may own the cell that surrounds a given point. 
[in]  points  A vector of points to consider. 
unsigned int
of the point in points
to the rank of the owner; these are points for which a single possible owner was found.unsigned int
of the point in points
to the ranks of the guessed owners; these are points for which multiple possible owners were found.return_type
, is Definition at line 3342 of file grid_tools.cc.
std::vector< std::set< typename Triangulation< dim, spacedim >::active_cell_iterator > > GridTools::vertex_to_cell_map  (  const Triangulation< dim, spacedim > &  triangulation  ) 
Return the adjacent cells of all the vertices. If a vertex is also a hanging node, the associated coarse cell is also returned. The vertices are ordered by the vertex index. This is the number returned by the function cell>vertex_index()
. Notice that only the indices marked in the array returned by Triangulation<dim,spacedim>::get_used_vertices() are used.
Definition at line 3392 of file grid_tools.cc.
std::vector< std::vector< Tensor< 1, spacedim > > > GridTools::vertex_to_cell_centers_directions  (  const Triangulation< dim, spacedim > &  mesh, 
const std::vector< std::set< typename Triangulation< dim, spacedim >::active_cell_iterator > > &  vertex_to_cells  
) 
Return a vector of normalized tensors for each vertexcell combination of the output of GridTools::vertex_to_cell_map() (which is expected as input parameter for this function). Each tensor represents a geometric vector from the vertex to the respective cell center.
An assertion will be thrown if the size of the input vector is not equal to the number of vertices of the triangulation.
result[v][c] is a unit Tensor for vertex index v, indicating the direction of the center of the cth cell with respect to the vertex v.
Definition at line 2731 of file grid_tools.cc.
unsigned int GridTools::find_closest_vertex_of_cell  (  const typename Triangulation< dim, spacedim >::active_cell_iterator &  cell, 
const Point< spacedim > &  position,  
const Mapping< dim, spacedim > &  mapping = (ReferenceCells::get_hypercube<dim>() .template get_default_linear_mapping<dim, spacedim>() ) 

) 
Return the local vertex index of cell cell
that is closest to the given location position
. The location of the vertices is extracted from the (optional) mapping
argument, to guarantee that the correct answer is returned when the underlying mapping modifies the position of the vertices.
Definition at line 3059 of file grid_tools.cc.
std::map< unsigned int, types::global_vertex_index > GridTools::compute_local_to_global_vertex_index_map  (  const parallel::distributed::Triangulation< dim, spacedim > &  triangulation  ) 
Compute a globally unique index for each vertex and hanging node associated with a locally owned active cell. The vertices of a ghost cell that are hanging nodes of a locally owned cells have a global index. However, the other vertices of the cells that do not touch an active cell do not have a global index on this processor.
The key of the map is the local index of the vertex and the value is the global index. The indices need to be recomputed after refinement or coarsening and may be different.
Definition at line 3441 of file grid_tools.cc.
std::pair< unsigned int, double > GridTools::get_longest_direction  (  typename Triangulation< dim, spacedim >::active_cell_iterator  cell  ) 
Return the highest value among ratios between extents in each of the coordinate directions of a cell
. Moreover, return the dimension relative to the highest elongation.
[in]  cell  an iterator pointing to the cell. 
first
value is the dimension of the highest elongation and the second
value is the ratio among the dimensions of the cell
. Definition at line 5197 of file grid_tools.cc.
void GridTools::get_face_connectivity_of_cells  (  const Triangulation< dim, spacedim > &  triangulation, 
DynamicSparsityPattern &  connectivity  
) 
Produce a sparsity pattern in which nonzero entries indicate that two cells are connected via a common face. The diagonal entries of the sparsity pattern are also set.
The rows and columns refer to the cells as they are traversed in their natural order using cell iterators.
Definition at line 3796 of file grid_tools.cc.
void GridTools::get_vertex_connectivity_of_cells  (  const Triangulation< dim, spacedim > &  triangulation, 
DynamicSparsityPattern &  connectivity  
) 
Produce a sparsity pattern in which nonzero entries indicate that two cells are connected via a common vertex. The diagonal entries of the sparsity pattern are also set.
The rows and columns refer to the cells as they are traversed in their natural order using cell iterators.
Definition at line 3830 of file grid_tools.cc.
void GridTools::get_vertex_connectivity_of_cells_on_level  (  const Triangulation< dim, spacedim > &  triangulation, 
const unsigned int  level,  
DynamicSparsityPattern &  connectivity  
) 
Produce a sparsity pattern for a given level mesh in which nonzero entries indicate that two cells are connected via a common vertex. The diagonal entries of the sparsity pattern are also set.
The rows and columns refer to the cells as they are traversed in their natural order using cell iterators.
Definition at line 3859 of file grid_tools.cc.
void GridTools::partition_triangulation  (  const unsigned int  n_partitions, 
Triangulation< dim, spacedim > &  triangulation,  
const SparsityTools::Partitioner  partitioner = SparsityTools::Partitioner::metis 

