MGTools Namespace Reference

Functions
template<int dim, int spacedim>
void	compute_row_length_vector (const DoFHandler< dim, spacedim > &dofs, const unsigned int level, std::vector< unsigned int > &row_lengths, const DoFTools::Coupling flux_couplings=DoFTools::none)
template<int dim, int spacedim>
void	compute_row_length_vector (const DoFHandler< dim, spacedim > &dofs, const unsigned int level, std::vector< unsigned int > &row_lengths, const Table< 2, DoFTools::Coupling > &couplings, const Table< 2, DoFTools::Coupling > &flux_couplings)
template<typename DoFHandlerType , typename SparsityPatternType >
void	make_sparsity_pattern (const DoFHandlerType &dof_handler, SparsityPatternType &sparsity, const unsigned int level)
template<int dim, typename SparsityPatternType , int spacedim>
void	make_flux_sparsity_pattern (const DoFHandler< dim, spacedim > &dof_handler, SparsityPatternType &sparsity, const unsigned int level)
template<int dim, typename SparsityPatternType , int spacedim>
void	make_flux_sparsity_pattern_edge (const DoFHandler< dim, spacedim > &dof_handler, SparsityPatternType &sparsity, const unsigned int level)
template<int dim, typename SparsityPatternType , int spacedim>
void	make_flux_sparsity_pattern (const DoFHandler< dim, spacedim > &dof, SparsityPatternType &sparsity, const unsigned int level, const Table< 2, DoFTools::Coupling > &int_mask, const Table< 2, DoFTools::Coupling > &flux_mask)
template<int dim, typename SparsityPatternType , int spacedim>
void	make_flux_sparsity_pattern_edge (const DoFHandler< dim, spacedim > &dof_handler, SparsityPatternType &sparsity, const unsigned int level, const Table< 2, DoFTools::Coupling > &flux_mask)
template<typename DoFHandlerType , typename SparsityPatternType >
void	make_interface_sparsity_pattern (const DoFHandlerType &dof_handler, const MGConstrainedDoFs &mg_constrained_dofs, SparsityPatternType &sparsity, const unsigned int level)
template<typename DoFHandlerType >
void	count_dofs_per_block (const DoFHandlerType &dof_handler, std::vector< std::vector< types::global_dof_index >> &dofs_per_block, std::vector< unsigned int > target_block={})
template<int dim, int spacedim>
void	count_dofs_per_component (const DoFHandler< dim, spacedim > &mg_dof, std::vector< std::vector< types::global_dof_index >> &result, const bool only_once=false, std::vector< unsigned int > target_component={})
template<int dim, int spacedim>
void	make_boundary_list (const DoFHandler< dim, spacedim > &mg_dof, const std::map< types::boundary_id, const Function< spacedim > * > &function_map, std::vector< std::set< types::global_dof_index >> &boundary_indices, const ComponentMask &component_mask=ComponentMask())
template<int dim, int spacedim>
void	make_boundary_list (const DoFHandler< dim, spacedim > &mg_dof, const std::map< types::boundary_id, const Function< spacedim > * > &function_map, std::vector< IndexSet > &boundary_indices, const ComponentMask &component_mask=ComponentMask())
template<int dim, int spacedim>
void	make_boundary_list (const DoFHandler< dim, spacedim > &mg_dof, const std::set< types::boundary_id > &boundary_ids, std::vector< IndexSet > &boundary_indices, const ComponentMask &component_mask=ComponentMask())
template<int dim, int spacedim>
void	extract_inner_interface_dofs (const DoFHandler< dim, spacedim > &mg_dof_handler, std::vector< IndexSet > &interface_dofs)
template<int dim, int spacedim>
void	extract_non_interface_dofs (const DoFHandler< dim, spacedim > &mg_dof_handler, std::vector< std::set< types::global_dof_index >> &non_interface_dofs)
template<int dim, int spacedim>
unsigned int	max_level_for_coarse_mesh (const Triangulation< dim, spacedim > &tria)
template<int dim, int spacedim>
double	workload_imbalance (const Triangulation< dim, spacedim > &tria)
template<>
void	compute_row_length_vector (const DoFHandler< 1, 1 > &, const unsigned int, std::vector< unsigned int > &, const DoFTools::Coupling)
template<>
void	compute_row_length_vector (const DoFHandler< 1, 1 > &, const unsigned int, std::vector< unsigned int > &, const Table< 2, DoFTools::Coupling > &, const Table< 2, DoFTools::Coupling > &)
template<>
void	compute_row_length_vector (const DoFHandler< 1, 2 > &, const unsigned int, std::vector< unsigned int > &, const DoFTools::Coupling)
template<>
void	compute_row_length_vector (const DoFHandler< 1, 2 > &, const unsigned int, std::vector< unsigned int > &, const Table< 2, DoFTools::Coupling > &, const Table< 2, DoFTools::Coupling > &)

