Reference documentation for deal.II version Git 3f75665 2017-01-19 16:58:38 -0500
Enumerations
DoFTools Namespace Reference

Enumerations

enum  Coupling { none, always, nonzero }
 

Functions

DoF couplings
template<int dim, int spacedim>
void convert_couplings_to_blocks (const hp::DoFHandler< dim, spacedim > &dof_handler, const Table< 2, Coupling > &table_by_component, std::vector< Table< 2, Coupling > > &tables_by_block)
 
template<int dim, int spacedim>
void convert_couplings_to_blocks (const DoFHandler< dim, spacedim > &dof_handler, const Table< 2, Coupling > &table_by_component, std::vector< Table< 2, Coupling > > &tables_by_block)
 
template<int dim, int spacedim>
Table< 2, Couplingdof_couplings_from_component_couplings (const FiniteElement< dim, spacedim > &fe, const Table< 2, Coupling > &component_couplings)
 
template<int dim, int spacedim>
std::vector< Table< 2, Coupling > > dof_couplings_from_component_couplings (const hp::FECollection< dim, spacedim > &fe, const Table< 2, Coupling > &component_couplings)
 
Sparsity pattern generation
template<typename DoFHandlerType , typename SparsityPatternType >
void make_sparsity_pattern (const DoFHandlerType &dof_handler, SparsityPatternType &sparsity_pattern, const ConstraintMatrix &constraints=ConstraintMatrix(), const bool keep_constrained_dofs=true, const types::subdomain_id subdomain_id=numbers::invalid_subdomain_id)
 
template<typename DoFHandlerType , typename SparsityPatternType >
void make_sparsity_pattern (const DoFHandlerType &dof_handler, const Table< 2, Coupling > &coupling, SparsityPatternType &sparsity_pattern, const ConstraintMatrix &constraints=ConstraintMatrix(), const bool keep_constrained_dofs=true, const types::subdomain_id subdomain_id=numbers::invalid_subdomain_id)
 
template<typename DoFHandlerType , typename SparsityPatternType >
void make_sparsity_pattern (const DoFHandlerType &dof_row, const DoFHandlerType &dof_col, SparsityPatternType &sparsity)
 
template<typename DoFHandlerType , typename SparsityPatternType >
void make_flux_sparsity_pattern (const DoFHandlerType &dof_handler, SparsityPatternType &sparsity_pattern)
 
template<typename DoFHandlerType , typename SparsityPatternType >
void make_flux_sparsity_pattern (const DoFHandlerType &dof_handler, SparsityPatternType &sparsity_pattern, const ConstraintMatrix &constraints, const bool keep_constrained_dofs=true, const types::subdomain_id subdomain_id=numbers::invalid_subdomain_id)
 
template<typename DoFHandlerType , typename SparsityPatternType >
void make_flux_sparsity_pattern (const DoFHandlerType &dof, SparsityPatternType &sparsity, const Table< 2, Coupling > &cell_integrals_mask, const Table< 2, Coupling > &face_integrals_mask, const types::subdomain_id subdomain_id=numbers::invalid_subdomain_id)
 
template<typename DoFHandlerType , typename SparsityPatternType >
void make_flux_sparsity_pattern (const DoFHandlerType &dof, SparsityPatternType &sparsity, const ConstraintMatrix &constraints, const bool keep_constrained_dofs, const Table< 2, Coupling > &couplings, const Table< 2, Coupling > &face_couplings, const types::subdomain_id subdomain_id)
 
template<typename DoFHandlerType , typename SparsityPatternType >
void make_boundary_sparsity_pattern (const DoFHandlerType &dof, const std::vector< types::global_dof_index > &dof_to_boundary_mapping, SparsityPatternType &sparsity_pattern)
 
template<typename DoFHandlerType , typename SparsityPatternType , typename number >
void make_boundary_sparsity_pattern (const DoFHandlerType &dof, const std::map< types::boundary_id, const Function< DoFHandlerType::space_dimension, number > * > &boundary_ids, const std::vector< types::global_dof_index > &dof_to_boundary_mapping, SparsityPatternType &sparsity)
 
Hanging nodes and other constraints
template<typename DoFHandlerType >
void make_hanging_node_constraints (const DoFHandlerType &dof_handler, ConstraintMatrix &constraints)
 
template<int dim, int spacedim>
void compute_intergrid_constraints (const DoFHandler< dim, spacedim > &coarse_grid, const unsigned int coarse_component, const DoFHandler< dim, spacedim > &fine_grid, const unsigned int fine_component, const InterGridMap< DoFHandler< dim, spacedim > > &coarse_to_fine_grid_map, ConstraintMatrix &constraints)
 
template<int dim, int spacedim>
void compute_intergrid_transfer_representation (const DoFHandler< dim, spacedim > &coarse_grid, const unsigned int coarse_component, const DoFHandler< dim, spacedim > &fine_grid, const unsigned int fine_component, const InterGridMap< DoFHandler< dim, spacedim > > &coarse_to_fine_grid_map, std::vector< std::map< types::global_dof_index, float > > &transfer_representation)
 
Periodic boundary conditions
template<typename FaceIterator >
void make_periodicity_constraints (const FaceIterator &face_1, const typename identity< FaceIterator >::type &face_2,::ConstraintMatrix &constraint_matrix, const ComponentMask &component_mask=ComponentMask(), const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false, const FullMatrix< double > &matrix=FullMatrix< double >(), const std::vector< unsigned int > &first_vector_components=std::vector< unsigned int >())
 
template<typename DoFHandlerType >
void make_periodicity_constraints (const std::vector< GridTools::PeriodicFacePair< typename DoFHandlerType::cell_iterator > > &periodic_faces,::ConstraintMatrix &constraint_matrix, const ComponentMask &component_mask=ComponentMask(), const std::vector< unsigned int > &first_vector_components=std::vector< unsigned int >())
 
template<typename DoFHandlerType >
void make_periodicity_constraints (const DoFHandlerType &dof_handler, const types::boundary_id b_id1, const types::boundary_id b_id2, const int direction,::ConstraintMatrix &constraint_matrix, const ComponentMask &component_mask=ComponentMask())
 
template<typename DoFHandlerType >
void make_periodicity_constraints (const DoFHandlerType &dof_handler, const types::boundary_id b_id, const int direction,::ConstraintMatrix &constraint_matrix, const ComponentMask &component_mask=ComponentMask())
 
Identifying subsets of degrees of freedom with particular properties
template<int dim, int spacedim>
void extract_hanging_node_dofs (const DoFHandler< dim, spacedim > &dof_handler, std::vector< bool > &selected_dofs)
 
template<int dim, int spacedim>
void extract_dofs (const DoFHandler< dim, spacedim > &dof_handler, const ComponentMask &component_mask, std::vector< bool > &selected_dofs)
 
template<int dim, int spacedim>
void extract_dofs (const hp::DoFHandler< dim, spacedim > &dof_handler, const ComponentMask &component_mask, std::vector< bool > &selected_dofs)
 
template<int dim, int spacedim>
void extract_dofs (const DoFHandler< dim, spacedim > &dof_handler, const BlockMask &block_mask, std::vector< bool > &selected_dofs)
 
template<int dim, int spacedim>
void extract_dofs (const hp::DoFHandler< dim, spacedim > &dof_handler, const BlockMask &block_mask, std::vector< bool > &selected_dofs)
 
template<typename DoFHandlerType >
void extract_level_dofs (const unsigned int level, const DoFHandlerType &dof, const ComponentMask &component_mask, std::vector< bool > &selected_dofs)
 
template<typename DoFHandlerType >
void extract_level_dofs (const unsigned int level, const DoFHandlerType &dof, const BlockMask &component_mask, std::vector< bool > &selected_dofs)
 
template<typename DoFHandlerType >
void extract_boundary_dofs (const DoFHandlerType &dof_handler, const ComponentMask &component_mask, std::vector< bool > &selected_dofs, const std::set< types::boundary_id > &boundary_ids=std::set< types::boundary_id >())
 
template<typename DoFHandlerType >
void extract_boundary_dofs (const DoFHandlerType &dof_handler, const ComponentMask &component_mask, IndexSet &selected_dofs, const std::set< types::boundary_id > &boundary_ids=std::set< types::boundary_id >())
 
template<typename DoFHandlerType >
void extract_dofs_with_support_on_boundary (const DoFHandlerType &dof_handler, const ComponentMask &component_mask, std::vector< bool > &selected_dofs, const std::set< types::boundary_id > &boundary_ids=std::set< types::boundary_id >())
 
template<typename DoFHandlerType >
void extract_constant_modes (const DoFHandlerType &dof_handler, const ComponentMask &component_mask, std::vector< std::vector< bool > > &constant_modes)
 