) 
Use graph partitioner to partition the active cells making up the entire domain. After calling this function, the subdomain ids of all active cells will have values between zero and n_partitions1
. You can access the subdomain id of a cell by using cell>subdomain_id()
.
Use the third argument to select between partitioning algorithms provided by METIS or ZOLTAN. METIS is the default partitioner.
If deal.II was not installed with ZOLTAN or METIS, this function will generate an error when the respective partition method is chosen, unless n_partitions
is one. I.e., you can write a program so that it runs in the singleprocessor singlepartition case without packages installed, and only requires them installed when multiple partitions are required.
weight
signal has been attached to the triangulation
, then this will be used and passed to the partitioner. Definition at line 3895 of file grid_tools.cc.
void GridTools::partition_triangulation  (  const unsigned int  n_partitions, 
const std::vector< unsigned int > &  cell_weights,  
Triangulation< dim, spacedim > &  triangulation,  
const SparsityTools::Partitioner  partitioner = SparsityTools::Partitioner::metis 

) 
This function performs the same operation as the one above, except that it takes into consideration a specific set of cell_weights
, which allow the partitioner to balance the graph while taking into consideration the computational effort expended on each cell.
cell_weights
vector is empty, then no weighting is taken into consideration. If not then the size of this vector must equal to the number of active cells in the triangulation. Definition at line 3953 of file grid_tools.cc.
void GridTools::partition_triangulation  (  const unsigned int  n_partitions, 
const SparsityPattern &  cell_connection_graph,  
Triangulation< dim, spacedim > &  triangulation,  
const SparsityTools::Partitioner  partitioner = SparsityTools::Partitioner::metis 

) 
This function does the same as the previous one, i.e. it partitions a triangulation using a partitioning algorithm into a number of subdomains identified by the cell>subdomain_id()
flag.
The difference to the previous function is the second argument, a sparsity pattern that represents the connectivity pattern between cells.
While the function above builds it directly from the triangulation by considering which cells neighbor each other, this function can take a more refined connectivity graph. The sparsity pattern needs to be of size \(N\times N\), where \(N\) is the number of active cells in the triangulation. If the sparsity pattern contains an entry at position \((i,j)\), then this means that cells \(i\) and \(j\) (in the order in which they are traversed by active cell iterators) are to be considered connected; partitioning algorithm will then try to partition the domain in such a way that (i) the subdomains are of roughly equal size, and (ii) a minimal number of connections are broken.
This function is mainly useful in cases where connections between cells exist that are not present in the triangulation alone (otherwise the previous function would be the simpler one to use). Such connections may include that certain parts of the boundary of a domain are coupled through symmetric boundary conditions or integrals (e.g. friction contact between the two sides of a crack in the domain), or if a numerical scheme is used that not only connects immediate neighbors but a larger neighborhood of cells (e.g. when solving integral equations).
In addition, this function may be useful in cases where the default sparsity pattern is not entirely sufficient. This can happen because the default is to just consider face neighbors, not neighboring cells that are connected by edges or vertices. While the latter couple when using continuous finite elements, they are typically still closely connected in the neighborship graph, and partitioning algorithm will not usually cut important connections in this case. However, if there are vertices in the mesh where many cells (many more than the common 4 or 6 in 2d and 3d, respectively) come together, then there will be a significant number of cells that are connected across a vertex, but several degrees removed in the connectivity graph built only using face neighbors. In a case like this, partitioning algorithm may sometimes make bad decisions and you may want to build your own connectivity graph.
weight
signal has been attached to the triangulation
, then this will be used and passed to the partitioner. Definition at line 3995 of file grid_tools.cc.
void GridTools::partition_triangulation  (  const unsigned int  n_partitions, 
const std::vector< unsigned int > &  cell_weights,  
const SparsityPattern &  cell_connection_graph,  
Triangulation< dim, spacedim > &  triangulation,  
const SparsityTools::Partitioner  partitioner = SparsityTools::Partitioner::metis 

) 
This function performs the same operation as the one above, except that it takes into consideration a specific set of cell_weights
, which allow the partitioner to balance the graph while taking into consideration the computational effort expended on each cell.
cell_weights
vector is empty, then no weighting is taken into consideration. If not then the size of this vector must equal to the number of active cells in the triangulation. Definition at line 4055 of file grid_tools.cc.
void GridTools::partition_triangulation_zorder  (  const unsigned int  n_partitions, 
Triangulation< dim, spacedim > &  triangulation,  
const bool  group_siblings = true 

