Preconditioners

Modules
	Parallel Algebraic Multigrid
	A Parallel Algebraic Multigrid based on Agglomeration.
	Fast (sequential) Algebraic Multigrid
	An Algebraic Multigrid based on Agglomeration that saves memory bandwidth.

Files
file	overlappingschwarz.hh
	Contains one level overlapping Schwarz preconditioners.
file	preconditioners.hh
	Define general preconditioner interface.

Classes
class	Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >
	Sequential overlapping Schwarz preconditioner. More...
class	Dune::OverlappingSchwarzInitializer< I, S, D >
	Initializer for SuperLU Matrices representing the subdomains. More...
struct	Dune::AdditiveSchwarzMode
	Tag that the tells the schwarz method to be additive. More...
struct	Dune::MultiplicativeSchwarzMode
	Tag that tells the Schwarz method to be multiplicative. More...
struct	Dune::SymmetricMultiplicativeSchwarzMode
	Tag that tells the Schwarz method to be multiplicative and symmetric. More...
class	Dune::DynamicMatrixSubdomainSolver< M, X, Y >
	Exact subdomain solver using Dune::DynamicMatrix<T>::solve. More...
struct	Dune::AdderSelector< T, X, S >
	template meta program for choosing how to add the correction. More...
struct	Dune::IteratorDirectionSelector< T1, T2, forward >
	Helper template meta program for application of overlapping schwarz. More...
struct	Dune::SeqOverlappingSchwarzApplier< T >
	Helper template meta program for application of overlapping schwarz. More...
struct	Dune::SeqOverlappingSchwarzDomainSize< M >
class	Dune::Preconditioner< X, Y >
	Base class for matrix free definition of preconditioners. More...
class	Dune::InverseOperator2Preconditioner< O, c >
	Turns an InverseOperator into a Preconditioner. More...
class	Dune::SeqSSOR< M, X, Y, l >
	Sequential SSOR preconditioner. More...
class	Dune::SeqSOR< M, X, Y, l >
	Sequential SOR preconditioner. More...
class	Dune::SeqGS< M, X, Y, l >
	Sequential Gauss Seidel preconditioner. More...
class	Dune::SeqJac< M, X, Y, l >
	The sequential jacobian preconditioner. More...
class	Dune::SeqILU0< M, X, Y, l >
	Sequential ILU0 preconditioner. More...
class	Dune::SeqILUn< M, X, Y, l >
	Sequential ILU(n) preconditioner. More...
class	Dune::Richardson< X, Y >
	Richardson preconditioner. More...
class	Dune::ParSSOR< M, X, Y, C >
	A parallel SSOR preconditioner. More...
class	Dune::BlockPreconditioner< X, Y, C, T >
	Block parallel preconditioner. More...

Functions
	Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >::SeqOverlappingSchwarz (const matrix_type &mat, const rowtodomain_vector &rowToDomain, field_type relaxationFactor=1, bool onTheFly_=true)
	Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >::SeqOverlappingSchwarz (const matrix_type &mat, const subdomain_vector &subDomains, field_type relaxationFactor=1, bool onTheFly_=true)
	Construct the overlapping Schwarz method. More...
virtual void	Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >::apply (X &v, const X &d)
	Apply the precondtioner. More...
	Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::OverlappingAssignerHelper (std::size_t maxlength, const BCRSMatrix< FieldMatrix< K, n, n >, Al > &mat_, const X &b_, Y &x_)
	Constructor. More...
void	Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::deallocate ()
	Deallocates memory of the local vector.
void	Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::resetIndexForNextDomain ()
	Resets the local index to zero.
DynamicVector< K > &	Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::lhs ()
	Get the local left hand side. More...
DynamicVector< K > &	Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::rhs ()
	Get the local right hand side. More...
void	Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::relaxResult (field_type relax)
	relax the result. More...
void	Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::operator() (const size_type &domainIndex)
	calculate one entry of the local defect. More...
void	Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::assignResult (block_type &res)
	Assigns the block to the current local index. At the same time the local defect is calculated for the index and stored in the rhs. Afterwards the is incremented for the next block.
	Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::OverlappingAssignerHelper (std::size_t maxlength, const matrix_type &mat, const range_type &b, range_type &x)
	Constructor. More...
void	Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::deallocate ()
	Deallocates memory of the local vector. More...
void	Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::operator() (const size_type &domain)
	calculate one entry of the local defect. More...
void	Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::relaxResult (field_type relax)
	relax the result. More...
void	Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::assignResult (block_type &res)
	Assigns the block to the current local index. At the same time the local defect is calculated for the index and stored in the rhs. Afterwards the is incremented for the next block.
field_type *	Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::lhs ()
	Get the local left hand side. More...
field_type *	Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::rhs ()
	Get the local right hand side. More...
	Dune::OverlappingAssignerILUBase< M, X, Y >::OverlappingAssignerILUBase (std::size_t maxlength, const M &mat, const Y &b, X &x)
	Constructor. More...
void	Dune::OverlappingAssignerILUBase< M, X, Y >::deallocate ()
	Deallocates memory of the local vector. More...
void	Dune::OverlappingAssignerILUBase< M, X, Y >::operator() (const size_type &domain)
	calculate one entry of the local defect. More...
void	Dune::OverlappingAssignerILUBase< M, X, Y >::relaxResult (field_type relax)
	relax the result. More...
void	Dune::OverlappingAssignerILUBase< M, X, Y >::assignResult (block_type &res)
	Assigns the block to the current local index. At the same time the local defect is calculated for the index and stored in the rhs. Afterwards the is incremented for the next block.
X &	Dune::OverlappingAssignerILUBase< M, X, Y >::lhs ()
	Get the local left hand side. More...
Y &	Dune::OverlappingAssignerILUBase< M, X, Y >::rhs ()
	Get the local right hand side. More...
void	Dune::OverlappingAssignerILUBase< M, X, Y >::resetIndexForNextDomain ()
	Resets the local index to zero.