Detailed Description

This is a collection of functions operating on, and manipulating the numbers of degrees of freedom in a multilevel triangulation. It is similar in purpose and function to the DoFTools namespace, but operates on levels of DoFHandler objects. See there and the documentation of the member functions for more information.

Author

Wolfgang Bangerth, Guido Kanschat, 1999 - 2005, 2012

Function Documentation

compute_row_length_vector() [1/6]

template<int dim, int spacedim>

void MGTools::compute_row_length_vector	(	const DoFHandler< dim, spacedim > &	dofs,
		const unsigned int	level,
		std::vector< unsigned int > &	row_lengths,
		const DoFTools::Coupling	flux_couplings = DoFTools::none
	)

Compute row length vector for multilevel methods.

Definition at line 105 of file mg_tools.cc.

compute_row_length_vector() [2/6]

template<int dim, int spacedim>

void MGTools::compute_row_length_vector	(	const DoFHandler< dim, spacedim > &	dofs,
		const unsigned int	level,
		std::vector< unsigned int > &	row_lengths,
		const Table< 2, DoFTools::Coupling > &	couplings,
		const Table< 2, DoFTools::Coupling > &	flux_couplings
	)

Compute row length vector for multilevel methods with optimization for block couplings.

Definition at line 285 of file mg_tools.cc.

make_sparsity_pattern()

template<typename DoFHandlerType , typename SparsityPatternType >

void MGTools::make_sparsity_pattern	(	const DoFHandlerType &	dof_handler,
		SparsityPatternType &	sparsity,
		const unsigned int	level
	)

Write the sparsity structure of the matrix belonging to the specified level. The sparsity pattern is not compressed, so before creating the actual matrix you have to compress the matrix yourself, using SparseMatrixStruct::compress().

There is no need to consider hanging nodes here, since only one level is considered.

Definition at line 565 of file mg_tools.cc.

make_flux_sparsity_pattern() [1/2]

template<int dim, typename SparsityPatternType , int spacedim>

void MGTools::make_flux_sparsity_pattern	(	const DoFHandler< dim, spacedim > &	dof_handler,
		SparsityPatternType &	sparsity,
		const unsigned int	level
	)

Make a sparsity pattern including fluxes of discontinuous Galerkin methods.

See also

make_sparsity_pattern and DoFTools

Definition at line 599 of file mg_tools.cc.

make_flux_sparsity_pattern_edge() [1/2]

template<int dim, typename SparsityPatternType , int spacedim>

void MGTools::make_flux_sparsity_pattern_edge	(	const DoFHandler< dim, spacedim > &	dof_handler,
		SparsityPatternType &	sparsity,
		const unsigned int	level
	)

Create sparsity pattern for the fluxes at refinement edges. The matrix maps a function of the fine level space level to the coarser space.

make_flux_sparsity_pattern()

Definition at line 674 of file mg_tools.cc.

make_flux_sparsity_pattern() [2/2]

template<int dim, typename SparsityPatternType , int spacedim>

void MGTools::make_flux_sparsity_pattern	(	const DoFHandler< dim, spacedim > &	dof,
		SparsityPatternType &	sparsity,
		const unsigned int	level,
		const Table< 2, DoFTools::Coupling > &	int_mask,
		const Table< 2, DoFTools::Coupling > &	flux_mask
	)

This function does the same as the other with the same name, but it gets two additional coefficient matrices. A matrix entry will only be generated for two basis functions, if there is a non-zero entry linking their associated components in the coefficient matrix.