) 
Generates a partitioning of the active cells making up the entire domain using the same partitioning scheme as in the p4est library if the flag group_siblings
is set to true (default behavior of this function). After calling this function, the subdomain ids of all active cells will have values between zero and n_partitions1
. You can access the subdomain id of a cell by using cell>subdomain_id()
.
group_siblings
is set to false, children of a cell might be placed on different processors even though they are all active, which is an assumption made by p4est. By relaxing this, we can create partitions owning a single cell (also for refined meshes). Definition at line 4136 of file grid_tools.cc.
void GridTools::partition_multigrid_levels  (  Triangulation< dim, spacedim > &  triangulation  ) 
Partitions the cells of a multigrid hierarchy by assigning level subdomain ids using the "youngest child" rule, that is, each cell in the hierarchy is owned by the processor who owns its left most child in the forest, and active cells have the same subdomain id and level subdomain id. You can access the level subdomain id of a cell by using cell>level_subdomain_id()
.
Note: This function assumes that the active cells have already been partitioned.
Definition at line 4242 of file grid_tools.cc.
std::vector< types::subdomain_id > GridTools::get_subdomain_association  (  const Triangulation< dim, spacedim > &  triangulation, 
const std::vector< CellId > &  cell_ids  
) 
This function allows to ask for the owning subdomain of cells identified by CellId objects that do not have to exist on the current process.
Definition at line 4341 of file grid_tools.cc.
void GridTools::get_subdomain_association  (  const Triangulation< dim, spacedim > &  triangulation, 
std::vector< types::subdomain_id > &  subdomain  
) 
For each active cell, return in the output array to which subdomain (as given by the cell>subdomain_id()
function) it belongs. The output array is supposed to have the right size already when calling this function.
This function returns the association of each cell with one subdomain. If you are looking for the association of each DoF with a subdomain, use the DoFTools::get_subdomain_association
function.
Definition at line 4397 of file grid_tools.cc.
unsigned int GridTools::count_cells_with_subdomain_association  (  const Triangulation< dim, spacedim > &  triangulation, 
const types::subdomain_id  subdomain  
) 
Count how many cells are uniquely associated with the given subdomain
index.
This function may return zero if there are no cells with the given subdomain
index. This can happen, for example, if you try to partition a coarse mesh into more partitions (one for each processor) than there are cells in the mesh.
This function returns the number of cells associated with one subdomain. If you are looking for the association of DoFs with this subdomain, use the DoFTools::count_dofs_with_subdomain_association
function.
Definition at line 4411 of file grid_tools.cc.
std::vector< bool > GridTools::get_locally_owned_vertices  (  const Triangulation< dim, spacedim > &  triangulation  ) 
For a triangulation, return a mask that represents which of its vertices are "owned" by the current process in the same way as we talk about locally owned cells or degrees of freedom (see GlossLocallyOwnedCell and GlossLocallyOwnedDof). For the purpose of this function, we define a locally owned vertex as follows: a vertex is owned by that processor with the smallest subdomain id (which equals the MPI rank of that processor) among all owners of cells adjacent to this vertex. In other words, vertices that are in the interior of a partition of the triangulation are owned by the owner of this partition; for vertices that lie on the boundary between two or more partitions, the owner is the processor with the least subdomain_id among all adjacent subdomains.
For sequential triangulations (as opposed to, for example, parallel::distributed::Triangulation), every user vertex is of course owned by the current processor, i.e., the function returns Triangulation::get_used_vertices(). For parallel triangulations, the returned mask is a subset of what Triangulation::get_used_vertices() returns.
triangulation  The triangulation of which the function evaluates which vertices are locally owned. 
Definition at line 4427 of file grid_tools.cc.
std::list< std::pair< typename MeshType::cell_iterator, typename MeshType::cell_iterator > > GridTools::get_finest_common_cells  (  const MeshType &  mesh_1, 
const MeshType &  mesh_2  
) 
Given two meshes (i.e. objects of type Triangulation or DoFHandler) that are based on the same coarse mesh, this function figures out a set of cells that are matched between the two meshes and where at most one of the meshes is more refined on this cell. In other words, it finds the smallest cells that are common to both meshes, and that together completely cover the domain.
This function is useful, for example, in timedependent or nonlinear application, where one has to integrate a solution defined on one mesh (e.g., the one from the previous time step or nonlinear iteration) against the shape functions of another mesh (the next time step, the next nonlinear iteration). If, for example, the new mesh is finer, then one has to obtain the solution on the coarse mesh (mesh_1) and interpolate it to the children of the corresponding cell of mesh_2. Conversely, if the new mesh is coarser, one has to express the coarse cell shape function by a linear combination of fine cell shape functions. In either case, one needs to loop over the finest cells that are common to both triangulations. This function returns a list of pairs of matching iterators to cells in the two meshes that can be used to this end.
Note that the list of these iterators is not necessarily ordered, and does also not necessarily coincide with the order in which cells are traversed in one, or both, of the meshes given as arguments.
MeshType  A type that satisfies the requirements of the MeshType concept. 
Definition at line 1148 of file grid_tools_dof_handlers.cc.
bool GridTools::have_same_coarse_mesh  (  const Triangulation< dim, spacedim > &  mesh_1, 
const Triangulation< dim, spacedim > &  mesh_2  
) 
Return true if the two triangulations are based on the same coarse mesh. This is determined by checking whether they have the same number of cells on the coarsest level, and then checking that they have the same vertices.
The two meshes may have different refinement histories beyond the coarse mesh.
Definition at line 1256 of file grid_tools_dof_handlers.cc.
bool GridTools::have_same_coarse_mesh  (  const MeshType &  mesh_1, 
const MeshType &  mesh_2  
) 
The same function as above, but working on arguments of type DoFHandler. This function is provided to allow calling have_same_coarse_mesh for all types of containers representing triangulations or the classes built on triangulations.
MeshType  A type that satisfies the requirements of the MeshType concept. 
Definition at line 1292 of file grid_tools_dof_handlers.cc.
Triangulation< dim, spacedim >::DistortedCellList GridTools::fix_up_distorted_child_cells  (  const typename Triangulation< dim, spacedim >::DistortedCellList &  distorted_cells, 
Triangulation< dim, spacedim > &  triangulation  
) 
Given a triangulation and a list of cells whose children have become distorted as a result of mesh refinement, try to fix these cells up by moving the center node around.
The function returns a list of cells with distorted children that couldn't be fixed up for whatever reason. The returned list is therefore a subset of the input argument.
For a definition of the concept of distorted cells, see the glossary entry. The first argument passed to the current function is typically the exception thrown by the Triangulation::execute_coarsening_and_refinement function.
Definition at line 4947 of file grid_tools.cc.
std::vector< typename MeshType::active_cell_iterator > GridTools::get_patch_around_cell  (  const typename MeshType::active_cell_iterator &  cell  ) 
