Dune::Amg::KAMG< M, X, S, PI, K, A > Class Template Reference

an algebraic multigrid method using a Krylov-cycle. More...

#include <dune/istl/paamg/kamg.hh>

Inheritance diagram for Dune::Amg::KAMG< M, X, S, PI, K, A >:

Public Types
typedef AMG< M, X, S, PI, A >	Amg
	The type of the underlying AMG.
typedef K	KrylovSolver
	The type of the Krylov solver for the cycle.
typedef Amg::OperatorHierarchy	OperatorHierarchy
	The type of the hierarchy of operators.
typedef Amg::CoarseSolver	CoarseSolver
	The type of the coarse solver.
typedef Amg::ParallelInformation	ParallelInformation
	the type of the parallelinformation to use.
typedef Amg::SmootherArgs	SmootherArgs
	The type of the arguments for construction of the smoothers.
typedef Amg::Operator	Operator
	the type of the lineatr operator.
typedef Amg::Domain	Domain
	the type of the domain.
typedef Amg::Range	Range
	The type of the range.
typedef Amg::ParallelInformationHierarchy	ParallelInformationHierarchy
	The type of the hierarchy of parallel information.
typedef Amg::ScalarProduct	ScalarProduct
	The type of the scalar product.
typedef X	domain_type
	The domain type of the preconditioner.
typedef X	range_type
	The range type of the preconditioner.
typedef X::field_type	field_type
	The field type of the preconditioner.

Public Member Functions
virtual SolverCategory::Category	category () const
	Category of the preconditioner (see SolverCategory::Category).
	KAMG (OperatorHierarchy &matrices, CoarseSolver &coarseSolver, const SmootherArgs &smootherArgs, const Parameters &parms, std::size_t maxLevelKrylovSteps=3, double minDefectReduction=1e-1)
	Construct a new amg with a specific coarse solver.
template<class C>
	KAMG (const Operator &fineOperator, const C &criterion, const SmootherArgs &smootherArgs=SmootherArgs(), std::size_t maxLevelKrylovSteps=3, double minDefectReduction=1e-1, const ParallelInformation &pinfo=ParallelInformation())
	Construct an AMG with an inexact coarse solver based on the smoother.
void	pre (Domain &x, Range &b)
	Prepare the preconditioner.
void	post (Domain &x)
	Clean up.
void	apply (Domain &v, const Range &d)
	Apply one step of the preconditioner to the system A(v)=d.
std::size_t	maxlevels ()
virtual void	pre (X &x, X &b)=0
	Prepare the preconditioner.
virtual void	apply (X &v, const X &d)=0
	Apply one step of the preconditioner to the system A(v)=d.
virtual void	post (X &x)=0
	Clean up.

Detailed Description

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>
class Dune::Amg::KAMG< M, X, S, PI, K, A >

an algebraic multigrid method using a Krylov-cycle.

The implementation is based on the paper [Notay and Vassilevski, 2007]

Template Parameters

M	The type of the linear operator.
X	The type of the range and domain.
PI	The parallel information object. Use SequentialInformation (default) for a sequential AMG, OwnerOverlapCopyCommunication for the parallel case.
K	The type of the Krylov method to use for the cycle.
A	The type of the allocator to use.

Member Typedef Documentation

Amg

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

typedef AMG<M,X,S,PI,A> Dune::Amg::KAMG< M, X, S, PI, K, A >::Amg

The type of the underlying AMG.

CoarseSolver

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

typedef Amg::CoarseSolver Dune::Amg::KAMG< M, X, S, PI, K, A >::CoarseSolver

The type of the coarse solver.

Domain

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

typedef Amg::Domain Dune::Amg::KAMG< M, X, S, PI, K, A >::Domain

the type of the domain.

domain_type

typedef X Dune::Preconditioner< X, X >::domain_type

inherited

The domain type of the preconditioner.

field_type

typedef X::field_type Dune::Preconditioner< X, X >::field_type

inherited

The field type of the preconditioner.

KrylovSolver

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

typedef K Dune::Amg::KAMG< M, X, S, PI, K, A >::KrylovSolver

The type of the Krylov solver for the cycle.

Operator

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

typedef Amg::Operator Dune::Amg::KAMG< M, X, S, PI, K, A >::Operator

the type of the lineatr operator.

OperatorHierarchy

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

typedef Amg::OperatorHierarchy Dune::Amg::KAMG< M, X, S, PI, K, A >::OperatorHierarchy

The type of the hierarchy of operators.

ParallelInformation

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

typedef Amg::ParallelInformation Dune::Amg::KAMG< M, X, S, PI, K, A >::ParallelInformation

the type of the parallelinformation to use.

ParallelInformationHierarchy

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

typedef Amg::ParallelInformationHierarchy Dune::Amg::KAMG< M, X, S, PI, K, A >::ParallelInformationHierarchy

The type of the hierarchy of parallel information.

Range

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

typedef Amg::Range Dune::Amg::KAMG< M, X, S, PI, K, A >::Range

The type of the range.

range_type

typedef X Dune::Preconditioner< X, X >::range_type

inherited

The range type of the preconditioner.