There is one matrix for couplings in a cell and one for the couplings occurring in fluxes.

Definition at line 743 of file mg_tools.cc.

make_flux_sparsity_pattern_edge() [2/2]

template<int dim, typename SparsityPatternType , int spacedim>

void MGTools::make_flux_sparsity_pattern_edge	(	const DoFHandler< dim, spacedim > &	dof_handler,
		SparsityPatternType &	sparsity,
		const unsigned int	level,
		const Table< 2, DoFTools::Coupling > &	flux_mask
	)

Create sparsity pattern for the fluxes at refinement edges. The matrix maps a function of the fine level space level to the coarser space. This is the version restricting the pattern to the elements actually needed.

make_flux_sparsity_pattern()

Definition at line 931 of file mg_tools.cc.

make_interface_sparsity_pattern()

template<typename DoFHandlerType , typename SparsityPatternType >

void MGTools::make_interface_sparsity_pattern	(	const DoFHandlerType &	dof_handler,
		const MGConstrainedDoFs &	mg_constrained_dofs,
		SparsityPatternType &	sparsity,
		const unsigned int	level
	)

Create sparsity pattern for interface_in/out matrices used in a multigrid computation. These matrices contain an entry representing the coupling of degrees of freedom on a refinement edge to those not on the refinement edge of a certain level.

Definition at line 1023 of file mg_tools.cc.

count_dofs_per_block()

template<typename DoFHandlerType >

void MGTools::count_dofs_per_block	(	const DoFHandlerType &	dof_handler,
		std::vector< std::vector< types::global_dof_index >> &	dofs_per_block,
		std::vector< unsigned int >	target_block = {}
	)

Count the dofs block-wise on each level.

Result is a vector containing for each level a vector containing the number of dofs for each block (access is result[level][block]).

Definition at line 1158 of file mg_tools.cc.

count_dofs_per_component()

template<int dim, int spacedim>

void MGTools::count_dofs_per_component	(	const DoFHandler< dim, spacedim > &	mg_dof,
		std::vector< std::vector< types::global_dof_index >> &	result,
		const bool	only_once = false,
		std::vector< unsigned int >	target_component = {}
	)

Count the dofs component-wise on each level.

Result is a vector containing for each level a vector containing the number of dofs for each component (access is result[level][component]).

Definition at line 1056 of file mg_tools.cc.

make_boundary_list() [1/3]

template<int dim, int spacedim>

void MGTools::make_boundary_list	(	const DoFHandler< dim, spacedim > &	mg_dof,
		const std::map< types::boundary_id, const Function< spacedim > * > &	function_map,
		std::vector< std::set< types::global_dof_index >> &	boundary_indices,
		const ComponentMask &	component_mask = ComponentMask()
	)

Generate a list of those degrees of freedom at the boundary of the domain that should be eliminated from the matrix because they will be constrained by Dirichlet boundary conditions.

This is the multilevel equivalent of VectorTools::interpolate_boundary_values, but since the multilevel method does not have its own right hand side, the function values returned by the function object that is part of the function_map argument are ignored.

• boundary_indices is a vector which on return contains all indices of degrees of freedom for each level that are at the part of the boundary identified by the function_map argument. Its length has to match the number of levels in the dof handler object.

Previous content in boundary_indices is not overwritten, but added to.

Definition at line 1243 of file mg_tools.cc.

make_boundary_list() [2/3]

template<int dim, int spacedim>

void MGTools::make_boundary_list	(	const DoFHandler< dim, spacedim > &	mg_dof,
		const std::map< types::boundary_id, const Function< spacedim > * > &	function_map,
		std::vector< IndexSet > &	boundary_indices,
		const ComponentMask &	component_mask = ComponentMask()
	)

The same function as above, but return an IndexSet rather than a std::set<unsigned int> on each level.

Previous content in boundary_indices is not overwritten, but added to.

