Reference documentation for deal.II version 8.1.0
Classes | Functions
GridTools Namespace Reference

Classes

struct  PeriodicFacePair
 

Functions

template<int dim, int spacedim>
double diameter (const Triangulation< dim, spacedim > &tria)
 
template<int dim, int spacedim>
double volume (const Triangulation< dim, spacedim > &tria, const Mapping< dim, spacedim > &mapping=(StaticMappingQ1< dim, spacedim >::mapping))
 
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, 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=1e-12)
 
template<int dim, typename Transformation , int spacedim>
void transform (const Transformation &transformation, Triangulation< dim, spacedim > &triangulation)
 
template<int dim, int spacedim>
void shift (const Point< spacedim > &shift_vector, Triangulation< dim, spacedim > &triangulation)
 
void rotate (const double angle, Triangulation< 2 > &triangulation)
 
template<int dim>
void laplace_transform (const std::map< unsigned int, Point< dim > > &new_points, Triangulation< dim > &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)
 
template<int dim, template< int, int > class Container, int spacedim>
unsigned int find_closest_vertex (const Container< dim, spacedim > &container, const Point< spacedim > &p)
 
template<int dim, template< int, int > class Container, int spacedim>
std::vector< typename Container< dim, spacedim >::active_cell_iterator > find_cells_adjacent_to_vertex (const Container< dim, spacedim > &container, const unsigned int vertex_index)
 
template<int dim, template< int, int > class Container, int spacedim>
Container< dim, spacedim >::active_cell_iterator find_active_cell_around_point (const Container< dim, spacedim > &container, const Point< spacedim > &p)
 
template<int dim, template< int, int > class Container, int spacedim>
std::pair< typename Container< dim, spacedim >::active_cell_iterator, Point< dim > > find_active_cell_around_point (const Mapping< dim, spacedim > &mapping, const Container< dim, spacedim > &container, const Point< spacedim > &p)
 
template<int dim, int spacedim>
std::pair< typename hp::DoFHandler< dim, spacedim >::active_cell_iterator, Point< dim > > find_active_cell_around_point (const hp::MappingCollection< dim, spacedim > &mapping, const hp::DoFHandler< dim, spacedim > &container, const Point< spacedim > &p)
 
template<class Container >
std::vector< typename Container::active_cell_iterator > get_active_child_cells (const typename Container::cell_iterator &cell)
 
template<class Container >
void get_active_neighbors (const typename Container::active_cell_iterator &cell, std::vector< typename Container::active_cell_iterator > &active_neighbors)
 
template<int dim, int spacedim>
void get_face_connectivity_of_cells (const Triangulation< dim, spacedim > &triangulation, SparsityPattern &connectivity)
 
template<int dim, int spacedim>
void partition_triangulation (const unsigned int n_partitions, Triangulation< dim, spacedim > &triangulation)
 
template<int dim, int spacedim>
void partition_triangulation (const unsigned int n_partitions, const SparsityPattern &cell_connection_graph, Triangulation< dim, spacedim > &triangulation)
 
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<typename Container >
std::list< std::pair< typename Container::cell_iterator, typename Container::cell_iterator > > get_finest_common_cells (const Container &mesh_1, const Container &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 Container >
bool have_same_coarse_mesh (const Container &mesh_1, const Container &mesh_2)
 
template<int dim, int spacedim>
double minimal_cell_diameter (const Triangulation< dim, spacedim > &triangulation)
 
template<int dim, int spacedim>
double maximal_cell_diameter (const Triangulation< dim, spacedim > &triangulation)
 
template<int dim, int spacedim>
void create_union_triangulation (const Triangulation< dim, spacedim > &triangulation_1, const Triangulation< dim, spacedim > &triangulation_2, Triangulation< dim, spacedim > &result)
 
