Dune::Amg::FastAMG< M, X, PI, A > Class Template Reference

A fast (sequential) algebraic multigrid based on agglomeration that saves memory bandwidth. More...

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

Public Types
typedef M	Operator
	The matrix operator type.
typedef PI	ParallelInformation
	The type of the parallel information. Either OwnerOverlapCommunication or another type describing the parallel data distribution and providing communication methods.
typedef MatrixHierarchy< M, ParallelInformation, A >	OperatorHierarchy
	The operator hierarchy type.
typedef OperatorHierarchy::ParallelInformationHierarchy	ParallelInformationHierarchy
	The parallal data distribution hierarchy type.
typedef X	Domain
	The domain type.
typedef X	Range
	The range type.
typedef InverseOperator< X, X >	CoarseSolver
	the type of the coarse solver.
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
	FastAMG (OperatorHierarchy &matrices, CoarseSolver &coarseSolver, const Parameters &parms, bool symmetric=true)
	Construct a new amg with a specific coarse solver. More...
template<class C >
	FastAMG (std::shared_ptr< const Operator > fineOperator, const C &criterion, const Parameters &parms=Parameters(), bool symmetric=true, const ParallelInformation &pinfo=ParallelInformation())
	Construct an AMG with an inexact coarse solver based on the smoother. More...
template<class C >
	FastAMG (const Operator &fineOperator, const C &criterion, const Parameters &parms=Parameters(), bool symmetric=true, const ParallelInformation &pinfo=ParallelInformation())
	Construct an AMG with an inexact coarse solver based on the smoother. More...
	FastAMG (const FastAMG &amg)
	Copy constructor.
void	pre (Domain &x, Range &b)
	Prepare the preconditioner. More...
void	apply (Domain &v, const Range &d)
	Apply one step of the preconditioner to the system A(v)=d. More...
virtual SolverCategory::Category	category () const
	Category of the preconditioner (see SolverCategory::Category)
void	post (Domain &x)
	Clean up. More...
template<class A1 >
void	getCoarsestAggregateNumbers (std::vector< std::size_t, A1 > &cont)
	Get the aggregate number of each unknown on the coarsest level. More...
void	recalculateHierarchy ()
	Recalculate the matrix hierarchy. More...
bool	usesDirectCoarseLevelSolver () const
	Check whether the coarse solver used is a direct solver. 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 PI = SequentialInformation, class A = std::allocator<X>>
class Dune::Amg::FastAMG< M, X, PI, A >

A fast (sequential) algebraic multigrid based on agglomeration that saves memory bandwidth.

It combines one Gauss-Seidel smoothing sweep with the defect calculation to reduce memory transfers.

Template Parameters

M	The matrix-operator type, e.g. MatrixAdapter or AssembledLinearOperator
X	The vector type
PI	Currently ignored.
A	An allocator for X

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 file:

• dune/istl/paamg/fastamg.hh