This function returns a list of all the active neighbor cells of the given, active cell. Here, a neighbor is defined as one having at least part of a face in common with the given cell, but not edge (in 3d) or vertex neighbors (in 2d and 3d).
The first element of the returned list is the cell provided as argument. The remaining ones are neighbors: The function loops over all faces of that given cell and checks if that face is not on the boundary of the domain. Then, if the neighbor cell does not have any children (i.e., it is either at the same refinement level as the current cell, or coarser) then this neighbor cell is added to the list of cells. Otherwise, if the neighbor cell is refined and therefore has children, then this function loops over all subfaces of current face adds the neighbors behind these subfaces to the list to be returned.
MeshType  A type that satisfies the requirements of the MeshType concept. In C++, the compiler can not determine MeshType from the function call. You need to specify it as an explicit template argument following the function name. 
[in]  cell  An iterator pointing to a cell of the mesh. 
Definition at line 1431 of file grid_tools_dof_handlers.cc.
std::vector< typename Container::cell_iterator > GridTools::get_cells_at_coarsest_common_level  (  const std::vector< typename Container::active_cell_iterator > &  patch_cells  ) 
This function takes a vector of active cells (hereafter named patch_cells
) as input argument, and returns a vector of their parent cells with the coarsest common level of refinement. In other words, find that set of cells living at the same refinement level so that all cells in the input vector are children of the cells in the set, or are in the set itself.
Container  In C++, the compiler can not determine the type of Container from the function call. You need to specify it as an explicit template argument following the function name. This type has to satisfy the requirements of a mesh container (see ConceptMeshType). 
[in]  patch_cells  A vector of active cells for which this function finds the parents at the coarsest common level. This vector of cells typically results from calling the function GridTools::get_patch_around_cell(). 
Definition at line 1479 of file grid_tools_dof_handlers.cc.
void GridTools::build_triangulation_from_patch  (  const std::vector< typename Container::active_cell_iterator > &  patch, 
Triangulation< Container::dimension, Container::space_dimension > &  local_triangulation,  
std::map< typename Triangulation< Container::dimension, Container::space_dimension >::active_cell_iterator, typename Container::active_cell_iterator > &  patch_to_global_tria_map  
) 
This function constructs a Triangulation (named local_triangulation
) from a given vector of active cells. This vector (which we think of the cells corresponding to a "patch") contains active cells that are part of an existing global Triangulation. The goal of this function is to build a local Triangulation that contains only the active cells given in patch
(and potentially a minimum number of additional cells required to form a valid Triangulation). The function also returns a map that allows to identify the cells in the output Triangulation and corresponding cells in the input list.
The function copies the location of vertices of cells from the cells of the source triangulation to the triangulation that is built from the list of patch cells. This adds support for triangulations which have been perturbed or smoothed in some manner which makes the triangulation deviate from the standard deal.II refinement strategy of placing new vertices at midpoints of faces or edges.
The operation implemented by this function is frequently used in the definition of error estimators that need to solve "local" problems on each cell and its neighbors. A similar construction is necessary in the definition of the Clement interpolation operator in which one needs to solve a local problem on all cells within the support of a shape function. This function then builds a complete Triangulation from a list of cells that make up such a patch; one can then later attach a DoFHandler to such a Triangulation.
If the list of input cells contains only cells at the same refinement level, then the output Triangulation simply consists of a Triangulation containing only exactly these patch cells. On the other hand, if the input cells live on different refinement levels, i.e., the Triangulation of which they are part is adaptively refined, then the construction of the output Triangulation is not so simple because the coarsest level of a Triangulation can not contain hanging nodes. Rather, we first have to find the common refinement level of all input cells, along with their common parents (see GridTools::get_cells_at_coarsest_common_level()), build a Triangulation from those, and then adaptively refine it so that the input cells all also exist in the output Triangulation.
A consequence of this procedure is that the output Triangulation may contain more active cells than the ones that exist in the input vector. On the other hand, one typically wants to solve the local problem not on the entire output Triangulation, but only on those cells of it that correspond to cells in the input list. In this case, a user typically wants to assign degrees of freedom only on cells that are part of the "patch", and somehow ignore those excessive cells. The current function supports this common requirement by setting the user flag for the cells in the output Triangulation that match with cells in the input list. Cells which are not part of the original patch will not have their user_flag
set; we can then avoid assigning degrees of freedom using the FE_Nothing<dim> element.
Container  In C++, the compiler can not determine the type of Container from the function call. You need to specify it as an explicit template argument following the function name. This type that satisfies the requirements of a mesh container (see ConceptMeshType). 
[in]  patch  A vector of active cells from a common triangulation. These cells may or may not all be at the same refinement level. 
[out]  local_triangulation  A triangulation whose active cells correspond to the given vector of active cells in patch . 
[out]  patch_to_global_tria_map  A map between the local triangulation which is built as explained above, and the cell iterators in the input list. 
Definition at line 1525 of file grid_tools_dof_handlers.cc.
std::map< types::global_dof_index, std::vector< typename DoFHandler< dim, spacedim >::active_cell_iterator > > GridTools::get_dof_to_support_patch_map  (  DoFHandler< dim, spacedim > &  dof_handler  ) 
This function runs through the degrees of freedom defined by the DoFHandler and for each dof constructs a vector of active_cell_iterators representing the cells of support of the associated basis element at that degree of freedom. This function was originally designed for the implementation of local projections, for instance the Clement interpolant, in conjunction with other local patch functions like GridTools::build_triangulation_from_patch.
DoFHandler's built on top of Triangulation or parallel:distributed::Triangulation are supported and handled appropriately.
The result is the patch of cells representing the support of the basis element associated to the degree of freedom. For instance using an FE_Q finite element, we obtain the standard patch of cells touching the degree of freedom and then add other cells that take care of possible hanging node constraints. Using a FE_DGQ finite element, the degrees of freedom are logically considered to be "interior" to the cells so the patch would consist exclusively of the single cell on which the degree of freedom is located.
[in]  dof_handler  The DoFHandler which could be built on a Triangulation or a parallel::distributed::Triangulation with a finite element that has degrees of freedom that are logically associated to a vertex, line, quad, or hex. 
Definition at line 1742 of file grid_tools_dof_handlers.cc.