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)
 
template<template< int, int > class Container, int dim, int spacedim>
std::map< typename Container< dim-1, spacedim >::cell_iterator, typename Container< dim, spacedim >::face_iterator > extract_boundary_mesh (const Container< dim, spacedim > &volume_mesh, Container< dim-1, spacedim > &surface_mesh, const std::set< types::boundary_id > &boundary_ids=std::set< types::boundary_id >())
 
template<typename FaceIterator >
bool orthogonal_equality (std::bitset< 3 > &orientation, const FaceIterator &face1, const FaceIterator &face2, const int direction, const ::Tensor< 1, FaceIterator::AccessorType::space_dimension > &offset)
 
template<typename FaceIterator >
bool orthogonal_equality (const FaceIterator &face1, const FaceIterator &face2, const int direction, const ::Tensor< 1, FaceIterator::AccessorType::space_dimension > &offset)
 
template<typename CONTAINER >
void collect_periodic_faces (const CONTAINER &container, const types::boundary_id b_id1, const types::boundary_id b_id2, const int direction, std::vector< PeriodicFacePair< typename CONTAINER::cell_iterator > > &matched_pairs, const ::Tensor< 1, CONTAINER::space_dimension > &offset=::Tensor< 1, CONTAINER::space_dimension >())
 
template<typename CONTAINER >
void collect_periodic_faces (const CONTAINER &container, const types::boundary_id b_id, const int direction, std::vector< PeriodicFacePair< typename CONTAINER::cell_iterator > > &matched_pairs, const ::Tensor< 1, CONTAINER::space_dimension > &offset=::Tensor< 1, CONTAINER::space_dimension >())
 
 DeclException1 (ExcInvalidNumberOfPartitions, int,<< "The number of partitions you gave is "<< arg1<< ", but must be greater than zero.")
 
 DeclException1 (ExcNonExistentSubdomain, int,<< "The subdomain id "<< arg1<< " has no cells associated with it.")
 
 DeclException0 (ExcTriangulationHasBeenRefined)
 
 DeclException1 (ExcScalingFactorNotPositive, double,<< "The scaling factor must be positive, but is "<< arg1)
 
template<int N>
 DeclException1 (ExcPointNotFoundInCoarseGrid, Point< N >,<< "The point <"<< arg1<< "> could not be found inside any of the "<< "coarse grid cells.")
 
template<int N>
 DeclException1 (ExcPointNotFound, Point< N >,<< "The point <"<< arg1<< "> could not be found inside any of the "<< "subcells of a coarse grid cell.")
 
 DeclException1 (ExcVertexNotUsed, unsigned int,<< "The given vertex "<< arg1<< " is not used in the given triangulation")
 
template<int dim, typename Predicate , int spacedim>
void transform (const Predicate &predicate, Triangulation< dim, spacedim > &triangulation)
 
template<class DH >
std::vector< typename DH::active_cell_iterator > get_active_child_cells (const typename DH::cell_iterator &cell)
 
template<>
double cell_measure< 3 > (const std::vector< Point< 3 > > &all_vertices, const unsigned int(&vertex_indices)[GeometryInfo< 3 >::vertices_per_cell])
 
template<>
double cell_measure< 2 > (const std::vector< Point< 2 > > &all_vertices, const unsigned int(&vertex_indices)[GeometryInfo< 2 >::vertices_per_cell])
 

Detailed Description

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.

Function Documentation

template<int dim, int spacedim>
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.

template<int dim, int spacedim>
double GridTools::volume ( const Triangulation< dim, spacedim > &  tria,
const Mapping< dim, spacedim > &  mapping = (StaticMappingQ1< dim, spacedim >::mapping) 
)

Compute the volume (i.e. the dim-dimensional measure) of the triangulation. We compute the measure using the integral $\int 1 \; dx$. The integral approximated is approximated via quadrature for which we need the mapping argument.

This function also works for objects of type parallel::distributed::Triangulation, in which case the function is a collective operation.

template<int dim>
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.

template<int dim, int spacedim>
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.

template<int dim, int spacedim>
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 = 1e-12 
)

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 quadratic and thus quite slow to begin with. However, if you wish to consider all vertices, simply pass an empty vector.

Two vertices are considered equal if their difference in each coordinate direction is less than tol.

template<int dim, typename Transformation , int spacedim>
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. Since the internal consistency of a triangulation can only be guaranteed if the transformation is applied to the vertices of only one level of hierarchically refined cells, this function may only be used if all cells of the triangulation are on the same refinement level.

The transformation given as argument is used to transform each vertex. Its respective type has to offer a function-like syntax, i.e. the predicate is either an object of a type that has an operator(), or it is a pointer to the function. In either case, argument and return value have to be of type Point<spacedim>.

