#include <deal.II/lac/precondition.h>

Inheritance diagram for PreconditionSOR< MatrixType >:

Public Types
using	AdditionalData = typename PreconditionRelaxation< MatrixType >::AdditionalData

Public Types inherited from PreconditionRelaxation< MatrixType >
using	size_type = typename MatrixType::size_type

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

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

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

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

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

void	clear ()

size_type	m () const

size_type	n () const

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

void	subscribe (const char *identifier=nullptr) const

void	unsubscribe (const char *identifier=nullptr) const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

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

Additional Inherited Members
Static Public Member Functions inherited from Subscriptor
static::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Protected Attributes inherited from PreconditionRelaxation< MatrixType >
SmartPointer< const MatrixType, PreconditionRelaxation< MatrixType > >	A

double	relaxation

Detailed Description

template<typename MatrixType = SparseMatrix<double>>
class PreconditionSOR< MatrixType >

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 MatrixType class used is required to have functions precondition_SOR(VectorType&, const VectorType&, double) and precondition_TSOR(VectorType&, const VectorType&, double). This class satisfies the relaxation concept.

// 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, PreconditionSOR<SparseMatrix<double>>::AdditionalData(.6));
solver.solve (A, x, b, precondition);

Author: Guido Kanschat, 2000

Definition at line 593 of file precondition.h.