Parallelization and domain decomposition
template<typename DoFHandlerType >
void extract_subdomain_dofs (const DoFHandlerType &dof_handler, const types::subdomain_id subdomain_id, std::vector< bool > &selected_dofs)
 
template<typename DoFHandlerType >
void extract_locally_owned_dofs (const DoFHandlerType &dof_handler, IndexSet &dof_set)
 
template<typename DoFHandlerType >
void extract_locally_active_dofs (const DoFHandlerType &dof_handler, IndexSet &dof_set)
 
template<typename DoFHandlerType >
void extract_locally_relevant_dofs (const DoFHandlerType &dof_handler, IndexSet &dof_set)
 
template<typename DoFHandlerType >
std::vector< IndexSetlocally_owned_dofs_per_subdomain (const DoFHandlerType &dof_handler)
 
template<typename DoFHandlerType >
std::vector< IndexSetlocally_relevant_dofs_per_subdomain (const DoFHandlerType &dof_handler)
 
template<typename DoFHandlerType >
void extract_locally_relevant_level_dofs (const DoFHandlerType &dof_handler, const unsigned int level, IndexSet &dof_set)
 
template<typename DoFHandlerType >
void get_subdomain_association (const DoFHandlerType &dof_handler, std::vector< types::subdomain_id > &subdomain)
 
template<typename DoFHandlerType >
unsigned int count_dofs_with_subdomain_association (const DoFHandlerType &dof_handler, const types::subdomain_id subdomain)
 
template<typename DoFHandlerType >
void count_dofs_with_subdomain_association (const DoFHandlerType &dof_handler, const types::subdomain_id subdomain, std::vector< unsigned int > &n_dofs_on_subdomain)
 
template<typename DoFHandlerType >
IndexSet dof_indices_with_subdomain_association (const DoFHandlerType &dof_handler, const types::subdomain_id subdomain)
 
DoF indices on patches of cells

Create structures containing a large set of degrees of freedom for small patches of cells. The resulting objects can be used in RelaxationBlockSOR and related classes to implement Schwarz preconditioners and smoothers, where the subdomains consist of small numbers of cells only.

template<typename DoFHandlerType >
std::vector< types::global_dof_indexget_dofs_on_patch (const std::vector< typename DoFHandlerType::active_cell_iterator > &patch)
 
template<int dim, int spacedim>
void make_cell_patches (SparsityPattern &block_list, const DoFHandler< dim, spacedim > &dof_handler, const unsigned int level, const std::vector< bool > &selected_dofs=std::vector< bool >(), const types::global_dof_index offset=0)
 
template<typename DoFHandlerType >
std::vector< unsigned int > make_vertex_patches (SparsityPattern &block_list, const DoFHandlerType &dof_handler, const unsigned int level, const bool interior_dofs_only, const bool boundary_patches=false, const bool level_boundary_patches=false, const bool single_cell_patches=false, const bool invert_vertex_mapping=false)
 
template<typename DoFHandlerType >
std::vector< unsigned int > make_vertex_patches (SparsityPattern &block_list, const DoFHandlerType &dof_handler, const unsigned int level, const BlockMask &exclude_boundary_dofs=BlockMask(), const bool boundary_patches=false, const bool level_boundary_patches=false, const bool single_cell_patches=false, const bool invert_vertex_mapping=false)
 
template<typename DoFHandlerType >
void make_child_patches (SparsityPattern &block_list, const DoFHandlerType &dof_handler, const unsigned int level, const bool interior_dofs_only, const bool boundary_dofs=false)
 
template<typename DoFHandlerType >
void make_single_patch (SparsityPattern &block_list, const DoFHandlerType &dof_handler, const unsigned int level, const bool interior_dofs_only=false)
 
Counting degrees of freedom and related functions
template<typename DoFHandlerType >
void count_dofs_per_component (const DoFHandlerType &dof_handler, std::vector< types::global_dof_index > &dofs_per_component, const bool vector_valued_once=false, std::vector< unsigned int > target_component=std::vector< unsigned int >())
 
template<typename DoFHandlerType >
void count_dofs_per_block (const DoFHandlerType &dof, std::vector< types::global_dof_index > &dofs_per_block, const std::vector< unsigned int > &target_block=std::vector< unsigned int >())
 
template<typename DoFHandlerType >
void get_active_fe_indices (const DoFHandlerType &dof_handler, std::vector< unsigned int > &active_fe_indices)
 
template<typename DoFHandlerType >
unsigned int count_dofs_on_patch (const std::vector< typename DoFHandlerType::active_cell_iterator > &patch)
 
Functions that return different DoF mappings
template<typename DoFHandlerType >
void map_dof_to_boundary_indices (const DoFHandlerType &dof_handler, std::vector< types::global_dof_index > &mapping)
 
template<typename DoFHandlerType >
void map_dof_to_boundary_indices (const DoFHandlerType &dof_handler, const std::set< types::boundary_id > &boundary_ids, std::vector< types::global_dof_index > &mapping)
 
template<int dim, int spacedim>
void map_dofs_to_support_points (const Mapping< dim, spacedim > &mapping, const DoFHandler< dim, spacedim > &dof_handler, std::vector< Point< spacedim > > &support_points)
 
template<int dim, int spacedim>
void map_dofs_to_support_points (const ::hp::MappingCollection< dim, spacedim > &mapping, const hp::DoFHandler< dim, spacedim > &dof_handler, std::vector< Point< spacedim > > &support_points)
 
template<int dim, int spacedim>
void map_dofs_to_support_points (const Mapping< dim, spacedim > &mapping, const DoFHandler< dim, spacedim > &dof_handler, std::map< types::global_dof_index, Point< spacedim > > &support_points)
 
template<int dim, int spacedim>
void map_dofs_to_support_points (const ::hp::MappingCollection< dim, spacedim > &mapping, const hp::DoFHandler< dim, spacedim > &dof_handler, std::map< types::global_dof_index, Point< spacedim > > &support_points)
 
template<typename DoFHandlerType , class Comp >
void map_support_points_to_dofs (const Mapping< DoFHandlerType::dimension, DoFHandlerType::space_dimension > &mapping, const DoFHandlerType &dof_handler, std::map< Point< DoFHandlerType::space_dimension >, types::global_dof_index, Comp > &point_to_index_map)
 
Miscellaneous
template<typename DoFHandlerType , typename Number >
void distribute_cell_to_dof_vector (const DoFHandlerType &dof_handler, const Vector< Number > &cell_data, Vector< double > &dof_data, const unsigned int component=0)
 
template<int spacedim>
void write_gnuplot_dof_support_point_info (std::ostream &out, const std::map< types::global_dof_index, Point< spacedim > > &support_points)
 
template<int dim, int spacedim, template< int, int > class DoFHandlerType>
void make_zero_boundary_constraints (const DoFHandlerType< dim, spacedim > &dof, const types::boundary_id boundary_id, ConstraintMatrix &zero_boundary_constraints, const ComponentMask &component_mask=ComponentMask())
 
template<int dim, int spacedim, template< int, int > class DoFHandlerType>
void make_zero_boundary_constraints (const DoFHandlerType< dim, spacedim > &dof, ConstraintMatrix &zero_boundary_constraints, const ComponentMask &component_mask=ComponentMask())
 
Exceptions
static::ExceptionBase & ExcFiniteElementsDontMatch ()
 
static::ExceptionBase & ExcGridNotCoarser ()
 
static::ExceptionBase & ExcGridsDontMatch ()
 
static::ExceptionBase & ExcNoFESelected ()
 
static::ExceptionBase & ExcInvalidBoundaryIndicator ()
 

Detailed Description

This is a collection of functions operating on, and manipulating the numbers of degrees of freedom. The documentation of the member functions will provide more information, but for functions that exist in multiple versions, there are sections in this global documentation stating some commonalities.

Setting up sparsity patterns

When assembling system matrices, the entries are usually of the form \(a_{ij} = a(\phi_i, \phi_j)\), where \(a\) is a bilinear functional, often an integral. When using sparse matrices, we therefore only need to reserve space for those \(a_{ij}\) only, which are nonzero, which is the same as to say that the basis functions \(\phi_i\) and \(\phi_j\) have a nonempty intersection of their support. Since the support of basis functions is bound only on cells on which they are located or to which they are adjacent, to determine the sparsity pattern it is sufficient to loop over all cells and connect all basis functions on each cell with all other basis functions on that cell. There may be finite elements for which not all basis functions on a cell connect with each other, but no use of this case is made since no examples where this occurs are known to the author.

