Multigrid< VectorType > Class Template Reference

#include <deal.II/multigrid/multigrid.h>

Inheritance diagram for Multigrid< VectorType >:

Public Types

Public Member Functions
template<int dim>
	Multigrid (const DoFHandler< dim > &mg_dof_handler, const MGMatrixBase< VectorType > &matrix, const MGCoarseGridBase< VectorType > &coarse, const MGTransferBase< VectorType > &transfer, const MGSmootherBase< VectorType > &pre_smooth, const MGSmootherBase< VectorType > &post_smooth, const unsigned int minlevel=0, const unsigned int maxlevel=numbers::invalid_unsigned_int, Cycle cycle=v_cycle)
	Multigrid (const MGMatrixBase< VectorType > &matrix, const MGCoarseGridBase< VectorType > &coarse, const MGTransferBase< VectorType > &transfer, const MGSmootherBase< VectorType > &pre_smooth, const MGSmootherBase< VectorType > &post_smooth, const unsigned int minlevel=0, const unsigned int maxlevel=numbers::invalid_unsigned_int, Cycle cycle=v_cycle)
void	reinit (const unsigned int minlevel, const unsigned int maxlevel)
void	cycle ()
void	vcycle ()
void	set_edge_matrices (const MGMatrixBase< VectorType > &edge_out, const MGMatrixBase< VectorType > &edge_in)
void	set_edge_flux_matrices (const MGMatrixBase< VectorType > &edge_down, const MGMatrixBase< VectorType > &edge_up)
unsigned int	get_maxlevel () const
unsigned int	get_minlevel () const
void	set_maxlevel (const unsigned int)
void	set_minlevel (const unsigned int level, bool relative=false)
void	set_cycle (Cycle)
void	set_debug (const unsigned int)
boost::signals2::connection	connect_coarse_solve (const std::function< void(const bool, const unsigned int)> &slot)
boost::signals2::connection	connect_restriction (const std::function< void(const bool, const unsigned int)> &slot)
boost::signals2::connection	connect_prolongation (const std::function< void(const bool, const unsigned int)> &slot)
boost::signals2::connection	connect_pre_smoother_step (const std::function< void(const bool, const unsigned int)> &slot)
boost::signals2::connection	connect_post_smoother_step (const std::function< void(const bool, const unsigned int)> &slot)
Public Member Functions inherited from Subscriptor
	Subscriptor ()
	Subscriptor (const Subscriptor &)
	Subscriptor (Subscriptor &&) noexcept
virtual	~Subscriptor ()
Subscriptor &	operator= (const Subscriptor &)
Subscriptor &	operator= (Subscriptor &&) noexcept
void	subscribe (const char *identifier=nullptr) const
void	unsubscribe (const char *identifier=nullptr) const
unsigned int	n_subscriptions () const
template<typename StreamType >
void	list_subscribers (StreamType &stream) const
void	list_subscribers () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Public Attributes
MGLevelObject< VectorType >	defect
MGLevelObject< VectorType >	solution

Private Member Functions
void	level_v_step (const unsigned int level)
void	level_step (const unsigned int level, Cycle cycle)

Private Attributes
mg::Signals	signals
Cycle	cycle_type
unsigned int	minlevel
unsigned int	maxlevel
MGLevelObject< VectorType >	t
MGLevelObject< VectorType >	defect2
SmartPointer< const MGMatrixBase< VectorType >, Multigrid< VectorType > >	matrix
SmartPointer< const MGCoarseGridBase< VectorType >, Multigrid< VectorType > >	coarse
SmartPointer< const MGTransferBase< VectorType >, Multigrid< VectorType > >	transfer
SmartPointer< const MGSmootherBase< VectorType >, Multigrid< VectorType > >	pre_smooth
SmartPointer< const MGSmootherBase< VectorType >, Multigrid< VectorType > >	post_smooth
SmartPointer< const MGMatrixBase< VectorType > >	edge_out
SmartPointer< const MGMatrixBase< VectorType > >	edge_in
SmartPointer< const MGMatrixBase< VectorType >, Multigrid< VectorType > >	edge_down
SmartPointer< const MGMatrixBase< VectorType >, Multigrid< VectorType > >	edge_up
unsigned int	debug

Friends
template<int dim, class OtherVectorType , class TRANSFER >
class	PreconditionMG

Additional Inherited Members
Static Public Member Functions inherited from Subscriptor
static::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)
static::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Detailed Description

template<typename VectorType>
class Multigrid< VectorType >

Implementation of the multigrid method. The implementation supports both continuous and discontinuous elements and follows the procedure described in the multigrid paper by Janssen and Kanschat.

