implements Gauss-Seidel preconditioner More...

#include <TSOR.hh>

Inheritance diagram for TGaussSeidel:

Public Member Functions
	TGaussSeidel (const TMatrix *A, const gs_type_t gs_type, const real damping=1.0)
	constructs Gauss-Seidel preconditioner of type gs_type

const TMatrix *	matrix () const
	return internal sparse matrix

gs_type_t	gs_type () const
	return GaussSeidel type

real	damping_factor () const
	return damping factor

bool	is_complex () const
	return true, if field type is complex

bool	is_self_adjoint () const
	return true, of operator is self adjoint

virtual void	apply (const TVector x, TVector y, const matop_t op=apply_normal) const

virtual void	apply_add (const real alpha, const TVector x, TVector y, const matop_t op=apply_normal) const

virtual auto	domain_vector () const -> std::unique_ptr< TVector >
	return vector in domain space

virtual auto	range_vector () const -> std::unique_ptr< TVector >
	return vector in range space

Public Member Functions inherited from TTypeInfo
virtual typeid_t	type () const =0
	return type ID of object

virtual bool	is_type (const typeid_t t) const
	return true if local object is of given type ID t

virtual std::string	typestr () const
	return string representation of type

Detailed Description

TGaussSeidel provides application of a Gauss-Seidel type preconditioner for a given matrix \(A = D - E - F\), with diagonal D, strictly lower triangular matrix E and strictly upper triangular matrix F.

For forward GS, the applied operator is \( ( D - E )^{-1}\), for backward GS \( ( D - F )^{-1}\) and the combination of both for the symmetric GS, i.e., \( ( D - F )^{-1} D ( D - E )^{-1}\).

TGaussSeidel implements point-wise and block-wise GS steps. However, point-wise GS is only supported for sparse matrices while block-wise GS is only supported for H-matrices

Member Function Documentation

◆ apply()

virtual void apply	(	const TVector *	x,
		TVector *	y,
		const matop_t	op = `apply_normal`
	)		const

virtual

mapping function of linear operator \(A\), e.g. \( y := A(x)\). Depending on op, either \(A\), \(A^T\) or \(A^H\) is applied.

Implements TLinearOperator.

◆ apply_add()

virtual void apply_add	(	const real	alpha,
		const TVector *	x,
		TVector *	y,
		const matop_t	op = `apply_normal`
	)		const