DoF numberings on boundaries

When projecting the traces of functions to the boundary or parts thereof, one needs to build matrices and vectors that act only on those degrees of freedom that are located on the boundary, rather than on all degrees of freedom. One could do that by simply building matrices in which the entries for all interior DoFs are zero, but such matrices are always very rank deficient and not very practical to work with.

What is needed instead in this case is a numbering of the boundary degrees of freedom, i.e. we should enumerate all the degrees of freedom that are sitting on the boundary, and exclude all other (interior) degrees of freedom. The map_dof_to_boundary_indices() function does exactly this: it provides a vector with as many entries as there are degrees of freedom on the whole domain, with each entry being the number in the numbering of the boundary or DoFHandler::invalid_dof_index if the dof is not on the boundary.

With this vector, one can get, for any given degree of freedom, a unique number among those DoFs that sit on the boundary; or, if your DoF was interior to the domain, the result would be DoFHandler::invalid_dof_index. We need this mapping, for example, to build the mass matrix on the boundary (for this, see make_boundary_sparsity_pattern() function, the corresponding section below, as well as the MatrixCreator namespace documentation).

Actually, there are two map_dof_to_boundary_indices() functions, one producing a numbering for all boundary degrees of freedom and one producing a numbering for only parts of the boundary, namely those parts for which the boundary indicator is listed in a set of indicators given to the function. The latter case is needed if, for example, we would only want to project the boundary values for the Dirichlet part of the boundary. You then give the function a list of boundary indicators referring to Dirichlet parts on which the projection is to be performed. The parts of the boundary on which you want to project need not be contiguous; however, it is not guaranteed that the indices of each of the boundary parts are continuous, i.e. the indices of degrees of freedom on different parts may be intermixed.

Degrees of freedom on the boundary but not on one of the specified boundary parts are given the index DoFHandler::invalid_dof_index, as if they were in the interior. If no boundary indicator was given or if no face of a cell has a boundary indicator contained in the given list, the vector of new indices consists solely of DoFHandler::invalid_dof_index.

(As a side note, for corner cases: The question what a degree of freedom on the boundary is, is not so easy. It should really be a degree of freedom of which the respective basis function has nonzero values on the boundary. At least for Lagrange elements this definition is equal to the statement that the off-point, or what deal.II calls support_point, of the shape function, i.e. the point where the function assumes its nominal value (for Lagrange elements this is the point where it has the function value 1), is located on the boundary. We do not check this directly, the criterion is rather defined through the information the finite element class gives: the FiniteElement class defines the numbers of basis functions per vertex, per line, and so on and the basis functions are numbered after this information; a basis function is to be considered to be on the face of a cell (and thus on the boundary if the cell is at the boundary) according to it belonging to a vertex, line, etc but not to the interior of the cell. The finite element uses the same cell-wise numbering so that we can say that if a degree of freedom was numbered as one of the dofs on lines, we assume that it is located on the line. Where the off-point actually is, is a secret of the finite element (well, you can ask it, but we don't do it here) and not relevant in this context.)

Setting up sparsity patterns for boundary matrices

In some cases, one wants to only work with DoFs that sit on the boundary. One application is, for example, if rather than interpolating non- homogenous boundary values, one would like to project them. For this, we need two things: a way to identify nodes that are located on (parts of) the boundary, and a way to build matrices out of only degrees of freedom that are on the boundary (i.e. much smaller matrices, in which we do not even build the large zero block that stems from the fact that most degrees of freedom have no support on the boundary of the domain). The first of these tasks is done by the map_dof_to_boundary_indices() function (described above).

The second part requires us first to build a sparsity pattern for the couplings between boundary nodes, and then to actually build the components of this matrix. While actually computing the entries of these small boundary matrices is discussed in the MatrixCreator namespace, the creation of the sparsity pattern is done by the create_boundary_sparsity_pattern() function. For its work, it needs to have a numbering of all those degrees of freedom that are on those parts of the boundary that we are interested in. You can get this from the map_dof_to_boundary_indices() function. It then builds the sparsity pattern corresponding to integrals like \(\int_\Gamma \varphi_{b2d(i)} \varphi_{b2d(j)} dx\), where \(i\) and \(j\) are indices into the matrix, and \(b2d(i)\) is the global DoF number of a degree of freedom sitting on a boundary (i.e., \(b2d\) is the inverse of the mapping returned by map_dof_to_boundary_indices() function).

Author
Wolfgang Bangerth, Guido Kanschat and others

Function Documentation

template<int dim, int spacedim>
void DoFTools::convert_couplings_to_blocks ( const hp::DoFHandler< dim, spacedim > &  dof_handler,
const Table< 2, Coupling > &  table_by_component,
std::vector< Table< 2, Coupling > > &  tables_by_block 
)

Map a coupling table from the user friendly organization by components to the organization by blocks. Specializations of this function for DoFHandler and hp::DoFHandler are required due to the different results of their finite element access.

The return vector will be initialized to the correct length inside this function.

Definition at line 2110 of file dof_tools.cc.

template<int dim, int spacedim>
void DoFTools::convert_couplings_to_blocks ( const DoFHandler< dim, spacedim > &  dof_handler,
const Table< 2, Coupling > &  table_by_component,
std::vector< Table< 2, Coupling > > &  tables_by_block 
)

Map a coupling table from the user friendly organization by components to the organization by blocks. Specializations of this function for DoFHandler and hp::DoFHandler are required due to the different results of their finite element access.

The return vector will be initialized to the correct length inside this function.

Definition at line 2085 of file dof_tools.cc.

template<int dim, int spacedim>
Table< 2, Coupling > DoFTools::dof_couplings_from_component_couplings ( const FiniteElement< dim, spacedim > &  fe,
const Table< 2, Coupling > &  component_couplings 
)

Given a finite element and a table how the vector components of it couple with each other, compute and return a table that describes how the individual shape functions couple with each other.

Definition at line 624 of file dof_tools_sparsity.cc.

template<int dim, int spacedim>
std::vector< Table< 2, Coupling > > DoFTools::dof_couplings_from_component_couplings ( const hp::FECollection< dim, spacedim > &  fe,
const Table< 2, Coupling > &  component_couplings 
)

Same function as above for a collection of finite elements, returning a collection of tables.

The function currently treats DoFTools::Couplings::nonzero the same as DoFTools::Couplings::always .

Definition at line 669 of file dof_tools_sparsity.cc.

template<typename FaceIterator >
void DoFTools::make_periodicity_constraints ( const FaceIterator &  face_1,
const typename identity< FaceIterator >::type &  face_2,
::ConstraintMatrix constraint_matrix,
const ComponentMask component_mask = ComponentMask(),
const bool  face_orientation = true,
const bool  face_flip = false,
const bool  face_rotation = false,
const FullMatrix< double > &  matrix = FullMatrix<double>(),
const std::vector< unsigned int > &  first_vector_components = std::vector<unsigned int>() 
)

Insert the (algebraic) constraints due to periodic boundary conditions into a ConstraintMatrix constraint_matrix.

Given a pair of not necessarily active boundary faces face_1 and face_2, this functions constrains all DoFs associated with the boundary described by face_1 to the respective DoFs of the boundary described by face_2. More precisely:

If face_1 and face_2 are both active faces it adds the DoFs of face_1 to the list of constrained DoFs in constraint_matrix and adds entries to constrain them to the corresponding values of the DoFs on face_2. This happens on a purely algebraic level, meaning, the global DoF with (local face) index i on face_1 gets constraint to the DoF with (local face) index i on face_2 (possibly corrected for orientation, see below).

Otherwise, if face_1 and face_2 are not active faces, this function loops recursively over the children of face_1 and face_2. If only one of the two faces is active, then we recursively iterate over the children of the non-active ones and make sure that the solution function on the refined side equals that on the non-refined face in much the same way as we enforce hanging node constraints at places where differently refined cells come together. (However, unlike hanging nodes, we do not enforce the requirement that there be only a difference of one refinement level between the two sides of the domain you would like to be periodic).

This routine only constrains DoFs that are not already constrained. If this routine encounters a DoF that already is constrained (for instance by Dirichlet boundary conditions), the old setting of the constraint (dofs the entry is constrained to, inhomogeneities) is kept and nothing happens.