inline 
An orthogonal equality test for faces.
face1
and face2
are considered equal, if a one to one matching between its vertices can be achieved via an orthogonal equality relation.
Here, two vertices v_1
and v_2
are considered equal, if \(M\cdot v_1 + offset  v_2\) is parallel to the unit vector in unit direction direction
. If the parameter matrix
is a reference to a spacedim x spacedim matrix, \(M\) is set to matrix
, otherwise \(M\) is the identity matrix.
If the matching was successful, the relative orientation of face1
with respect to face2
is returned in the bitset orientation
, where
In 2d face_orientation
is always true
, face_rotation
is always false
, and face_flip has the meaning of line_flip
. More precisely in 3d:
face_orientation
: true
if face1
and face2
have the same orientation. Otherwise, the vertex indices of face1
match the vertex indices of face2
in the following manner:
face_flip
: true
if the matched vertices are rotated by 180 degrees:
face_rotation
: true
if the matched vertices are rotated by 90 degrees counterclockwise:
and any combination of that... More information on the topic can be found in the glossary article.
Definition at line 2458 of file grid_tools_dof_handlers.cc.

inline 
Same function as above, but doesn't return the actual orientation
Definition at line 2511 of file grid_tools_dof_handlers.cc.
void GridTools::collect_periodic_faces  (  const MeshType &  mesh, 
const types::boundary_id  b_id1,  
const types::boundary_id  b_id2,  
const unsigned int  direction,  
std::vector< PeriodicFacePair< typename MeshType::cell_iterator > > &  matched_pairs,  
const Tensor< 1, MeshType::space_dimension > &  offset = ::Tensor<1, MeshType::space_dimension>() , 

const FullMatrix< double > &  matrix = FullMatrix<double>() 