The function which starts a multigrid cycle on the finest level is cycle(). Depending on the cycle type chosen with the constructor (see enum Cycle), this function triggers one of the cycles level_v_step() or level_step(), where the latter one can do different types of cycles.

Using this class, it is expected that the right hand side has been converted from a vector living on the locally finest level to a multilevel vector. This is a nontrivial operation, usually initiated automatically by the class PreconditionMG and performed by the classes derived from MGTransferBase.

Note

The interface of this class is still very clumsy. In particular, you will have to set up quite a few auxiliary objects before you can use it. Unfortunately, it seems that this can be avoided only be restricting the flexibility of this class in an unacceptable way.

Author

Guido Kanschat, 1999 - 2005

Definition at line 137 of file multigrid.h.

Member Enumeration Documentation

template<typename VectorType>

enum Multigrid::Cycle

List of implemented cycle types.

Enumerator
v_cycle	The V-cycle.
w_cycle	The W-cycle.
f_cycle	The F-cycle.

Definition at line 143 of file multigrid.h.

Constructor & Destructor Documentation

template<typename VectorType>

template<int dim>

Multigrid< VectorType >::Multigrid	(	const DoFHandler< dim > &	mg_dof_handler,
		const MGMatrixBase< VectorType > &	matrix,
		const MGCoarseGridBase< VectorType > &	coarse,
		const MGTransferBase< VectorType > &	transfer,
		const MGSmootherBase< VectorType > &	pre_smooth,
		const MGSmootherBase< VectorType > &	post_smooth,
		const unsigned int	minlevel = 0,
		const unsigned int	maxlevel = numbers::invalid_unsigned_int,
		Cycle	cycle = v_cycle
	)

Constructor. The DoFHandler is used to check whether the provided minlevel and maxlevel are in the range of valid levels. If maxlevel is set to the default value, the highest valid level is used. transfer is an object performing prolongation and restriction.

This function already initializes the vectors which will be used later in the course of the computations. You should therefore create objects of this type as late as possible.

Deprecated:

Use the other constructor instead. The DoFHandler is actually not needed.

template<typename VectorType>

Multigrid< VectorType >::Multigrid	(	const MGMatrixBase< VectorType > &	matrix,
		const MGCoarseGridBase< VectorType > &	coarse,
		const MGTransferBase< VectorType > &	transfer,
		const MGSmootherBase< VectorType > &	pre_smooth,
		const MGSmootherBase< VectorType > &	post_smooth,
		const unsigned int	minlevel = 0,
		const unsigned int	maxlevel = numbers::invalid_unsigned_int,
		Cycle	cycle = v_cycle
	)

Constructor. transfer is an object performing prolongation and restriction. For levels in [minlevel, maxlevel] matrix has to contain valid matrices. By default the maxlevel is set to the maximal valid level.

This function already initializes the vectors which will be used later in the course of the computations. You should therefore create objects of this type as late as possible.

Member Function Documentation

template<typename VectorType>

void Multigrid< VectorType >::reinit	(	const unsigned int	minlevel,
		const unsigned int	maxlevel
	)

Reinit this class according to minlevel and maxlevel.

template<typename VectorType>

void Multigrid< VectorType >::cycle

(

)

Execute one multigrid cycle. The type of cycle is selected by the constructor argument cycle. See the enum Cycle for available types.

template<typename VectorType>

void Multigrid< VectorType >::vcycle

(

)

Execute one step of the V-cycle algorithm. This function assumes, that the multilevel vector defect is filled with the residual of an outer defect correction scheme. This is usually taken care of by PreconditionMG). After vcycle(), the result is in the multilevel vector solution. See copy_*_mg in the MGTools namespace if you want to use these vectors yourself.