The flags in the component_mask (see GlossComponentMask) denote which components of the finite element space shall be constrained with periodic boundary conditions. If it is left as specified by the default value all components are constrained. If it is different from the default value, it is assumed that the number of entries equals the number of components of the finite element. This can be used to enforce periodicity in only one variable in a system of equations.

face_orientation, face_flip and face_rotation describe an orientation that should be applied to face_1 prior to matching and constraining DoFs. This has nothing to do with the actual orientation of the given faces in their respective cells (which for boundary faces is always the default) but instead how you want to see periodicity to be enforced. For example, by using these flags, you can enforce a condition of the kind \(u(0,y)=u(1,1-y)\) (i.e., a Moebius band) or in 3d a twisted torus. More precisely, these flags match local face DoF indices in the following manner:

In 2d: face_orientation must always be true, face_rotation is always false, and face_flip has the meaning of line_flip; this implies e.g. for Q1:

face_orientation = true, face_flip = false, face_rotation = false:
face1: face2:
1 1
| <--> |
0 0
Resulting constraints: 0 <-> 0, 1 <-> 1
(Numbers denote local face DoF indices.)
face_orientation = true, face_flip = true, face_rotation = false:
face1: face2:
0 1
| <--> |
1 0
Resulting constraints: 1 <-> 0, 0 <-> 1

And similarly for the case of Q1 in 3d:

face_orientation = true, face_flip = false, face_rotation = false:
face1: face2:
2 - 3 2 - 3
| | <--> | |
0 - 1 0 - 1
Resulting constraints: 0 <-> 0, 1 <-> 1, 2 <-> 2, 3 <-> 3
(Numbers denote local face DoF indices.)
face_orientation = false, face_flip = false, face_rotation = false:
face1: face2:
1 - 3 2 - 3
| | <--> | |
0 - 2 0 - 1
Resulting constraints: 0 <-> 0, 2 <-> 1, 1 <-> 2, 3 <-> 3
face_orientation = true, face_flip = true, face_rotation = false:
face1: face2:
1 - 0 2 - 3
| | <--> | |
3 - 2 0 - 1
Resulting constraints: 3 <-> 0, 2 <-> 1, 1 <-> 2, 0 <-> 3
face_orientation = true, face_flip = false, face_rotation = true
face1: face2:
0 - 2 2 - 3
| | <--> | |
1 - 3 0 - 1
Resulting constraints: 1 <-> 0, 3 <-> 1, 0 <-> 2, 2 <-> 3
and any combination of that...

Optionally a matrix matrix along with an std::vector first_vector_components can be specified that describes how DoFs on face_1 should be modified prior to constraining to the DoFs of face_2. Here, two declarations are possible: If the std::vector first_vector_components is non empty the matrix is interpreted as a dim \(\times\) dim rotation matrix that is applied to all vector valued blocks listed in first_vector_components of the FESystem. If first_vector_components is empty the matrix is interpreted as an interpolation matrix with size no_face_dofs \(\times\) no_face_dofs.

Detailed information can be found in the see Glossary entry on periodic boundary conditions.

Author
Matthias Maier, 2012 - 2015

Definition at line 2163 of file dof_tools_constraints.cc.

template<typename DoFHandlerType >
void DoFTools::make_periodicity_constraints ( const std::vector< GridTools::PeriodicFacePair< typename DoFHandlerType::cell_iterator > > &  periodic_faces,
::ConstraintMatrix constraint_matrix,
const ComponentMask component_mask = ComponentMask(),
const std::vector< unsigned int > &  first_vector_components = std::vector<unsigned int>() 
)

Insert the (algebraic) constraints due to periodic boundary conditions into a ConstraintMatrix constraint_matrix.

This is the main high level interface for above low level variant of make_periodicity_constraints(). It takes a std::vector periodic_faces as argument and applies above make_periodicity_constraints() on each entry. periodic_faces can be created by GridTools::collect_periodic_faces.

Note
For DoFHandler objects that are built on a parallel::distributed::Triangulation object parallel::distributed::Triangulation::add_periodicity has to be called before calling this function..
See also
Glossary entry on periodic boundary conditions and step-45 for further information.
Author
Daniel Arndt, Matthias Maier, 2013 - 2015

Definition at line 2388 of file dof_tools_constraints.cc.

template<typename DoFHandlerType >
void DoFTools::make_periodicity_constraints ( const DoFHandlerType &  dof_handler,
const types::boundary_id  b_id1,
const types::boundary_id  b_id2,
const int  direction,
::ConstraintMatrix constraint_matrix,
const ComponentMask component_mask = ComponentMask() 
)

Insert the (algebraic) constraints due to periodic boundary conditions into a ConstraintMatrix constraint_matrix.

This function serves as a high level interface for the make_periodicity_constraints() function.

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().

If this matching is successful it constrains all DoFs associated with the 'first' boundary to the respective DoFs of the 'second' boundary respecting the relative orientation of the two faces.

Note
: This function is a convenience wrapper. It internally calls GridTools::collect_periodic_faces() with the supplied paramaters and feeds the output to above make_periodicity_constraints() variant. If you need more functionality use GridTools::collect_periodic_faces() directly.
See also
Glossary entry on periodic boundary conditions for further information.
Author
Matthias Maier, 2012

Definition at line 2433 of file dof_tools_constraints.cc.

template<typename DoFHandlerType >
void DoFTools::make_periodicity_constraints ( const DoFHandlerType &  dof_handler,
const types::boundary_id  b_id,
const int  direction,
::ConstraintMatrix constraint_matrix,
const ComponentMask component_mask = ComponentMask() 
)

This compatibility version of make_periodicity_constraints 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*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.

Note
This version of make_periodicity_constraints will not work on meshes with cells not in standard orientation.
: This function is a convenience wrapper. It internally calls GridTools::collect_periodic_faces() with the supplied paramaters and feeds the output to above make_periodicity_constraints() variant. If you need more functionality use GridTools::collect_periodic_faces() directly.
See also
Glossary entry on periodic boundary conditions for further information.

Definition at line 2464 of file dof_tools_constraints.cc.

template<int dim, int spacedim>
void DoFTools::extract_hanging_node_dofs ( const DoFHandler< dim, spacedim > &  dof_handler,
std::vector< bool > &  selected_dofs 
)

Select all dofs that will be constrained by interface constraints, i.e. all hanging nodes.

The size of selected_dofs shall equal dof_handler.n_dofs(). Previous contents of this array or overwritten.

Definition at line 888 of file dof_tools.cc.

template<int dim, int spacedim>
void DoFTools::extract_dofs ( const DoFHandler< dim, spacedim > &  dof_handler,
const ComponentMask component_mask,
std::vector< bool > &  selected_dofs 
)

Extract the indices of the degrees of freedom belonging to certain vector components of a vector-valued finite element. The component_mask defines which components or blocks of an FESystem are to be extracted from the DoFHandler dof. The entries in the output array selected_dofs corresponding to degrees of freedom belonging to these components are then flagged true, while all others are set to false.

The size of component_mask must be compatible with the number of components in the FiniteElement used by dof. The size of selected_dofs must equal DoFHandler::n_dofs(). Previous contents of this array are overwritten.

If the finite element under consideration is not primitive, i.e., some or all of its shape functions are non-zero in more than one vector component (which holds, for example, for FE_Nedelec or FE_RaviartThomas elements), then shape functions cannot be associated with a single vector component. In this case, if one shape vector component of this element is flagged in component_mask (see GlossComponentMask), then this is equivalent to selecting all vector components corresponding to this non-primitive base element.

Definition at line 372 of file dof_tools.cc.

template<int dim, int spacedim>
void DoFTools::extract_dofs ( const hp::DoFHandler< dim, spacedim > &  dof_handler,
const ComponentMask component_mask,
std::vector< bool > &  selected_dofs 
)

The same function as above, but for a hp::DoFHandler.

Definition at line 418 of file dof_tools.cc.

template<int dim, int spacedim>
void DoFTools::extract_dofs ( const DoFHandler< dim, spacedim > &  dof_handler,
const BlockMask block_mask,
std::vector< bool > &  selected_dofs 
)

This function is the equivalent to the DoFTools::extract_dofs() functions above except that the selection of which degrees of freedom to extract is not done based on components (see GlossComponent) but instead based on whether they are part of a particular block (see GlossBlock). Consequently, the second argument is not a ComponentMask but a BlockMask object.

Parameters
dof_handlerThe DoFHandler object from which to extract degrees of freedom
block_maskThe block mask that describes which blocks to consider (see GlossBlockMask)
selected_dofsA vector of length DoFHandler::n_dofs() in which those entries are true that correspond to the selected blocks.