) 
This function will collect periodic face pairs on the coarsest mesh level of the given mesh
(a Triangulation or DoFHandler) and add them to the vector matched_pairs
leaving the original contents intact.
Define a 'first' boundary as all boundary faces having boundary_id b_id1
and a 'second' boundary consisting of all faces belonging to b_id2
.
This function tries to match all faces belonging to the first boundary with faces belonging to the second boundary with the help of orthogonal_equality().
The bitset that is returned inside of PeriodicFacePair encodes the relative orientation of the first face with respect to the second face, see the documentation of orthogonal_equality() for further details.
The direction
refers to the space direction in which periodicity is enforced. When matching periodic faces this vector component is ignored.
The offset
is a vector tangential to the faces that is added to the location of vertices of the 'first' boundary when attempting to match them to the corresponding vertices of the 'second' boundary. This can be used to implement conditions such as \(u(0,y)=u(1,y+1)\).
Optionally, a \(dim\times dim\) rotation matrix
can be specified that describes how vector valued DoFs of the first face should be modified prior to constraining to the DoFs of the second face. The matrix
is used in two places. First, matrix
will be supplied to orthogonal_equality() and used for matching faces: Two vertices \(v_1\) and \(v_2\) match if \(\text{matrix}\cdot v_1 + \text{offset}  v_2\) is parallel to the unit vector in unit direction direction
. (For more details see DoFTools::make_periodicity_constraints(), the glossary glossary entry on periodic conditions and step45). Second, matrix
will be stored in the PeriodicFacePair collection matched_pairs
for further use.
MeshType  A type that satisfies the requirements of the MeshType concept. 
matched_pairs
(and existing entries will be preserved), it is possible to call this function several times with different boundary ids to generate a vector with all periodic pairs.Definition at line 2232 of file grid_tools_dof_handlers.cc.
void GridTools::collect_periodic_faces  (  const MeshType &  mesh, 
const types::boundary_id  b_id,  
const unsigned int  direction,  
std::vector< PeriodicFacePair< typename MeshType::cell_iterator > > &  matched_pairs,  
const ::Tensor< 1, MeshType::space_dimension > &  offset = ::Tensor< 1, MeshType::space_dimension >() , 

const FullMatrix< double > &  matrix = FullMatrix< double >() 

) 
This compatibility version of collect_periodic_faces() only works on grids with cells in standard orientation.
Instead of defining a 'first' and 'second' boundary with the help of two boundary_ids this function defines a 'left' boundary as all faces with local face index 2*direction
and boundary indicator b_id
and, similarly, a 'right' boundary consisting of all face with local face index 2*direction+1
and boundary indicator b_id
. Faces with coordinates only differing in the direction
component are identified.
This function will collect periodic face pairs on the coarsest mesh level and add them to matched_pairs
leaving the original contents intact.
See above function for further details.
void GridTools::exchange_cell_data_to_ghosts  (  const MeshType &  mesh, 
const std::function< std_cxx17::optional< DataType >(const typename MeshType::active_cell_iterator &)> &  pack,  
const std::function< void(const typename MeshType::active_cell_iterator &, const DataType &)> &  unpack,  
const std::function< bool(const typename MeshType::active_cell_iterator &)> &  cell_filter = always_return< typename MeshType::active_cell_iterator, bool >{true} 