ScalarProduct

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

typedef Amg::ScalarProduct Dune::Amg::KAMG< M, X, S, PI, K, A >::ScalarProduct

The type of the scalar product.

SmootherArgs

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

typedef Amg::SmootherArgs Dune::Amg::KAMG< M, X, S, PI, K, A >::SmootherArgs

The type of the arguments for construction of the smoothers.

Member Function Documentation

apply()

virtual void Dune::Preconditioner< X, X >::apply ( X & v, const X & d )

pure virtualinherited

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 where is the approximate inverse of the operator characterizing the preconditioner.

Parameters

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

Implemented in Dune::Amg::AMG< M, X, S, PI, A >, Dune::Amg::AMG< M, X, S, PI, A >, Dune::Amg::AMG< M, X, S, SequentialInformation, std::allocator< X > >, Dune::Amg::AMG< Operator, X, Smoother >, Dune::Amg::FastAMG< M, X, PI, A >, Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >, Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >, Dune::SeqOverlappingSchwarz< M, X, MultiplicativeSchwarzMode, MS, TA >, Dune::SeqOverlappingSchwarz< M, X, MultiplicativeSchwarzMode, MS, TA >, Dune::SeqOverlappingSchwarz< M, X, SymmetricMultiplicativeSchwarzMode, TD, TA >, Dune::SeqOverlappingSchwarz< M, X, SymmetricMultiplicativeSchwarzMode, TD, TA >, Dune::SeqOverlappingSchwarz< M, X, TM, TS, TA >, Dune::SeqSSOR< typename M::matrix_type, X, X >, Dune::subdomain_vector< M, X, TM, TS, TA >, and Dune::subdomain_vector< M, X, TM, TS, TA >.

category()

template<class M, class X, class S, class PI = SequentialInformation, class K = GeneralizedPCGSolver<X>, class A = std::allocator<X>>

virtual SolverCategory::Category Dune::Amg::KAMG< M, X, S, PI, K, A >::category ( ) const

inlinevirtual

Category of the preconditioner (see SolverCategory::Category).

Implements Dune::Preconditioner< X, X >.

post()

virtual void Dune::Preconditioner< X, X >::post ( X & x )

pure virtualinherited

Clean up.

This method is called after the last apply call for the linear system to be solved. Memory may be deallocated safely here. x is the solution of the linear equation.

Parameters

x	The right hand side of the equation.

Implemented in Dune::Amg::AMG< M, X, S, PI, A >, Dune::Amg::AMG< M, X, S, PI, A >, Dune::Amg::AMG< M, X, S, SequentialInformation, std::allocator< X > >, Dune::Amg::AMG< Operator, X, Smoother >, Dune::Amg::FastAMG< M, X, PI, A >, Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >, Dune::SeqOverlappingSchwarz< M, X, MultiplicativeSchwarzMode, MS, TA >, Dune::SeqOverlappingSchwarz< M, X, SymmetricMultiplicativeSchwarzMode, TD, TA >, Dune::SeqOverlappingSchwarz< M, X, TM, TS, TA >, Dune::SeqSSOR< typename M::matrix_type, X, X >, and Dune::subdomain_vector< M, X, TM, TS, TA >.

pre()

virtual void Dune::Preconditioner< X, X >::pre ( X & x, X & b )

pure virtualinherited

Prepare the preconditioner.

A solver solves a linear operator equation A(x)=b by applying one or several steps of the preconditioner. The method pre() is called before the first apply operation. b and x are right hand side and solution vector of the linear system respectively. It may. e.g., scale the system, allocate memory or compute a (I)LU decomposition. Note: The ILU decomposition could also be computed in the constructor or with a separate method of the derived method if several linear systems with the same matrix are to be solved.

Note

if a preconditioner is copied (e.g. for a second thread) again the pre() method has to be called to ensure proper memory management.

X x(0.0);
Y b = ...; // rhs
Preconditioner<X,Y> prec(...);
prec.pre(x,b);   // prepare the preconditioner
prec.apply(x,b); // can be called multiple times now...
prec.post(x);    // cleanup internal state

Parameters

x	The left hand side of the equation.
b	The right hand side of the equation.

Implemented in Dune::Amg::AMG< M, X, S, PI, A >, Dune::Amg::AMG< M, X, S, PI, A >, Dune::Amg::AMG< M, X, S, SequentialInformation, std::allocator< X > >, Dune::Amg::AMG< Operator, X, Smoother >, Dune::Amg::FastAMG< M, X, PI, A >, Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >, Dune::SeqOverlappingSchwarz< M, X, MultiplicativeSchwarzMode, MS, TA >, Dune::SeqOverlappingSchwarz< M, X, SymmetricMultiplicativeSchwarzMode, TD, TA >, Dune::SeqOverlappingSchwarz< M, X, TM, TS, TA >, Dune::SeqSSOR< typename M::matrix_type, X, X >, and Dune::subdomain_vector< M, X, TM, TS, TA >.

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

• amg.hh
• kamg.hh