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>

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. More...
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. More...
void	pre (Domain &x, Range &b)
	Prepare the preconditioner. More...
void	post (Domain &x)
	Clean up. More...
void	apply (Domain &v, const Range &d)
	Apply one step of the preconditioner to the system A(v)=d. More...
virtual void	pre (X &x, X &b)=0
	Prepare the preconditioner. More...
virtual void	apply (X &v, const X &d)=0
	Apply one step of the preconditioner to the system A(v)=d. More...

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 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 \( v = M^{-1} d \) 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.

Implemented in Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >, Dune::SeqOverlappingSchwarz< M, X, TM, TS, TA >, Dune::SeqOverlappingSchwarz< M, X, TM, TD, TA >, and Dune::SeqOverlappingSchwarz< 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::SeqOverlappingSchwarz< M, X, TM, TD, TA >, and Dune::SeqOverlappingSchwarz< M, X, TM, TS, TA >.

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

• dune/istl/paamg/amg.hh
• dune/istl/paamg/kamg.hh