Detailed Description

All of our Krylow solvers are preconditioned versions. There are sequential preconditioners (e,g. SeqJacobi, SeqSOR, SeqSSOR) as well as parallel preconditioners (e.g. AMG, BlockPreconditioner) available for plugging them into the solvers together with matching ScalarProducts.

Some of the available perconditioners (e.g. SeqJacobi, SeqSOR, SeqSSOR)) may be given an aditional int as a template parameter, the block recursion level. These preconditioners can be used on blockrecursive matrices with an arbitrary hierarchy depths (eg. BCRSMatrix<BCRSMatrix<FieldMatrix,n,m> > >. Given a block recursion level \(k\) those preconditioners work as normal on the offdiagonal blocks, treating them as traditional matrix entries. For the diagonal values a special procedure applies: If \(k>1\) the diagonal is treated as a matrix itself and the preconditioner is applied recursively on the matrix representing the diagonal value \(D=A_{ii}\) with block level \(k-1\). For the case that \(k=1\) the diagonal is treated as a matrix entry resulting in a linear solve or an identity operation depending on the algorithm.

Function Documentation

apply()

template<class M , class X , class TM , class TD , class TA >

void Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >::apply ( X &  v, const X &  d  )

virtual

Apply the precondtioner.

Apply one step of the preconditioner to the system A(v)=d.

On entry v=0 and d=b-A(x) (although this might not be computed in that way. On exit v contains the update, i.e one step computes \( v = M^{-1} d \) where \( M \) is the approximate inverse of the operator \( A \) characterizing the preconditioner.

Parameters

[out]	v	The update to be computed
	d	The current defect.

Implements Dune::Preconditioner< X, X >.

deallocate() [1/2]

template<template< class > class S, int n, int m, typename T , typename A >

void Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::deallocate

Deallocates memory of the local vector.

Warning

memory is released by the destructor as this Functor is copied and the copy needs to still have the data.

deallocate() [2/2]

template<class M , class X , class Y >

void Dune::OverlappingAssignerILUBase< M, X, Y >::deallocate

Deallocates memory of the local vector.

Warning

memory is released by the destructor as this Functor is copied and the copy needs to still have the data.

lhs() [1/3]

template<class K , int n, class Al , class X , class Y >

DynamicVector< K > & Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::lhs

inline

Get the local left hand side.

Returns

The local left hand side.

lhs() [2/3]

template<template< class > class S, int n, int m, typename T , typename A >

OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::field_type * Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::lhs

Get the local left hand side.

Returns

The local left hand side.

lhs() [3/3]

template<class M , class X , class Y >

X & Dune::OverlappingAssignerILUBase< M, X, Y >::lhs

Get the local left hand side.

Returns

The local left hand side.

operator()() [1/3]

template<template< class > class S, int n, int m, typename T , typename A >

void Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::operator()

(

const size_type &

domain

)

calculate one entry of the local defect.

Parameters

domain

One index of the domain.

operator()() [2/3]

template<class M , class X , class Y >

void Dune::OverlappingAssignerILUBase< M, X, Y >::operator()

(

const size_type &

domain

)

calculate one entry of the local defect.