The actual work for this function is done in level_v_step().

template<typename VectorType>

void Multigrid< VectorType >::set_edge_matrices	(	const MGMatrixBase< VectorType > &	edge_out,
		const MGMatrixBase< VectorType > &	edge_in
	)

Set additional matrices to correct residual computation at refinement edges. Since we only smoothen in the interior of the refined part of the mesh, the coupling across the refinement edge is missing. This coupling is provided by these two matrices.

Note

While edge_out.vmult is used, for the second argument, we use edge_in.Tvmult. Thus, edge_in should be assembled in transposed form. This saves a second sparsity pattern for edge_in. In particular, for symmetric operators, both arguments can refer to the same matrix, saving assembling of one of them.

template<typename VectorType>

void Multigrid< VectorType >::set_edge_flux_matrices	(	const MGMatrixBase< VectorType > &	edge_down,
		const MGMatrixBase< VectorType > &	edge_up
	)

Set additional matrices to correct residual computation at refinement edges. These matrices originate from discontinuous Galerkin methods (see FE_DGQ etc.), where they correspond to the edge fluxes at the refinement edge between two levels.

Note

While edge_down.vmult is used, for the second argument, we use edge_up.Tvmult. Thus, edge_up should be assembled in transposed form. This saves a second sparsity pattern for edge_up. In particular, for symmetric operators, both arguments can refer to the same matrix, saving assembling of one of them.

template<typename VectorType>

unsigned int Multigrid< VectorType >::get_maxlevel

(

)

const

Return the finest level for multigrid.

template<typename VectorType>

unsigned int Multigrid< VectorType >::get_minlevel

(

)

const

Return the coarsest level for multigrid.

template<typename VectorType>

void Multigrid< VectorType >::set_maxlevel

(

const unsigned

int

)

Set the highest level for which the multilevel method is performed. By default, this is the finest level of the Triangulation. Accepted are values not smaller than the current minlevel.

template<typename VectorType>

void Multigrid< VectorType >::set_minlevel	(	const unsigned int	level,
		bool	relative = false
	)

Set the coarsest level for which the multilevel method is performed. By default, this is zero. Accepted are non-negative values not larger than the current maxlevel.

If relative is true, then this function determines the number of levels used, that is, it sets minlevel to maxlevel-level.

Note

The mesh on the coarsest level must cover the whole domain. There may not be hanging nodes on minlevel.

If minlevel is set to a nonzero value, do not forget to adjust your coarse grid solver!

template<typename VectorType>

void Multigrid< VectorType >::set_cycle

(

Cycle

)

Chance cycle_type used in cycle().

template<typename VectorType>

void Multigrid< VectorType >::set_debug

(

const unsigned

int

)

Deprecated:

Debug output will go away. Use signals instead.

Set the debug level. Higher values will create more debugging output during the multigrid cycles.

template<typename VectorType>

boost::signals2::connection Multigrid< VectorType >::connect_coarse_solve

(

const std::function< void(const bool, const unsigned int)> &

slot

)

Connect a function to mg::Signals::coarse_solve.

template<typename VectorType>

boost::signals2::connection Multigrid< VectorType >::connect_restriction

(

const std::function< void(const bool, const unsigned int)> &

slot

)

Connect a function to mg::Signals::restriction.

template<typename VectorType>

boost::signals2::connection Multigrid< VectorType >::connect_prolongation

(

const std::function< void(const bool, const unsigned int)> &

slot

)

Connect a function to mg::Signals::prolongation.

template<typename VectorType>

boost::signals2::connection Multigrid< VectorType >::connect_pre_smoother_step

(

const std::function< void(const bool, const unsigned int)> &

slot

)

Connect a function to mg::Signals::pre_smoother_step.

template<typename VectorType>

boost::signals2::connection Multigrid< VectorType >::connect_post_smoother_step

(

const std::function< void(const bool, const unsigned int)> &

slot

)

Connect a function to mg::Signals::post_smoother_step.

template<typename VectorType>

void Multigrid< VectorType >::level_v_step ( const unsigned int  level )

private

The V-cycle multigrid method. level is the level the function starts on. It will usually be called for the highest level from outside, but will then call itself recursively for level-1, unless we are on minlevel where the coarse grid solver solves the problem exactly.

template<typename VectorType>

void Multigrid< VectorType >::level_step ( const unsigned int  level, Cycle  cycle  )

private

The actual W-cycle or F-cycle multigrid method. level is the level the function starts on. It will usually be called for the highest level from outside, but will then call itself recursively for level-1, unless we are on minlevel where the coarse grid solver solves the problem exactly.