Definition at line 463 of file dof_tools.cc.

template<int dim, int spacedim>
void DoFTools::extract_dofs ( const hp::DoFHandler< dim, spacedim > &  dof_handler,
const BlockMask block_mask,
std::vector< bool > &  selected_dofs 
)

The same function as above, but for a hp::DoFHandler.

Definition at line 476 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::extract_level_dofs ( const unsigned int  level,
const DoFHandlerType &  dof,
const ComponentMask component_mask,
std::vector< bool > &  selected_dofs 
)

Do the same thing as the corresponding extract_dofs() function for one level of a multi-grid DoF numbering.

Definition at line 489 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::extract_level_dofs ( const unsigned int  level,
const DoFHandlerType &  dof,
const BlockMask component_mask,
std::vector< bool > &  selected_dofs 
)

Do the same thing as the corresponding extract_dofs() function for one level of a multi-grid DoF numbering.

Definition at line 541 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::extract_boundary_dofs ( const DoFHandlerType &  dof_handler,
const ComponentMask component_mask,
std::vector< bool > &  selected_dofs,
const std::set< types::boundary_id > &  boundary_ids = std::set<types::boundary_id>() 
)

Extract all degrees of freedom which are at the boundary and belong to specified components of the solution. The function returns its results in the last non-default-valued parameter which contains true if a degree of freedom is at the boundary and belongs to one of the selected components, and false otherwise. The function is used in step-15.

By specifying the boundary_id variable, you can select which boundary indicators the faces have to have on which the degrees of freedom are located that shall be extracted. If it is an empty list, then all boundary indicators are accepted.

The size of component_mask (see GlossComponentMask) shall equal the number of components in the finite element used by dof. The size of selected_dofs shall equal dof_handler.n_dofs(). Previous contents of this array or overwritten.

Using the usual convention, if a shape function is non-zero in more than one component (i.e. it is non-primitive), then the element in the component mask is used that corresponds to the first non-zero components. Elements in the mask corresponding to later components are ignored.

Note
This function will not work for DoFHandler objects that are built on a parallel::distributed::Triangulation object. The reasons is that the output argument selected_dofs has to have a length equal to all global degrees of freedom. Consequently, this does not scale to very large problems. If you need the functionality of this function for parallel triangulations, then you need to use the other DoFTools::extract_boundary_dofs function.
Parameters
[in]dof_handlerThe object that describes which degrees of freedom live on which cell
[in]component_maskA mask denoting the vector components of the finite element that should be considered (see also GlossComponentMask).
[out]selected_dofsA vector of booleans that is returned and for which an element will be true if the corresponding index is a degree of freedom that is located on the boundary (and correspond to the selected vector components and boundary indicators, depending on the values of the component_mask and boundary_ids arguments).
[in]boundary_idsIf empty, this function extracts the indices of the degrees of freedom for all parts of the boundary. If it is a non- empty list, then the function only considers boundary faces with the boundary indicators listed in this argument.
See also
Glossary entry on boundary indicators

Definition at line 555 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::extract_boundary_dofs ( const DoFHandlerType &  dof_handler,
const ComponentMask component_mask,
IndexSet selected_dofs,
const std::set< types::boundary_id > &  boundary_ids = std::set<types::boundary_id>() 
)

This function does the same as the previous one but it returns its result as an IndexSet rather than a std::vector<bool>. Thus, it can also be called for DoFHandler objects that are defined on parallel::distributed::Triangulation objects.

Note
If the DoFHandler object is indeed defined on a parallel::distributed::Triangulation, then the selected_dofs index set will contain only those degrees of freedom on the boundary that belong to the locally relevant set (see locally relevant DoFs).
Parameters
[in]dof_handlerThe object that describes which degrees of freedom live on which cell
[in]component_maskA mask denoting the vector components of the finite element that should be considered (see also GlossComponentMask).
[out]selected_dofsThe IndexSet object that is returned and that will contain the indices of degrees of freedom that are located on the boundary (and correspond to the selected vector components and boundary indicators, depending on the values of the component_mask and boundary_ids arguments).
[in]boundary_idsIf empty, this function extracts the indices of the degrees of freedom for all parts of the boundary. If it is a non- empty list, then the function only considers boundary faces with the boundary indicators listed in this argument.
See also
Glossary entry on boundary indicators

Definition at line 581 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::extract_dofs_with_support_on_boundary ( const DoFHandlerType &  dof_handler,
const ComponentMask component_mask,
std::vector< bool > &  selected_dofs,
const std::set< types::boundary_id > &  boundary_ids = std::set<types::boundary_id>() 
)

This function is similar to the extract_boundary_dofs() function but it extracts those degrees of freedom whose shape functions are nonzero on at least part of the selected boundary. For continuous elements, this is exactly the set of shape functions whose degrees of freedom are defined on boundary faces. On the other hand, if the finite element in used is a discontinuous element, all degrees of freedom are defined in the inside of cells and consequently none would be boundary degrees of freedom. Several of those would have shape functions that are nonzero on the boundary, however. This function therefore extracts all those for which the FiniteElement::has_support_on_face function says that it is nonzero on any face on one of the selected boundary parts.

See also
Glossary entry on boundary indicators

Definition at line 689 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::extract_constant_modes ( const DoFHandlerType &  dof_handler,
const ComponentMask component_mask,
std::vector< std::vector< bool > > &  constant_modes 
)

Extract a vector that represents the constant modes of the DoFHandler for the components chosen by component_mask (see GlossComponentMask). The constant modes on a discretization are the null space of a Laplace operator on the selected components with Neumann boundary conditions applied. The null space is a necessary ingredient for obtaining a good AMG preconditioner when using the class TrilinosWrappers::PreconditionAMG. Since the ML AMG package only works on algebraic properties of the respective matrix, it has no chance to detect whether the matrix comes from a scalar or a vector valued problem. However, a near null space supplies exactly the needed information about the components placement of vector components within the matrix. The null space (or rather, the constant modes) is provided by the finite element underlying the given DoFHandler and for most elements, the null space will consist of as many vectors as there are true arguments in component_mask (see GlossComponentMask), each of which will be one in one vector component and zero in all others. However, the representation of the constant function for e.g. FE_DGP is different (the first component on each element one, all other components zero), and some scalar elements may even have two constant modes (FE_Q_DG0). Therefore, we store this object in a vector of vectors, where the outer vector contains the collection of the actual constant modes on the DoFHandler. Each inner vector has as many components as there are (locally owned) degrees of freedom in the selected components. Note that any matrix associated with this null space must have been constructed using the same component_mask argument, since the numbering of DoFs is done relative to the selected dofs, not to all dofs.

The main reason for this program is the use of the null space with the AMG preconditioner.

Definition at line 1065 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::extract_subdomain_dofs ( const DoFHandlerType &  dof_handler,
const types::subdomain_id  subdomain_id,
std::vector< bool > &  selected_dofs 
)

Flag all those degrees of freedom which are on cells with the given subdomain id. Note that DoFs on faces can belong to cells with differing subdomain ids, so the sets of flagged degrees of freedom are not mutually exclusive for different subdomain ids.

If you want to get a unique association of degree of freedom with subdomains, use the get_subdomain_association function.

Definition at line 899 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::extract_locally_owned_dofs ( const DoFHandlerType &  dof_handler,
IndexSet dof_set 
)

Extract the set of global DoF indices that are owned by the current processor. For regular DoFHandler objects, this set is the complete set with all DoF indices. In either case, it equals what DoFHandler::locally_owned_dofs() returns.

Definition at line 932 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::extract_locally_active_dofs ( const DoFHandlerType &  dof_handler,
IndexSet dof_set 
)

Extract the set of global DoF indices that are active on the current DoFHandler. For regular DoFHandlers, these are all DoF indices, but for DoFHandler objects built on parallel::distributed::Triangulation this set is a superset of DoFHandler::locally_owned_dofs() and contains all DoF indices that live on all locally owned cells (including on the interface to ghost cells). However, it does not contain the DoF indices that are exclusively defined on ghost or artificial cells (see the glossary).

The degrees of freedom identified by this function equal those obtained from the dof_indices_with_subdomain_association() function when called with the locally owned subdomain id.

Definition at line 944 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::extract_locally_relevant_dofs ( const DoFHandlerType &  dof_handler,
IndexSet dof_set 
)

Extract the set of global DoF indices that are active on the current DoFHandler. For regular DoFHandlers, these are all DoF indices, but for DoFHandler objects built on parallel::distributed::Triangulation this set is the union of DoFHandler::locally_owned_dofs() and the DoF indices on all ghost cells. In essence, it is the DoF indices on all cells that are not artificial (see the glossary).