Definition at line 1268 of file mg_tools.cc.

make_boundary_list() [3/3]

template<int dim, int spacedim>

void MGTools::make_boundary_list	(	const DoFHandler< dim, spacedim > &	mg_dof,
		const std::set< types::boundary_id > &	boundary_ids,
		std::vector< IndexSet > &	boundary_indices,
		const ComponentMask &	component_mask = ComponentMask()
	)

The same function as above, but return an IndexSet rather than a std::set<unsigned int> on each level and use a std::set of boundary_ids as input.

Previous content in boundary_indices is not overwritten, but added to.

Definition at line 1289 of file mg_tools.cc.

extract_inner_interface_dofs()

template<int dim, int spacedim>

void MGTools::extract_inner_interface_dofs	(	const DoFHandler< dim, spacedim > &	mg_dof_handler,
		std::vector< IndexSet > &	interface_dofs
	)

For each level in a multigrid hierarchy, produce an IndexSet that indicates which of the degrees of freedom are along interfaces of this level to cells that only exist on coarser levels.

Definition at line 1528 of file mg_tools.cc.

extract_non_interface_dofs()

template<int dim, int spacedim>

void MGTools::extract_non_interface_dofs	(	const DoFHandler< dim, spacedim > &	mg_dof_handler,
		std::vector< std::set< types::global_dof_index >> &	non_interface_dofs
	)

For each level in a multigrid hierarchy, produce a std::set of degrees of freedoms that are not located along interfaces of this level to cells that only exist on coarser levels.

Definition at line 1450 of file mg_tools.cc.

max_level_for_coarse_mesh()

template<int dim, int spacedim>

unsigned int MGTools::max_level_for_coarse_mesh

(

const Triangulation< dim, spacedim > &

tria

)

Return the highest possible level that can be used as the coarsest level in a Multigrid computation, that is, the highest level in the hierarchy whose mesh covers the entire domain. This corresponds to the minimum level of a cell on the active mesh. Since each processor only has a local view of the mesh, each processor must call this function. Note that this is a global minimum over the entire mesh and therefore each processor will return the same value.

Definition at line 1625 of file mg_tools.cc.

workload_imbalance()

template<int dim, int spacedim>

double MGTools::workload_imbalance

(

const Triangulation< dim, spacedim > &

tria

)

Return the imbalance of the parallel distribution of the multigrid mesh hierarchy. Ideally this value is equal to 1 (every processor owns the same number of cells on each level, approximately true for most globally refined meshes). Values greater than 1 estimate the slowdown one should see in a geometric multigrid v-cycle as compared with the same computation on a perfectly distributed mesh hierarchy.

This function is a collective MPI call between all ranks of the Triangulation and therefore needs to be called from all ranks.

Note

This function requires that parallel::TriangulationBase::is_multilevel_hierarchy_constructed() is true, which can be controlled by setting the construct_multigrid_hierarchy flag when constructing the Triangulation.

Definition at line 1660 of file mg_tools.cc.

compute_row_length_vector() [3/6]

template<>

void MGTools::compute_row_length_vector	(	const DoFHandler< 1, 1 > &	,
		const unsigned int	,
		std::vector< unsigned int > &	,
		const DoFTools::Coupling
	)

Definition at line 55 of file mg_tools.cc.

compute_row_length_vector() [4/6]

template<>

void MGTools::compute_row_length_vector	(	const DoFHandler< 1, 1 > &	,
		const unsigned int	,
		std::vector< unsigned int > &	,
		const Table< 2, DoFTools::Coupling > &	,
		const Table< 2, DoFTools::Coupling > &
	)

Definition at line 67 of file mg_tools.cc.

compute_row_length_vector() [5/6]

template<>

void MGTools::compute_row_length_vector	(	const DoFHandler< 1, 2 > &	,
		const unsigned int	,
		std::vector< unsigned int > &	,
		const DoFTools::Coupling
	)

Definition at line 80 of file mg_tools.cc.

compute_row_length_vector() [6/6]

template<>

void MGTools::compute_row_length_vector	(	const DoFHandler< 1, 2 > &	,
		const unsigned int	,
		std::vector< unsigned int > &	,
		const Table< 2, DoFTools::Coupling > &	,
		const Table< 2, DoFTools::Coupling > &
	)

Definition at line 91 of file mg_tools.cc.