This function is used in the "Possibilities for extensions" section of step-38. It is also used in step-49.

template<int dim, int spacedim>
void GridTools::shift ( const Point< 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.

void GridTools::rotate ( const double  angle,
Triangulation< 2 > &  triangulation 
)

Rotate all vertices of the given two-dimensional triangulation in counter-clockwise 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.

template<int dim>
void GridTools::laplace_transform ( const std::map< unsigned int, Point< dim > > &  new_points,
Triangulation< dim > &  tria 
)

Transform the given triangulation smoothly to a different domain where each of the vertices at the boundary of the triangulation is mapped to the corresponding points in the new_points map.

The way this function works is that it solves a Laplace equation for each of the dim components of a displacement field that maps the current domain into one described by new_points . The new_points array therefore represents the boundary values of this displacement field. The function then evaluates this displacement field at each vertex in the interior 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.

Parameters
[in]new_pointsThe 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]triaThe Triangulation object. This object is changed in-place, i.e., the previous locations of vertices are overwritten.
Note
This function is not currently implemented for the 1d case.
template<int dim, int spacedim>
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.

template<int dim, int spacedim>
void GridTools::distort_random ( const double  factor,
Triangulation< dim, spacedim > &  triangulation,
const bool  keep_boundary = true 
)

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.

template<int dim, template< int, int > class Container, int spacedim>
unsigned int GridTools::find_closest_vertex ( const Container< dim, spacedim > &  container,
const Point< spacedim > &  p 
)

Find and return the number of the used vertex in a given Container that is located closest to a given point p. The type of the first parameter may be either Triangulation, DoFHandler, hp::DoFHandler, or MGDoFHandler.

Author
Ralf B. Schulz, 2006
template<int dim, template< int, int > class Container, int spacedim>
std::vector<typename Container<dim,spacedim>::active_cell_iterator> GridTools::find_cells_adjacent_to_vertex ( const Container< dim, spacedim > &  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. The type of the first parameter may be either Triangulation, DoFHandler, hp::DoFHandler, or MGDoFHandler.

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.

Note
If the point requested does not lie in any of the cells of the mesh given, then this function throws an exception of type GridTools::ExcPointNotFound. You can catch this exception and decide what to do in that case.
It isn't entirely clear at this time whether the function does the right thing with anisotropically refined meshes. It needs to be checked for this case.
template<int dim, template< int, int > class Container, int spacedim>
Container<dim,spacedim>::active_cell_iterator GridTools::find_active_cell_around_point ( const Container< dim, spacedim > &  container,
const Point< spacedim > &  p 
)

Find and return an iterator to the active cell that surrounds a given point ref. The type of the first parameter may be either Triangulation, or one of the DoF handler classes, i.e. we can find the cell around a point for iterators into each of these classes.

This is solely a wrapper function for the function of same name below. A Q1 mapping is used for the boundary, and the iterator to the cell in which the point resides is returned.

It is recommended to use the other version of this function, as it simultaneously delivers the local coordinate of the given point without additional computational cost.

Note
If the point requested does not lie in any of the cells of the mesh given, then this function throws an exception of type GridTools::ExcPointNotFound. You can catch this exception and decide what to do in that case.
When applied to a triangulation or DoF handler object based on a parallel::distributed::Triangulation object, the cell returned may in fact be a ghost or artificial cell (see GlossArtificialCell and GlossGhostCell). If so, many of the operations one may want to do on this cell (e.g., evaluating the solution) may not be possible and you will have to decide what to do in that case.
template<int dim, template< int, int > class Container, int spacedim>
std::pair<typename Container<dim,spacedim>::active_cell_iterator, Point<dim> > GridTools::find_active_cell_around_point ( const Mapping< dim, spacedim > &  mapping,
const Container< dim, spacedim > &  container,
const Point< spacedim > &  p 
)

Find and return an iterator to the active cell that surrounds a given point p. The type of the first parameter may be either Triangulation, DoFHandler, hp::DoFHandler, or MGDoFHandler, i.e., we can find the cell around a point for iterators into each of these classes.

The algorithm used in this function proceeds by first looking for vertex located closest to the given point, see find_closest_vertex(). Secondly, all adjacent cells to this point are found in the mesh, see find_cells_adjacent_to_vertex(). Lastly, for each of these cells, it is tested whether the point is inside. This check is performed using arbitrary boundary mappings. Still, it is possible that due to roundoff errors, the point cannot be located exactly inside the unit cell. In this case, even points at a very small distance outside the unit cell are allowed.