Definition at line 980 of file dof_tools.cc.

template<typename DoFHandlerType >
std::vector< IndexSet > DoFTools::locally_owned_dofs_per_subdomain ( const DoFHandlerType &  dof_handler)

For each processor, determine the set of locally owned degrees of freedom as an IndexSet. This function then returns a vector of index sets, where the vector has size equal to the number of MPI processes that participate in the DoF handler object.

The function can be used for objects of type Triangulation or parallel::shared::Triangulation. It will not work for objects of type parallel::distributed::Triangulation since for such triangulations we do not have information about all cells of the triangulation available locally, and consequently can not say anything definitive about the degrees of freedom active on other processors' locally owned cells.

Author
Denis Davydov, 2015

Definition at line 1166 of file dof_tools.cc.

template<typename DoFHandlerType >
std::vector< IndexSet > DoFTools::locally_relevant_dofs_per_subdomain ( const DoFHandlerType &  dof_handler)

For each processor, determine the set of locally relevant degrees of freedom as an IndexSet. This function then returns a vector of index sets, where the vector has size equal to the number of MPI processes that participate in the DoF handler object.

The function can be used for objects of type Triangulation or parallel::shared::Triangulation. It will not work for objects of type parallel::distributed::Triangulation since for such triangulations we do not have information about all cells of the triangulation available locally, and consequently can not say anything definitive about the degrees of freedom active on other processors' locally owned cells.

Author
Jean-Paul Pelteret, 2015

Definition at line 1246 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::extract_locally_relevant_level_dofs ( const DoFHandlerType &  dof_handler,
const unsigned int  level,
IndexSet dof_set 
)

Same as extract_locally_relevant_dofs() but for multigrid DoFs for the given level.

Definition at line 1019 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::get_subdomain_association ( const DoFHandlerType &  dof_handler,
std::vector< types::subdomain_id > &  subdomain 
)

For each degree of freedom, 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.

Note that degrees of freedom associated with faces, edges, and vertices may be associated with multiple subdomains if they are sitting on partition boundaries. In these cases, we put them into one of the associated partitions in an undefined way. This may sometimes lead to different numbers of degrees of freedom in partitions, even if the number of cells is perfectly equidistributed. While this is regrettable, it is not a problem in practice since the number of degrees of freedom on partition boundaries is asymptotically vanishing as we refine the mesh as long as the number of partitions is kept constant.

This function returns the association of each DoF with one subdomain. If you are looking for the association of each cell with a subdomain, either query the cell->subdomain_id() function, or use the GridTools::get_subdomain_association function.

Note that this function is of questionable use for DoFHandler objects built on parallel::distributed::Triangulation since in that case ownership of individual degrees of freedom by MPI processes is controlled by the DoF handler object, not based on some geometric algorithm in conjunction with subdomain id. In particular, the degrees of freedom identified by the functions in this namespace as associated with a subdomain are not the same the DoFHandler class identifies as those it owns.

Definition at line 1309 of file dof_tools.cc.

template<typename DoFHandlerType >
unsigned int DoFTools::count_dofs_with_subdomain_association ( const DoFHandlerType &  dof_handler,
const types::subdomain_id  subdomain 
)

Count how many degrees of freedom are uniquely associated with the given subdomain index.

Note that there may be rare cases where cells with the given subdomain index exist, but none of its degrees of freedom are actually associated with it. In that case, the returned value will be zero.

This function will generate an exception if there are no cells with the given subdomain index.

This function returns the number of DoFs associated with one subdomain. If you are looking for the association of cells with this subdomain, use the GridTools::count_cells_with_subdomain_association function.

Note that this function is of questionable use for DoFHandler objects built on parallel::distributed::Triangulation since in that case ownership of individual degrees of freedom by MPI processes is controlled by the DoF handler object, not based on some geometric algorithm in conjunction with subdomain id. In particular, the degrees of freedom identified by the functions in this namespace as associated with a subdomain are not the same the DoFHandler class identifies as those it owns.

Definition at line 1400 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::count_dofs_with_subdomain_association ( const DoFHandlerType &  dof_handler,
const types::subdomain_id  subdomain,
std::vector< unsigned int > &  n_dofs_on_subdomain 
)

Count how many degrees of freedom are uniquely associated with the given subdomain index.

This function does what the previous one does except that it splits the result among the vector components of the finite element in use by the DoFHandler object. The last argument (which must have a length equal to the number of vector components) will therefore store how many degrees of freedom of each vector component are associated with the given subdomain.

Note that this function is of questionable use for DoFHandler objects built on parallel::distributed::Triangulation since in that case ownership of individual degrees of freedom by MPI processes is controlled by the DoF handler object, not based on some geometric algorithm in conjunction with subdomain id. In particular, the degrees of freedom identified by the functions in this namespace as associated with a subdomain are not the same the DoFHandler class identifies as those it owns.

Definition at line 1473 of file dof_tools.cc.

template<typename DoFHandlerType >
IndexSet DoFTools::dof_indices_with_subdomain_association ( const DoFHandlerType &  dof_handler,
const types::subdomain_id  subdomain 
)

Return a set of indices that denotes the degrees of freedom that live on the given subdomain, i.e. that are on cells owned by the current processor. Note that this includes the ones that this subdomain "owns" (i.e. the ones for which get_subdomain_association() returns a value equal to the subdomain given here and that are selected by the extract_locally_owned_dofs() function) but also all of those that sit on the boundary between the given subdomain and other subdomain. In essence, degrees of freedom that sit on boundaries between subdomain will be in the index sets returned by this function for more than one subdomain.

Note that this function is of questionable use for DoFHandler objects built on parallel::distributed::Triangulation since in that case ownership of individual degrees of freedom by MPI processes is controlled by the DoF handler object, not based on some geometric algorithm in conjunction with subdomain id. In particular, the degrees of freedom identified by the functions in this namespace as associated with a subdomain are not the same the DoFHandler class identifies as those it owns.

Definition at line 1415 of file dof_tools.cc.

template<typename DoFHandlerType >
std::vector< types::global_dof_index > DoFTools::get_dofs_on_patch ( const std::vector< typename DoFHandlerType::active_cell_iterator > &  patch)

Return the set of degrees of freedom that live on a set of cells (i.e., a patch) described by the argument.

Patches are often used in defining error estimators that require the solution of a local problem on the patch surrounding each of the cells of the mesh. You can get a list of cells that form the patch around a given cell using GridTools::get_patch_around_cell(). While DoFTools::count_dofs_on_patch() can be used to determine the size of these local problems, so that one can assemble the local system and then solve it, it is still necessary to provide a mapping between the global indices of the degrees of freedom that live on the patch and a local enumeration. This function provides such a local enumeration by returning the set of degrees of freedom that live on the patch.

Since this set is returned in the form of a std::vector, one can also think of it as a mapping

where i is an index into the returned vector (i.e., a the local index of a degree of freedom on the patch) and global_dof_index is the global index of a degree of freedom located on the patch. The array returned has size equal to DoFTools::count_dofs_on_patch().

Note
The array returned is sorted by global DoF index. Consequently, if one considers the index into this array a local DoF index, then the local system that results retains the block structure of the global system.
Template Parameters
DoFHandlerTypeA type that is either DoFHandler or hp::DoFHandler. In C++, the compiler can not determine the type of DoFHandlerType from the function call. You need to specify it as an explicit template argument following the function name.
Parameters
patchA collection of cells within an object of type DoFHandlerType
Returns
A list of those global degrees of freedom located on the patch, as defined above.
Note
In the context of a parallel distributed computation, it only makes sense to call this function on patches around locally owned cells. This is because the neighbors of locally owned cells are either locally owned themselves, or ghost cells. For both, we know that these are in fact the real cells of the complete, parallel triangulation. We can also query the degrees of freedom on these. In other words, this function can only work if all cells in the patch are either locally owned or ghost cells.
Author
Arezou Ghesmati, Wolfgang Bangerth, 2014

Definition at line 2477 of file dof_tools.cc.

template<int dim, int spacedim>
void DoFTools::make_cell_patches ( SparsityPattern block_list,
const DoFHandler< dim, spacedim > &  dof_handler,
const unsigned int  level,
const std::vector< bool > &  selected_dofs = std::vector<bool>(),
const types::global_dof_index  offset = 0 
)

Creates a sparsity pattern, which lists the degrees of freedom associated to each cell on the given level. This pattern can be used in RelaxationBlock classes as block list for additive and multiplicative Schwarz methods.

