Local operator that can be used to create a fully matrix-free Jacobi preconditioner. More...

#include <dune/pdelab/backend/istl/matrixfree/iterativeblockjacobipreconditioner.hh>

Public Types
Flags selective assembly
enum
	Whether to do selective assembly on the elements, i.e. whether or not skip_entity() should be called.

enum
	Whether to do selective assembly on the intersections, i.e. whether or not skip_intersection() should be called.

Flags for the sparsity pattern
enum
	Whether to assemble the pattern on the elements, i.e. whether or not pattern_volume() should be called.

enum
	Whether to assemble the pattern on the elements after the skeleton has been handled, i.e. whether or not pattern_volume_post_skeleton() should be called.

enum
	Whether to assemble the pattern on the interior intersections, i.e. whether or not pattern_skeleton() should be called.

enum
	Whether to assemble the pattern on the boundary intersections, i.e. whether or not pattern_boundary() should be called.

Flags for the non-constant part of the residual and the jacobian
enum
	Whether to call the local operator's alpha_volume(), jacobian_apply_volume() and jacobian_volume().

enum
	Whether to call the local operator's alpha_volume_post_skeleton(), jacobian_apply_volume_post_skeleton() and jacobian_volume_post_skeleton().

enum
	Whether to call the local operator's alpha_skeleton(), jacobian_apply_skeleton() and jacobian_skeleton().

enum
	Whether to call the local operator's alpha_boundary(), jacobian_apply_boundary() and jacobian_boundary().

Flags for the constant part of the residual
enum
	Whether to call the local operator's lambda_volume().

enum
	Whether to call the local operator's lambda_volume_post_skeleton().

enum
	Whether to call the local operator's lambda_skeleton().

enum
	Whether to call the local operator's lambda_boundary().

Special flags
enum
	Whether to visit the skeleton methods from both sides.

enum
	Wheter the local operator describes a linear problem.

Public Member Functions
	IterativeBlockJacobiPreconditionerLocalOperator (const BlockDiagonalLocalOperator &blockDiagonalLocalOperator, const PointDiagonalLocalOperator &pointDiagonalLocalOperator, const GridFunctionSpace &gridFunctionSpace, SolverStatistics< int > &solverStatiscits, BlockSolverOptions solveroptions, const bool verbose=0)
	Constructor. More...

template<typename EG , typename LFSU , typename X , typename LFSV , typename Y >
void	alpha_volume (const EG &eg, const LFSU &lfsu, const X &x, const LFSV &lfsv, Y &y) const
	Prepare fully matrix-free preconditioner. More...

template<typename EG , typename LFSU , typename Z , typename LFSV , typename Y >
void	jacobian_apply_volume (const EG &eg, const LFSU &lfsu, const Z &z, const LFSV &lfsv, Y &y) const
	Apply fully matrix-free preconditioner - linear case.

template<typename EG , typename LFSU , typename X , typename Z , typename LFSV , typename Y >
void	jacobian_apply_volume (const EG &eg, const LFSU &lfsu, const X &x, const Z &z, const LFSV &lfsv, Y &y) const
	Apply fully matrix-free preconditioner - nonlinear case. More...

Detailed Description

template<typename BlockDiagonalLocalOperator, typename PointDiagonalLocalOperator, typename GridFunctionSpace, typename DomainField, template< typename > class IterativeSolver>
class Dune::PDELab::IterativeBlockJacobiPreconditionerLocalOperator< BlockDiagonalLocalOperator, PointDiagonalLocalOperator, GridFunctionSpace, DomainField, IterativeSolver >

Local operator that can be used to create a fully matrix-free Jacobi preconditioner.

Similar to the partial matrix-free class AssembledBlockJacobiPreconditionerLocalOperator this implements a local operator that can be used to implement a matrix-free Jacobi preconditioner. In contrast to the other class this implementation will be fully matrix-free.