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.

The function returns an iterator to the cell, as well as the local position of the point inside the unit cell. This local position might be located slightly outside an actual unit cell, due to numerical roundoff. Therefore, the point returned by this function should be projected onto the unit cell, using GeometryInfo::project_to_unit_cell. This is not automatically performed by the algorithm.

Note
If the point requested does not lie in any of the cells of the mesh given, then this function throws an exception of type GridTools::ExcPointNotFound. You can catch this exception and decide what to do in that case.
When applied to a triangulation or DoF handler object based on a parallel::distributed::Triangulation object, the cell returned may in fact be a ghost or artificial cell (see GlossArtificialCell and GlossGhostCell). If so, many of the operations one may want to do on this cell (e.g., evaluating the solution) may not be possible and you will have to decide what to do in that case.
template<int dim, int spacedim>
std::pair<typename hp::DoFHandler<dim,spacedim>::active_cell_iterator, Point<dim> > GridTools::find_active_cell_around_point ( const hp::MappingCollection< dim, spacedim > &  mapping,
const hp::DoFHandler< dim, spacedim > &  container,
const Point< spacedim > &  p 
)

A version of the previous function 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 hp problems, since the active finite element index for all other DoF handlers is always zero.

Note
If the point requested does not lie in any of the cells of the mesh given, then this function throws an exception of type GridTools::ExcPointNotFound. You can catch this exception and decide what to do in that case.
When applied to a triangulation or DoF handler object based on a parallel::distributed::Triangulation object, the cell returned may in fact be a ghost or artificial cell (see GlossArtificialCell and GlossGhostCell). If so, many of the operations one may want to do on this cell (e.g., evaluating the solution) may not be possible and you will have to decide what to do in that case.
template<class Container >
std::vector<typename Container::active_cell_iterator> GridTools::get_active_child_cells ( const typename Container::cell_iterator &  cell)

Return a list of all descendents 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).

Since in C++ the type of the Container template argument (which can be Triangulation, DoFHandler, MGDoFHandler, or hp::DoFHandler) can not be deduced from a function call, you will have to specify it after the function name, as for example in GridTools::get_active_child_cells<DoFHandler<dim> > (cell).

template<class Container >
void GridTools::get_active_neighbors ( const typename Container::active_cell_iterator &  cell,
std::vector< typename Container::active_cell_iterator > &  active_neighbors 
)

Extract the active cells around a given cell cell and return them in the vector active_neighbors.

Definition at line 1267 of file grid_tools.h.

template<int dim, int spacedim>
void GridTools::get_face_connectivity_of_cells ( const Triangulation< dim, spacedim > &  triangulation,
SparsityPattern 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.

template<int dim, int spacedim>
void GridTools::partition_triangulation ( const unsigned int  n_partitions,
Triangulation< dim, spacedim > &  triangulation 
)

Use the METIS partitioner to generate a partitioning of 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_partitions-1. You can access the subdomain id of a cell by using cell->subdomain_id().

This function will generate an error if METIS is not installed unless n_partitions is one. I.e., you can write a program so that it runs in the single-processor single-partition case without METIS installed, and only requires METIS when multiple partitions are required.

template<int dim, int spacedim>
void GridTools::partition_triangulation ( const unsigned int  n_partitions,
const SparsityPattern cell_connection_graph,
Triangulation< dim, spacedim > &  triangulation 
)

This function does the same as the previous one, i.e. it partitions a triangulation using METIS 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; METIS 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 METIS 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, METIS may sometimes make bad decisions and you may want to build your own connectivity graph.

template<int dim, int spacedim>
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.

template<int dim, int spacedim>
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.

template<typename Container >
std::list<std::pair<typename Container::cell_iterator, typename Container::cell_iterator> > GridTools::get_finest_common_cells ( const Container &  mesh_1,
const Container &  mesh_2 
)

Given two mesh containers (i.e. objects of type Triangulation, DoFHandler, hp::DoFHandler, or MGDoFHandler) 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 time-dependent 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 order, and does also not necessarily coincide with the order in which cells are traversed in one, or both, of the meshes given as arguments.