The row index in this pattern is the cell index resulting from standard iteration through a level of the Triangulation. For a parallel::distributed::Triangulation, only locally owned cells are entered.

The sparsity pattern is resized in this function to contain as many rows as there are locally owned cells on a given level, as many columns as there are degrees of freedom on this level.

selected_dofs is a vector indexed by the local degrees of freedom on a cell. If it is used, only such dofs are entered into the block list which are selected. This allows for instance the exclusion of components or of dofs on the boundary.

Definition at line 2139 of file dof_tools.cc.

template<typename DoFHandlerType >
std::vector< unsigned int > DoFTools::make_vertex_patches ( SparsityPattern block_list,
const DoFHandlerType &  dof_handler,
const unsigned int  level,
const bool  interior_dofs_only,
const bool  boundary_patches = false,
const bool  level_boundary_patches = false,
const bool  single_cell_patches = false,
const bool  invert_vertex_mapping = false 
)

Create an incidence matrix that for every vertex on a given level of a multilevel DoFHandler flags which degrees of freedom are associated with the adjacent cells. This data structure is a matrix with as many rows as there are vertices on a given level, as many columns as there are degrees of freedom on this level, and entries that are either true or false. This data structure is conveniently represented by a SparsityPattern object. The sparsity pattern may be empty when entering this function and will be reinitialized to the correct size.

The function has some boolean arguments (listed below) controlling details of the generated patches. The default settings are those for Arnold-Falk-Winther type smoothers for divergence and curl conforming finite elements with essential boundary conditions. Other applications are possible, in particular changing boundary_patches for non- essential boundary conditions.

This function returns the vertex_mapping, that contains the mapping from the vertex indices to the block indices of the block_list. For vertices that do not lead to a vertex patch, the entry in vertex_mapping contains the value invalid_unsigned_int. If invert_vertex_mapping is set to true, then the vertex_mapping is inverted such that it contains the mapping from the block indices to the corresponding vertex indices.

  • dof_handler: the multilevel dof handler providing the topology operated on.
  • interior_dofs_only: for each patch of cells around a vertex, collect only the interior degrees of freedom of the patch and disregard those on the boundary of the patch. This is for instance the setting for smoothers of Arnold-Falk-Winther type.
  • boundary_patches: include patches around vertices at the boundary of the domain. If not, only patches around interior vertices will be generated.
  • level_boundary_patches: same for refinement edges towards coarser cells.
  • single_cell_patches: if not true, patches containing a single cell are eliminated.
  • invert_vertex_mapping: if true, then the return value contains one vertex index for each block; if false, then the return value contains one block index or invalid_unsigned_int for each vertex.

Definition at line 2288 of file dof_tools.cc.

template<typename DoFHandlerType >
std::vector< unsigned int > DoFTools::make_vertex_patches ( SparsityPattern block_list,
const DoFHandlerType &  dof_handler,
const unsigned int  level,
const BlockMask exclude_boundary_dofs = BlockMask(),
const bool  boundary_patches = false,
const bool  level_boundary_patches = false,
const bool  single_cell_patches = false,
const bool  invert_vertex_mapping = false 
)

Same as above but allows boundary dofs on blocks to be excluded individually.

This is helpful if you want to use, for example, Taylor Hood elements as it allows you to not include the boundary DoFs for the velocity block on the patches while also letting you include the boundary DoFs for the pressure block.

Parameters
exclude_boundary_dofsFor each patch of cells around a vertex, collect all of the interior degrees of freedom of the patch and disregard those on the boundary of the patch if the boolean value for the corresponding block in the BlockMask is false.

Definition at line 2311 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::make_child_patches ( SparsityPattern block_list,
const DoFHandlerType &  dof_handler,
const unsigned int  level,
const bool  interior_dofs_only,
const bool  boundary_dofs = false 
)

Create an incidence matrix that for every cell on a given level of a multilevel DoFHandler flags which degrees of freedom are associated with children of this cell. This data structure is conveniently represented by a SparsityPattern object.

The function thus creates a sparsity pattern which in each row (with rows corresponding to the cells on this level) lists the degrees of freedom associated to the cells that are the children of this cell. The DoF indices used here are level dof indices of a multilevel hierarchy, i.e., they may be associated with children that are not themselves active. The sparsity pattern may be empty when entering this function and will be reinitialized to the correct size.

The function has some boolean arguments (listed below) controlling details of the generated patches. The default settings are those for Arnold-Falk-Winther type smoothers for divergence and curl conforming finite elements with essential boundary conditions. Other applications are possible, in particular changing boundary_dofs for non- essential boundary conditions.

  • dof_handler: The multilevel dof handler providing the topology operated on.
  • interior_dofs_only: for each patch of cells around a vertex, collect only the interior degrees of freedom of the patch and disregard those on the boundary of the patch. This is for instance the setting for smoothers of Arnold-Falk-Winther type.
  • boundary_dofs: include degrees of freedom, which would have excluded by interior_dofs_only, but are lying on the boundary of the domain, and thus need smoothing. This parameter has no effect if interior_dofs_only is false.

Definition at line 2224 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::make_single_patch ( SparsityPattern block_list,
const DoFHandlerType &  dof_handler,
const unsigned int  level,
const bool  interior_dofs_only = false 
)

Create a block list with only a single patch, which in turn contains all degrees of freedom on the given level.

This function is mostly a closure on level 0 for functions like make_child_patches() and make_vertex_patches(), which may produce an empty patch list.

  • dof_handler: The multilevel dof handler providing the topology operated on.
  • level The grid level used for building the list.
  • interior_dofs_only: if true, exclude degrees of freedom on the boundary of the domain.

Definition at line 2181 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::count_dofs_per_component ( const DoFHandlerType &  dof_handler,
std::vector< types::global_dof_index > &  dofs_per_component,
const bool  vector_valued_once = false,
std::vector< unsigned int >  target_component = std::vector<unsigned int>() 
)

Count how many degrees of freedom out of the total number belong to each component. If the number of components the finite element has is one (i.e. you only have one scalar variable), then the number in this component obviously equals the total number of degrees of freedom. Otherwise, the sum of the DoFs in all the components needs to equal the total number.

However, the last statement does not hold true if the finite element is not primitive, i.e. some or all of its shape functions are non-zero in more than one vector component. This applies, for example, to the Nedelec or Raviart-Thomas elements. In this case, a degree of freedom is counted in each component in which it is non-zero, so that the sum mentioned above is greater than the total number of degrees of freedom.

This behavior can be switched off by the optional parameter vector_valued_once. If this is true, the number of components of a nonprimitive vector valued element is collected only in the first component. All other components will have a count of zero.

The additional optional argument target_component allows for a re- sorting and grouping of components. To this end, it contains for each component the component number it shall be counted as. Having the same number entered several times sums up several components as the same. One of the applications of this argument is when you want to form block matrices and vectors, but want to pack several components into the same block (for example, when you have dim velocities and one pressure, to put all velocities into one block, and the pressure into another).

The result is returned in dofs_per_component. Note that the size of dofs_per_component needs to be enough to hold all the indices specified in target_component. If this is not the case, an assertion is thrown. The indices not targeted by target_components are left untouched.

Definition at line 1632 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::count_dofs_per_block ( const DoFHandlerType &  dof,
std::vector< types::global_dof_index > &  dofs_per_block,
const std::vector< unsigned int > &  target_block = std::vector<unsigned int>() 
)

Count the degrees of freedom in each block. This function is similar to count_dofs_per_component(), with the difference that the counting is done by blocks. See blocks in the glossary for details. Again the vectors are assumed to have the correct size before calling this function. If this is not the case, an assertion is thrown.

This function is used in the step-22, step-31, and step-32 tutorial programs.

Precondition
The dofs_per_block variable has as many components as the finite element used by the dof_handler argument has blocks, or alternatively as many blocks as are enumerated in the target_blocks argument if given.

Definition at line 1719 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::get_active_fe_indices ( const DoFHandlerType &  dof_handler,
std::vector< unsigned int > &  active_fe_indices 
)

For each active cell of a DoFHandler or hp::DoFHandler, extract the active finite element index and fill the vector given as second argument. This vector is assumed to have as many entries as there are active cells.

For non-hp DoFHandler objects given as first argument, the returned vector will consist of only zeros, indicating that all cells use the same finite element. For a hp::DoFHandler, the values may be different, though.