) 
Exchange arbitrary data of type DataType
provided by the function objects from locally owned cells to ghost cells on other processors.
After this call, you typically will have received data from unpack
on every ghost cell as it was given by pack
on the owning processor. Whether you do or do not receive information to unpack
on a given ghost cell depends on whether the pack
function decided that something needs to be sent. It does so using the std_cxx17::optional mechanism: if the std_cxx17::optional return object of the pack
function is empty, then this implies that no data has to be sent for the locally owned cell it was called on. In that case, unpack
will also not be called on the ghost cell that corresponds to it on the receiving side. On the other hand, if the std_cxx17::optional object is not empty, then the data stored within it will be sent to the received and the unpack
function called with it.
DataType  The type of the data to be communicated. It is assumed to be serializable by boost::serialization. In many cases, this data type can not be deduced by the compiler, e.g., if you provide lambda functions for the second and third argument to this function. In this case, you have to explicitly specify the DataType as a template argument to the function call. 
MeshType  The type of mesh . 
mesh  A variable of a type that satisfies the requirements of the MeshType concept. 
pack  The function that will be called on each locally owned cell that is a ghost cell somewhere else. As mentioned above, the function may return a regular data object of type DataType to indicate that data should be sent, or an empty std_cxx17::optional<DataType> to indicate that nothing has to be sent for this cell. 
unpack  The function that will be called for each ghost cell for which data was sent, i.e., for which the pack function on the sending side returned a nonempty std_cxx17::optional object. The unpack function is then called with the data sent by the processor that owns that cell. 
cell_filter  Only cells are communicated where this filter function returns the value true . In the default case, the function returns true on all cells and thus, all relevant cells are communicated. 
Here is an example that shows how this function is to be used in a concrete context. It is taken from the code that makes sure that the active_fe_index
(a single unsigned integer) is transported from locally owned cells where one can set it in DoFHandler objects with hpcapabilities, to the corresponding ghost cells on other processors to ensure that one can query the right value also on those processors:
You will notice that the pack
lambda function returns an unsigned int
, not a std_cxx17::optional<unsigned int>
. The former converts automatically to the latter, implying that data will always be transported to the other processor.
(In reality, the unpack
function needs to be a bit more complicated because it is not allowed to call DoFAccessor::set_active_fe_index() on ghost cells. Rather, the unpack
function directly accesses internal data structures. But you get the idea – the code could, just as well, have exchanged material ids, user indices, boundary indicators, or any kind of other data with similar calls as the ones above.)
void GridTools::exchange_cell_data_to_level_ghosts  (  const MeshType &  mesh, 
const std::function< std_cxx17::optional< DataType >(const typename MeshType::level_cell_iterator &)> &  pack,  
const std::function< void(const typename MeshType::level_cell_iterator &, const DataType &)> &  unpack,  
const std::function< bool(const typename MeshType::level_cell_iterator &)> &  cell_filter = always_return< typename MeshType::level_cell_iterator, bool >{ true} 

) 
Exchange arbitrary data of type DataType
provided by the function objects from locally owned level cells to ghost level cells on other processes.
In addition to the parameters of exchange_cell_data_to_ghosts(), this function allows to provide a cell_filter
function, which can be used to only communicate marked cells. In the default case, all relevant cells are communicated.
std::vector< std::vector< BoundingBox< spacedim > > > GridTools::exchange_local_bounding_boxes  (  const std::vector< BoundingBox< spacedim > > &  local_bboxes, 
const MPI_Comm  mpi_communicator  
) 
Definition at line 6875 of file grid_tools.cc.
RTree< std::pair< BoundingBox< spacedim >, unsigned int > > GridTools::build_global_description_tree  (  const std::vector< BoundingBox< spacedim > > &  local_description, 
const MPI_Comm  mpi_communicator  
) 
In this collective operation each process provides a vector of bounding boxes and a communicator. All these vectors are gathered on each of the processes, organized in a search tree, and then returned.
The idea is that the vector of bounding boxes describes a relevant property of the computations on each process individually, which could also be of use to other processes. An example would be if the input vector of bounding boxes corresponded to a covering of the locally owned partition of a mesh (see GlossLocallyOwnedCell) of a parallel::distributed::Triangulation object. While these may overlap the bounding boxes of other processes, finding which process owns the cell that encloses a given point is vastly easier if the process trying to figure this out has a (relatively small) list of processes whose bounding boxes contain that point.
The returned search tree object is an rtree with packing algorithm, which is provided by boost library. See https://www.boost.org/doc/libs/1_67_0/libs/geometry/doc/html/geometry/spatial_indexes/introduction.html for more information.
In the returned tree, each node contains a pair of elements: the first being a bounding box, the second being the rank of the process for which at least some of the locally owned cells overlap with the bounding box.
Definition at line 6971 of file grid_tools.cc.
void GridTools::collect_coinciding_vertices  (  const Triangulation< dim, spacedim > &  tria, 
std::map< unsigned int, std::vector< unsigned int > > &  coinciding_vertex_groups,  
std::map< unsigned int, unsigned int > &  vertex_to_coinciding_vertex_group  
) 
Collect for a given triangulation all locally relevant vertices that coincide due to periodicity.
Coinciding vertices are put into a group, e.g.: [1, 25, 51], which is labeled by an arbitrary element from it, e.g.: "1". All coinciding vertices store the label to its group, so that they can quickly access all the coinciding vertices in that group: e.g.: 51 > "1" > [1, 25, 51]
[in]  tria  Triangulation. 
[out]  coinciding_vertex_groups  A map of equivalence classes (of coinciding vertices) labeled by an arbitrary element from them. Vertices not coinciding are ignored. 
[out]  vertex_to_coinciding_vertex_group  Map of a vertex to the label of a group of coinciding vertices. Vertices not contained in this vector are not coinciding with any other vertex. 
Definition at line 7034 of file grid_tools.cc.
std::map< unsigned int, std::set<::types::subdomain_id > > GridTools::compute_vertices_with_ghost_neighbors  (  const Triangulation< dim, spacedim > &  tria  ) 
Return a map that, for each vertex of the given triangulation, provides a set of all the process subdomain ids whose subdomains are adjacent to that vertex. The set excludes the subdomain id of the current process. As a consequence, for a given vertex, the returned set consists of exactly those subdomain ids that correspond to the ghost cells adjacent to that vertex, assuming there are any such ghost cells.
For vertices that are not adjacent to a ghost cell, the map contains no entries, and this should be interpreted in the same way as if the map contained an entry for a given vertex index, but that the std::set
associated with that map entry is simply empty. For nonparallel triangulations, the map is consequently empty since no vertex has adjacent ghost cells.
[in]  tria  Triangulation. 
Definition at line 7157 of file grid_tools.cc.