template<int dim, int spacedim>
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.

template<typename Container >
bool GridTools::have_same_coarse_mesh ( const Container &  mesh_1,
const Container &  mesh_2 
)

The same function as above, but working on arguments of type DoFHandler, hp::DoFHandler, or MGDoFHandler. This function is provided to allow calling have_same_coarse_mesh for all types of containers representing triangulations or the classes built on triangulations.

template<int dim, int spacedim>
double GridTools::minimal_cell_diameter ( const Triangulation< dim, spacedim > &  triangulation)

Return the diamater of the smallest active cell of a triangulation. See step-24 for an example of use of this function.

template<int dim, int spacedim>
double GridTools::maximal_cell_diameter ( const Triangulation< dim, spacedim > &  triangulation)

Return the diamater of the largest active cell of a triangulation.

template<int dim, int spacedim>
void GridTools::create_union_triangulation ( const Triangulation< dim, spacedim > &  triangulation_1,
const Triangulation< dim, spacedim > &  triangulation_2,
Triangulation< dim, spacedim > &  result 
)

Given the two triangulations specified as the first two arguments, create the triangulation that contains the finest cells of both triangulation and store it in the third parameter. Previous content of result will be deleted.

Note
This function is intended to create an adaptively refined triangulation that contains the most refined cells from two input triangulations that were derived from the same coarse grid by adaptive refinement. This is an operation sometimes needed when one solves for two variables of a coupled problem on separately refined meshes on the same domain (for example because these variables have boundary layers in different places) but then needs to compute something that involves both variables or wants to output the result into a single file. In both cases, in order not to lose information, the two solutions can not be interpolated onto the respectively other mesh because that may be coarser than the ones on which the variable was computed. Rather, one needs to have a mesh for the domain that is at least as fine as each of the two initial meshes. This function computes such a mesh.
If you want to create a mesh that is the merger of two other coarse meshes, for example in order to compose a mesh for a complicated geometry from meshes for simpler geometries, take a look at GridGenerator::merge_triangulations .
template<int dim, int spacedim>
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.

template<template< int, int > class Container, int dim, int spacedim>
std::map<typename Container<dim-1,spacedim>::cell_iterator, typename Container<dim,spacedim>::face_iterator> GridTools::extract_boundary_mesh ( const Container< dim, spacedim > &  volume_mesh,
Container< dim-1, spacedim > &  surface_mesh,
const std::set< types::boundary_id > &  boundary_ids = std::set< types::boundary_id >() 
)

This function implements a boundary subgrid extraction. Given a <dim,spacedim>-Triangulation (the "volume mesh") the function extracts a subset of its boundary (the "surface mesh"). The boundary to be extracted is specified by a list of boundary_ids. If none is specified the whole boundary will be extracted. The function is used in step-38.

It also builds a mapping linking the cells on the surface mesh to the corresponding faces on the volume one. This mapping is the return value of the function.

Note
The function builds the surface mesh by creating a coarse mesh from the selected faces of the coarse cells of the volume mesh. It copies the boundary indicators of these faces to the cells of the coarse surface mesh. The surface mesh is then refined in the same way as the faces of the volume mesh are. In order to ensure that the surface mesh has the same vertices as the volume mesh, it is therefore important that you assign appropriate boundary objects through Triangulation::set_boundary to the surface mesh object before calling this function. If you don't, the refinement will happen under the assumption that all faces are straight (i.e using the StraightBoundary class) rather than any curved boundary object you may want to use to determine the location of new vertices.
Oftentimes, the Container template type will be of kind Triangulation; in that case, the map that is returned will be between Triangulation cell iterators of the surface mesh and Triangulation face iterators of the volume mesh. However, one often needs to have this mapping between DoFHandler (or hp::DoFHandler) iterators. In that case, you can pass DoFHandler arguments as first and second parameter; the function will in that case re-build the triangulation underlying the second argument and return a map between DoFHandler iterators. However, the function will not actually distribute degrees of freedom on this newly created surface mesh.
The algorithm outlined above assumes that all faces on higher refinement levels always have exactly the same boundary indicator as their parent face. Consequently, we can start with coarse level faces and build the surface mesh based on that. It would not be very difficult to extend the function to also copy boundary indicators from finer level faces to their corresponding surface mesh cells, for example to accommodate different geometry descriptions in the case of curved boundaries.
template<typename FaceIterator >
bool GridTools::orthogonal_equality ( std::bitset< 3 > &  orientation,
const FaceIterator &  face1,
const FaceIterator &  face2,
const int  direction,
const ::Tensor< 1, FaceIterator::AccessorType::space_dimension > &  offset 
)

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: Two vertices v_1 and v_2 are considered equal, if (v_1 + offset) - v_2 is parallel to the unit vector in direction.