Definition at line 1152 of file dof_tools.cc.

template<typename DoFHandlerType >
unsigned int DoFTools::count_dofs_on_patch ( const std::vector< typename DoFHandlerType::active_cell_iterator > &  patch)

Count how many degrees of freedom live on a set of cells (i.e., a patch) described by the argument.

Patches are often used in defining error estimators that require the solution of a local problem on the patch surrounding each of the cells of the mesh. You can get a list of cells that form the patch around a given cell using GridTools::get_patch_around_cell(). This function is then useful in setting up the size of the linear system used to solve the local problem on the patch around a cell. The function DoFTools::get_dofs_on_patch() will then help to make the connection between global degrees of freedom and the local ones.

Template Parameters
DoFHandlerTypeA type that is either DoFHandler or hp::DoFHandler. In C++, the compiler can not determine the type of DoFHandlerType from the function call. You need to specify it as an explicit template argument following the function name.
Parameters
patchA collection of cells within an object of type DoFHandlerType
Returns
The number of degrees of freedom associated with the cells of this patch.
Note
In the context of a parallel distributed computation, it only makes sense to call this function on patches around locally owned cells. This is because the neighbors of locally owned cells are either locally owned themselves, or ghost cells. For both, we know that these are in fact the real cells of the complete, parallel triangulation. We can also query the degrees of freedom on these. In other words, this function can only work if all cells in the patch are either locally owned or ghost cells.
Author
Arezou Ghesmati, Wolfgang Bangerth, 2014

Definition at line 2449 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::map_dof_to_boundary_indices ( const DoFHandlerType &  dof_handler,
std::vector< types::global_dof_index > &  mapping 
)

Create a mapping from degree of freedom indices to the index of that degree of freedom on the boundary. After this operation, mapping[dof] gives the index of the degree of freedom with global number dof in the list of degrees of freedom on the boundary. If the degree of freedom requested is not on the boundary, the value of mapping[dof] is invalid_dof_index. This function is mainly used when setting up matrices and vectors on the boundary from the trial functions, which have global numbers, while the matrices and vectors use numbers of the trial functions local to the boundary.

Prior content of mapping is deleted.

Definition at line 1799 of file dof_tools.cc.

template<typename DoFHandlerType >
void DoFTools::map_dof_to_boundary_indices ( const DoFHandlerType &  dof_handler,
const std::set< types::boundary_id > &  boundary_ids,
std::vector< types::global_dof_index > &  mapping 
)

Same as the previous function, except that only those parts of the boundary are considered for which the boundary indicator is listed in the second argument.

See the general doc of this class for more information.

See also
Glossary entry on boundary indicators

Definition at line 1838 of file dof_tools.cc.

template<int dim, int spacedim>
void DoFTools::map_dofs_to_support_points ( const Mapping< dim, spacedim > &  mapping,
const DoFHandler< dim, spacedim > &  dof_handler,
std::vector< Point< spacedim > > &  support_points 
)

Return a list of support points (see this glossary entry) for all the degrees of freedom handled by this DoF handler object. This function, of course, only works if the finite element object used by the DoF handler object actually provides support points, i.e. no edge elements or the like. Otherwise, an exception is thrown.

Precondition
The given array must have a length of as many elements as there are degrees of freedom.
Note
The precondition to this function that the output argument needs to have size equal to the total number of degrees of freedom makes this function unsuitable for the case that the given DoFHandler object derives from a parallel::distributed::Triangulation object. Consequently, this function will produce an error if called with such a DoFHandler.

Definition at line 1960 of file dof_tools.cc.

template<int dim, int spacedim>
void DoFTools::map_dofs_to_support_points ( const ::hp::MappingCollection< dim, spacedim > &  mapping,
const hp::DoFHandler< dim, spacedim > &  dof_handler,
std::vector< Point< spacedim > > &  support_points 
)

Same as the previous function but for the hp case.

template<int dim, int spacedim>
void DoFTools::map_dofs_to_support_points ( const Mapping< dim, spacedim > &  mapping,
const DoFHandler< dim, spacedim > &  dof_handler,
std::map< types::global_dof_index, Point< spacedim > > &  support_points 
)

This function is a version of the above map_dofs_to_support_points function that doesn't simply return a vector of support points (see this glossary entry) with one entry for each global degree of freedom, but instead a map that maps from the DoFs index to its location. The point of this function is that it is also usable in cases where the DoFHandler is based on a parallel::distributed::Triangulation object. In such cases, each processor will not be able to determine the support point location of all DoFs, and worse no processor may be able to hold a vector that would contain the locations of all DoFs even if they were known. As a consequence, this function constructs a map from those DoFs for which we can know the locations (namely, those DoFs that are locally relevant (see locally relevant DoFs) to their locations.

For non-distributed triangulations, the map returned as support_points is of course dense, i.e., every DoF is to be found in it.

Parameters
mappingThe mapping from the reference cell to the real cell on which DoFs are defined.
dof_handlerThe object that describes which DoF indices live on which cell of the triangulation.
support_pointsA map that for every locally relevant DoF index contains the corresponding location in real space coordinates. Previous content of this object is deleted in this function.

Definition at line 2006 of file dof_tools.cc.

template<int dim, int spacedim>
void DoFTools::map_dofs_to_support_points ( const ::hp::MappingCollection< dim, spacedim > &  mapping,
const hp::DoFHandler< dim, spacedim > &  dof_handler,
std::map< types::global_dof_index, Point< spacedim > > &  support_points 
)

Same as the previous function but for the hp case.

template<typename DoFHandlerType , class Comp >
void DoFTools::map_support_points_to_dofs ( const Mapping< DoFHandlerType::dimension, DoFHandlerType::space_dimension > &  mapping,
const DoFHandlerType &  dof_handler,
std::map< Point< DoFHandlerType::space_dimension >, types::global_dof_index, Comp > &  point_to_index_map 
)

This is the opposite function to the one above. It generates a map where the keys are the support points of the degrees of freedom, while the values are the DoF indices. For a definition of support points, see this glossary entry.

Since there is no natural order in the space of points (except for the 1d case), you have to provide a map with an explicitly specified comparator object. This function is therefore templatized on the comparator object. Previous content of the map object is deleted in this function.

Just as with the function above, it is assumed that the finite element in use here actually supports the notion of support points of all its components.

Todo:
This function should generate a multimap, rather than just a map, since several dofs may be located at the same support point. Currently, only the last value in the map returned by map_dofs_to_support_points() for each point will be returned.
template<typename DoFHandlerType , typename Number >
void DoFTools::distribute_cell_to_dof_vector ( const DoFHandlerType &  dof_handler,
const Vector< Number > &  cell_data,
Vector< double > &  dof_data,
const unsigned int  component = 0 
)

Take a vector of values which live on cells (e.g. an error per cell) and distribute it to the dofs in such a way that a finite element field results, which can then be further processed, e.g. for output. You should note that the resulting field will not be continuous at hanging nodes. This can, however, easily be arranged by calling the appropriate distribute function of a ConstraintMatrix object created for this DoFHandler object, after the vector has been fully assembled.

It is assumed that the number of elements in cell_data equals the number of active cells and that the number of elements in dof_data equals dof_handler.n_dofs().

Note that the input vector may be a vector of any data type as long as it is convertible to double. The output vector, being a data vector on a DoF handler, always consists of elements of type double.

In case the finite element used by this DoFHandler consists of more than one component, you need to specify which component in the output vector should be used to store the finite element field in; the default is zero (no other value is allowed if the finite element consists only of one component). All other components of the vector remain untouched, i.e. their contents are not changed.

This function cannot be used if the finite element in use has shape functions that are non-zero in more than one vector component (in deal.II speak: they are non-primitive).

Definition at line 290 of file dof_tools.cc.

template<int spacedim>
void DoFTools::write_gnuplot_dof_support_point_info ( std::ostream &  out,
const std::map< types::global_dof_index, Point< spacedim > > &  support_points 
)

Generate text output readable by gnuplot with point data based on the given map support_points. For each support point location, a string label containing a list of all DoFs from the map is generated. The map can be generated with a call to map_dofs_to_support_points() and is useful to visualize location and global numbering of unknowns.

An example for the format of each line in the output is:

x [y] [z] "dof1, dof2"

where x, y, and z (present only in corresponding dimension) are the coordinates of the support point, followed by a list of DoF numbers.

The points with labels can be plotted as follows in gnuplot:

plot "./points.gpl" using 1:2:3 with labels point offset 1,1

Examples (this also includes the grid written separately using GridOut):

support_point_dofs1.png
support_point_dofs2.png

Definition at line 2039 of file dof_tools.cc.