A matrix-free Jacobi preconditioner needs to be able to apply the inverse of the block diagonal D to a vector. In the partial matrix-free class mentioned above this was done by assembling the diagonal blocks and inverting this matrix. In order to get a fully matrix-free version we instead use a Krylow solver on the diagonal block. This can once again be done in a matrix-free way but we will need a preconditioner for iterative solver. For this purpose we use another Jacobi preconditioner that operates on a single block. This means we need to assemble the point diagonal of this block and apply the inverse.

For examples see dune-pdelab/dune/pdelab/test/matrixfree/.

Template Parameters

BlockDiagonalLocalOperator	A lop for local application of diagonal blocks
PointDiagonalLocalOperator	A lop for local assembly of point diagonal
GridFunctionSpace	A grid function space
DomainField	Domain field
IterativeSolver	Solver that will be used to 'invert' the diagonal blocks

Constructor & Destructor Documentation

◆ IterativeBlockJacobiPreconditionerLocalOperator()

template<typename BlockDiagonalLocalOperator , typename PointDiagonalLocalOperator , typename GridFunctionSpace , typename DomainField , template< typename > class IterativeSolver>

Dune::PDELab::IterativeBlockJacobiPreconditionerLocalOperator< BlockDiagonalLocalOperator, PointDiagonalLocalOperator, GridFunctionSpace, DomainField, IterativeSolver >::IterativeBlockJacobiPreconditionerLocalOperator	(	const BlockDiagonalLocalOperator &	blockDiagonalLocalOperator,
		const PointDiagonalLocalOperator &	pointDiagonalLocalOperator,
		const GridFunctionSpace &	gridFunctionSpace,
		SolverStatistics< int > &	solverStatiscits,
		BlockSolverOptions	solveroptions,
		const bool	verbose = `0`
	)

inline

Constructor.

Parameters

blockDiagonalLocalOperator	A local operator that can be used to (locally) apply a diagonal block through the <applyLocalDiagonalBlock> function. You can create such a local operator by wrapping your local operator into a <BlockDiagonalLocalOperatorWrapper>
pointDiagonalLocalOperator	A local operator that can be used to (locally) assemble the point diagonal of a diagonal block. You can create such a local operator by wrapping your local operator into a <PointDiagonalLocalOperatorWrapper>
gridFunctionSpace	A grid function space
solverStat	A class for export solver statistics
solveroptions	A class for configuring your solver
verbose	Controls the amount of output

Member Function Documentation

◆ alpha_volume()

template<typename BlockDiagonalLocalOperator , typename PointDiagonalLocalOperator , typename GridFunctionSpace , typename DomainField , template< typename > class IterativeSolver>

template<typename EG , typename LFSU , typename X , typename LFSV , typename Y >

void Dune::PDELab::IterativeBlockJacobiPreconditionerLocalOperator< BlockDiagonalLocalOperator, PointDiagonalLocalOperator, GridFunctionSpace, DomainField, IterativeSolver >::alpha_volume	(	const EG &	eg,
		const LFSU &	lfsu,
		const X &	x,
		const LFSV &	lfsv,
		Y &	y
	)		const

inline

Prepare fully matrix-free preconditioner.

This assembles the point diagonal of the diagonal block and stores its inverse. During the apply step this will be used as a preconditioner for the solver on the local block.

References Dune::SingleCodimSingleGeomTypeMapper< GV, c >::index(), and Dune::size().

◆ jacobian_apply_volume()

template<typename BlockDiagonalLocalOperator , typename PointDiagonalLocalOperator , typename GridFunctionSpace , typename DomainField , template< typename > class IterativeSolver>

template<typename EG , typename LFSU , typename X , typename Z , typename LFSV , typename Y >

void Dune::PDELab::IterativeBlockJacobiPreconditionerLocalOperator< BlockDiagonalLocalOperator, PointDiagonalLocalOperator, GridFunctionSpace, DomainField, IterativeSolver >::jacobian_apply_volume	(	const EG &	eg,
		const LFSU &	lfsu,
		const X &	x,
		const Z &	z,
		const LFSV &	lfsv,
		Y &	y
	)		const