If the matching was successful, the relative orientation of face1 with respect to face2 is returned in the bitset orientation, where

orientation[0] -> face_orientation
orientation[1] -> face_flip
orientation[2] -> face_rotation

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:

face1: face2:
1 - 3 2 - 3
| | <--> | |
0 - 2 0 - 1

face_flip: true if the matched vertices are rotated by 180 degrees:

face1: face2:
1 - 0 2 - 3
| | <--> | |
3 - 2 0 - 1

face_rotation: true if the matched vertices are rotated by 90 degrees counterclockwise:

face1: face2:
0 - 2 2 - 3
| | <--> | |
1 - 3 0 - 1

and any combination of that... More information on the topic can be found in the glossary article.

Author
Matthias Maier, 2012
template<typename FaceIterator >
bool GridTools::orthogonal_equality ( const FaceIterator &  face1,
const FaceIterator &  face2,
const int  direction,
const ::Tensor< 1, FaceIterator::AccessorType::space_dimension > &  offset 
)

Same function as above, but doesn't return the actual orientation

template<typename CONTAINER >
void GridTools::collect_periodic_faces ( const CONTAINER &  container,
const types::boundary_id  b_id1,
const types::boundary_id  b_id2,
const int  direction,
std::vector< PeriodicFacePair< typename CONTAINER::cell_iterator > > &  matched_pairs,
const ::Tensor< 1, CONTAINER::space_dimension > &  offset = ::Tensor< 1, CONTAINER::space_dimension >() 
)

This function will collect periodic face pairs on the coarsest mesh level of the given container (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.

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 $u(0,y)=u(1,y+1)$.

Note
The created std::vector can be used in DoFTools::make_periodicity_constraints and in parallel::distributed::Triangulation::add_periodicity to enforce periodicity algebraically.
Because elements will be added to 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.
Author
Daniel Arndt, Matthias Maier, 2013
template<typename CONTAINER >
void GridTools::collect_periodic_faces ( const CONTAINER &  container,
const types::boundary_id  b_id,
const int  direction,
std::vector< PeriodicFacePair< typename CONTAINER::cell_iterator > > &  matched_pairs,
const ::Tensor< 1, CONTAINER::space_dimension > &  offset = ::Tensor< 1, CONTAINER::space_dimension >() 
)

This compatibility version of collect_periodic_face_pairs only works on grids with cells in standard orientation.

Instead of defining a 'first' and 'second' boundary with the help of two boundary_indicators this function defines a 'left' boundary as all faces with local face index 2*dimension and boundary indicator b_id and, similarly, a 'right' boundary consisting of all face with local face index 2*dimension+1 and boundary indicator b_id.

This function will collect periodic face pairs on the coarsest mesh level and add them to matched_pairs leaving the original contents intact.

Note
This version of collect_periodic_face_pairs will not work on meshes with cells not in standard orientation.
Author
Daniel Arndt, Matthias Maier, 2013
GridTools::DeclException1 ( ExcInvalidNumberOfPartitions  ,
int  ,
<< "The number of partitions you gave is "<< arg1<< "  ,
but must be greater than zero."   
)

Exception

GridTools::DeclException1 ( ExcNonExistentSubdomain  ,
int  ,
<< "The subdomain id "<< arg1<< " has no cells associated with it."   
)

Exception

GridTools::DeclException0 ( ExcTriangulationHasBeenRefined  )

Exception

GridTools::DeclException1 ( ExcScalingFactorNotPositive  ,
double  ,
<< "The scaling factor must be  positive,
but is"<<  arg1 
)

Exception

template<int N>
GridTools::DeclException1 ( ExcPointNotFoundInCoarseGrid  ,
Point< N >   
)

Exception

template<int N>
GridTools::DeclException1 ( ExcPointNotFound  ,
Point< N >   
)

Exception