inline 
Output operator which outputs assemble flags as a set of or'd text values.
Definition at line 106 of file grid_tools_cache_update_flags.h.

inline 
Global operator which returns an object in which all bits are set which are either set in the first or the second argument. This operator exists since if it did not then the result of the bitor operator 
would be an integer which would in turn trigger a compiler warning when we tried to assign it to an object of type CacheUpdateFlags.
Definition at line 130 of file grid_tools_cache_update_flags.h.

inline 
Global operator which returns an object in which all bits are set which are not set in the argument. This operator exists since if it did not then the result of the bitnegation operator ~
would be an integer which would in turn trigger a compiler warning when we tried to assign it to an object of type CacheUpdateFlags.
Definition at line 146 of file grid_tools_cache_update_flags.h.

inline 
Global operator which sets the bits from the second argument also in the first one.
Definition at line 161 of file grid_tools_cache_update_flags.h.

inline 
Global operator which returns an object in which all bits are set which are set in the first as well as the second argument. This operator exists since if it did not then the result of the bitand operator &
would be an integer which would in turn trigger a compiler warning when we tried to assign it to an object of type CacheUpdateFlags.
Definition at line 178 of file grid_tools_cache_update_flags.h.

inline 
Global operator which clears all the bits in the first argument if they are not also set in the second argument.
Definition at line 192 of file grid_tools_cache_update_flags.h.
void GridTools::rotate  (  const double  angle, 
Triangulation< 1, 2 > &  triangulation  
) 
Definition at line 2160 of file grid_tools.cc.
void GridTools::rotate  (  const double  angle, 
Triangulation< 2, 2 > &  triangulation  
) 
Definition at line 2169 of file grid_tools.cc.
void GridTools::laplace_transform  (  const std::map< unsigned int, Point< dim > > &  new_points, 
Triangulation< dim > &  triangulation,  
const Function< dim > *  coefficient,  
const bool  solve_for_absolute_positions  
) 
Definition at line 2246 of file grid_tools.cc.
void GridTools::match_periodic_face_pairs  (  std::set< std::pair< CellIterator, unsigned int > > &  pairs1, 
std::set< std::pair< std_cxx20::type_identity_t< CellIterator >, unsigned int > > &  pairs2,  
const unsigned int  direction,  
std::vector< PeriodicFacePair< CellIterator > > &  matched_pairs,  
const ::Tensor< 1, CellIterator::AccessorType::space_dimension > &  offset,  
const FullMatrix< double > &  matrix  
) 
Definition at line 2057 of file grid_tools_dof_handlers.cc.
void GridTools::collect_periodic_faces  (  const MeshType &  mesh, 
const types::boundary_id  b_id,  
const unsigned int  direction,  
std::vector< PeriodicFacePair< typename MeshType::cell_iterator > > &  matched_pairs,  
const Tensor< 1, MeshType::space_dimension > &  offset,  
const FullMatrix< double > &  matrix  
) 
Definition at line 2151 of file grid_tools_dof_handlers.cc.

inline 
Definition at line 2321 of file grid_tools_dof_handlers.cc.
double GridTools::cell_measure< 1 >  (  const std::vector< Point< 1 > > &  all_vertices, 
const ArrayView< const unsigned int > &  vertex_indices  
) 
Definition at line 33 of file grid_tools_nontemplates.cc.
double GridTools::cell_measure< 2 >  (  const std::vector< Point< 2 > > &  all_vertices, 
const ArrayView< const unsigned int > &  vertex_indices  
) 
Definition at line 46 of file grid_tools_nontemplates.cc.
double GridTools::cell_measure< 3 >  (  const std::vector< Point< 3 > > &  all_vertices, 
const ArrayView< const unsigned int > &  vertex_indices  
) 
Definition at line 120 of file grid_tools_nontemplates.cc.