Member Data Documentation

template<typename VectorType>

mg::Signals Multigrid< VectorType >::signals

private

Signals for the various actions that the Multigrid algorithm uses.

Definition at line 353 of file multigrid.h.

template<typename VectorType>

Cycle Multigrid< VectorType >::cycle_type

private

Cycle type performed by the method cycle().

Definition at line 377 of file multigrid.h.

template<typename VectorType>

unsigned int Multigrid< VectorType >::minlevel

private

Level for coarse grid solution.

Definition at line 382 of file multigrid.h.

template<typename VectorType>

unsigned int Multigrid< VectorType >::maxlevel

private

Highest level of cells.

Definition at line 387 of file multigrid.h.

template<typename VectorType>

MGLevelObject<VectorType> Multigrid< VectorType >::defect

Input vector for the cycle. Contains the defect of the outer method projected to the multilevel vectors.

Definition at line 394 of file multigrid.h.

template<typename VectorType>

MGLevelObject<VectorType> Multigrid< VectorType >::solution

The solution update after the multigrid step.

Definition at line 399 of file multigrid.h.

template<typename VectorType>

MGLevelObject<VectorType> Multigrid< VectorType >::t

private

Auxiliary vector.

Definition at line 405 of file multigrid.h.

template<typename VectorType>

MGLevelObject<VectorType> Multigrid< VectorType >::defect2

private

Auxiliary vector for W- and F-cycles. Left uninitialized in V-cycle.

Definition at line 410 of file multigrid.h.

template<typename VectorType>

SmartPointer<const MGMatrixBase<VectorType>, Multigrid<VectorType> > Multigrid< VectorType >::matrix

private

The matrix for each level.

Definition at line 416 of file multigrid.h.

template<typename VectorType>

SmartPointer<const MGCoarseGridBase<VectorType>, Multigrid<VectorType> > Multigrid< VectorType >::coarse

private

The matrix for each level.

Definition at line 422 of file multigrid.h.

template<typename VectorType>

SmartPointer<const MGTransferBase<VectorType>, Multigrid<VectorType> > Multigrid< VectorType >::transfer

private

Object for grid transfer.

Definition at line 428 of file multigrid.h.

template<typename VectorType>

SmartPointer<const MGSmootherBase<VectorType>, Multigrid<VectorType> > Multigrid< VectorType >::pre_smooth

private

The pre-smoothing object.

Definition at line 434 of file multigrid.h.

template<typename VectorType>

SmartPointer<const MGSmootherBase<VectorType>, Multigrid<VectorType> > Multigrid< VectorType >::post_smooth

private

The post-smoothing object.

Definition at line 440 of file multigrid.h.

template<typename VectorType>

SmartPointer<const MGMatrixBase<VectorType> > Multigrid< VectorType >::edge_out

private

Edge matrix from the interior of the refined part to the refinement edge.

Note

Only vmult is used for these matrices.

Definition at line 447 of file multigrid.h.

template<typename VectorType>

SmartPointer<const MGMatrixBase<VectorType> > Multigrid< VectorType >::edge_in

private

Transpose edge matrix from the refinement edge to the interior of the refined part.

Note

Only Tvmult is used for these matrices.

Definition at line 455 of file multigrid.h.

template<typename VectorType>

SmartPointer<const MGMatrixBase<VectorType>, Multigrid<VectorType> > Multigrid< VectorType >::edge_down

private

Edge matrix from fine to coarse.

Note

Only vmult is used for these matrices.

Definition at line 462 of file multigrid.h.

template<typename VectorType>

SmartPointer<const MGMatrixBase<VectorType>, Multigrid<VectorType> > Multigrid< VectorType >::edge_up

private

Transpose edge matrix from coarse to fine.

Note

Only Tvmult is used for these matrices.

Definition at line 469 of file multigrid.h.

template<typename VectorType>

unsigned int Multigrid< VectorType >::debug

private

Level for debug output. Defaults to zero and can be set by set_debug().

Definition at line 474 of file multigrid.h.

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The documentation for this class was generated from the following file:

• deal.II/multigrid/multigrid.h