#include <precondition.h>

Inheritance diagram for PreconditionSOR< MATRIX >:

Public Member Functions
template<class VECTOR >
void	vmult (VECTOR &, const VECTOR &) const

template<class VECTOR >
void	Tvmult (VECTOR &, const VECTOR &) const

template<class VECTOR >
void	step (VECTOR &x, const VECTOR &rhs) const

template<class VECTOR >
void	Tstep (VECTOR &x, const VECTOR &rhs) const

Public Member Functions inherited from PreconditionRelaxation< MATRIX >
void	initialize (const MATRIX &A, const AdditionalData &parameters=AdditionalData())

void	clear ()

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

void	subscribe (const char *identifier=0) const

void	unsubscribe (const char *identifier=0) const

unsigned int	n_subscriptions () const

void	list_subscribers () const

	DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.")

	DeclException2 (ExcNoSubscriber, char , char ,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1)

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Additional Inherited Members
Protected Attributes inherited from PreconditionRelaxation< MATRIX >
SmartPointer< const MATRIX, PreconditionRelaxation< MATRIX > >	A

double	relaxation

Detailed Description

template<class MATRIX = SparseMatrix<double>>
class PreconditionSOR< MATRIX >

SOR preconditioner using matrix built-in function.

Assuming the matrix A = D + L + U is split into its diagonal D as well as the strict lower and upper triangles L and U, then the SOR preconditioner with relaxation parameter r is

$P^{-1} = r (D+rL)^{-1}.$

It is this operator P^-1, which is implemented by vmult() through forward substitution. Analogously, Tvmult() implements the operation of r(D+rU)^-1.

The SOR iteration itself can be directly written as

$x^{k+1} = x^k - r D^{-1} \bigl(L x^{k+1} + U x^k - b\bigr).$

Using the right hand side b and the previous iterate x, this is the operation implemented by step().

The MATRIX class used is required to have functions precondition_SOR(VECTOR&, const VECTOR&, double) and precondition_TSOR(VECTOR&, const VECTOR&, double).

    // Declare related objects
SparseMatrix<double> A;
Vector<double> x;
Vector<double> b;
SolverCG<> solver(...);
//...initialize and build A
    // Define and initialize preconditioner
PreconditionSOR<SparseMatrix<double> > precondition;
precondition.initialize (A, .6);
solver.solve (A, x, b, precondition);

Author: Guido Kanschat, 2000

Definition at line 516 of file precondition.h.

Member Function Documentation

template<class MATRIX = SparseMatrix<double>>

template<class VECTOR >

void PreconditionSOR< MATRIX >::vmult	(	VECTOR &	,
		const VECTOR &
	)		const

Apply preconditioner.

template<class MATRIX = SparseMatrix<double>>

template<class VECTOR >

void PreconditionSOR< MATRIX >::Tvmult	(	VECTOR &	,
		const VECTOR &
	)		const

Apply transpose preconditioner.

template<class MATRIX = SparseMatrix<double>>

template<class VECTOR >

void PreconditionSOR< MATRIX >::step	(	VECTOR &	x,
		const VECTOR &	rhs
	)		const

Perform one step of the preconditioned Richardson iteration.

template<class MATRIX = SparseMatrix<double>>

template<class VECTOR >

void PreconditionSOR< MATRIX >::Tstep	(	VECTOR &	x,
		const VECTOR &	rhs
	)		const

Perform one transposed step of the preconditioned Richardson iteration.

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

include/deal.II/lac/precondition.h

Public Member Functions

Additional Inherited Members

Detailed Description

template<class MATRIX = SparseMatrix<double>> class PreconditionSOR< MATRIX >

Member Function Documentation

template<class MATRIX = SparseMatrix<double>>
class PreconditionSOR< MATRIX >