Parameters

domain

One index of the domain.

operator()() [3/3]

template<class K , int n, class Al , class X , class Y >

void Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::operator()

(

const size_type &

domainIndex

)

calculate one entry of the local defect.

Parameters

domainIndex

One index of the domain.

OverlappingAssignerHelper() [1/2]

template<class K , int n, class Al , class X , class Y >

Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::OverlappingAssignerHelper	(	std::size_t	maxlength,
		const BCRSMatrix< FieldMatrix< K, n, n >, Al > &	mat_,
		const X &	b_,
		Y &	x_
	)

Constructor.

Parameters

maxlength	The maximum entries over all subdomains.
mat_	The global matrix.
b_	the global right hand side.
x_	the global left hand side.

OverlappingAssignerHelper() [2/2]

template<template< class > class S, int n, int m, typename T , typename A >

Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::OverlappingAssignerHelper	(	std::size_t	maxlength,
		const matrix_type &	mat,
		const range_type &	b,
		range_type &	x
	)

Constructor.

Parameters

maxlength	The maximum entries over all subdomains.
mat	The global matrix.
b	the global right hand side.
x	the global left hand side.

OverlappingAssignerILUBase()

template<class M , class X , class Y >

Dune::OverlappingAssignerILUBase< M, X, Y >::OverlappingAssignerILUBase	(	std::size_t	maxlength,
		const M &	mat,
		const Y &	b,
		X &	x
	)

Constructor.

Parameters

maxlength	The maximum entries over all subdomains.
mat	The global matrix.
b	the global right hand side.
x	the global left hand side.

relaxResult() [1/3]

template<class K , int n, class Al , class X , class Y >

void Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::relaxResult ( field_type  relax )

inline

relax the result.

Parameters

relax

The relaxation parameter.

relaxResult() [2/3]

template<template< class > class S, int n, int m, typename T , typename A >

void Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::relaxResult

(

field_type

relax

)

relax the result.

Parameters

relax

The relaxation parameter.

relaxResult() [3/3]

template<class M , class X , class Y >

void Dune::OverlappingAssignerILUBase< M, X, Y >::relaxResult

(

field_type

relax

)

relax the result.

Parameters

relax

The relaxation parameter.

rhs() [1/3]

template<class K , int n, class Al , class X , class Y >

DynamicVector< K > & Dune::OverlappingAssignerHelper< DynamicMatrixSubdomainSolver< BCRSMatrix< FieldMatrix< K, n, n >, Al >, X, Y >, false >::rhs

inline

Get the local right hand side.

Returns

The local right hand side.

rhs() [2/3]

template<template< class > class S, int n, int m, typename T , typename A >

OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::field_type * Dune::OverlappingAssignerHelper< S< BCRSMatrix< FieldMatrix< T, n, m >, A > >, true >::rhs

Get the local right hand side.

Returns

The local right hand side.

rhs() [3/3]

template<class M , class X , class Y >

Y & Dune::OverlappingAssignerILUBase< M, X, Y >::rhs

Get the local right hand side.

Returns

The local right hand side.

SeqOverlappingSchwarz() [1/2]

template<class M , class X , class TM , class TD , class TA >

Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >::SeqOverlappingSchwarz	(	const matrix_type &	mat,
		const rowtodomain_vector &	rowToDomain,
		field_type	relaxationFactor = 1,
		bool	onTheFly_ = true
	)

Construct the overlapping Schwarz method

Parameters

mat	The matrix to precondition.
rowToDomain	The mapping of the rows onto the domains.
relaxationFactor	relaxation factor
onTheFly_	If true the decomposition of the exact local solvers is computed on the fly for each subdomain and iteration step. If false all decompositions are computed in pre and only forward and backward substitution takes place in the iteration steps.

SeqOverlappingSchwarz() [2/2]

template<class M , class X , class TM , class TD , class TA >

Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >::SeqOverlappingSchwarz	(	const matrix_type &	mat,
		const subdomain_vector &	subDomains,
		field_type	relaxationFactor = 1,
		bool	onTheFly_ = true
	)

Construct the overlapping Schwarz method.

Parameters

mat	The matrix to precondition.
subDomains	Array of sets of rowindices belonging to an overlapping subdomain
relaxationFactor	relaxation factor
onTheFly_	If true the decomposition of the exact local solvers is computed on the fly for each subdomain and iteration step. If false all decompositions are computed in pre and only forward and backward substitution takes place in the iteration steps.

Warning

Each rowindex should be part of at least one subdomain!