Projected GaussSeidel (SOR) -method. More...

#include <proj_gauss_seidel.h>

Inheritance diagram for ug::ProjGaussSeidel< TDomain, TAlgebra >:

Public Types
typedef TAlgebra	algebra_type
	Algebra type.

typedef IProjGaussSeidel< TDomain, TAlgebra >	base_type
	Base class type.

typedef algebra_type::matrix_type	matrix_type
	Matrix type.

typedef algebra_type::vector_type	vector_type
	Vector type.

Public Types inherited from ug::IProjGaussSeidel< TDomain, TAlgebra >
typedef TAlgebra	algebra_type
	Algebra type.

typedef GaussSeidelBase< TAlgebra >	base_type
	Base class type.

typedef GridFunction< TDomain, TAlgebra >	GF
	Grid Function type.

typedef algebra_type::matrix_type	matrix_type
	Matrix type.

typedef vector_type::value_type	value_type
	Value type.

typedef algebra_type::vector_type	vector_type
	Vector type.

Public Types inherited from ug::GaussSeidelBase< TAlgebra >
typedef TAlgebra	algebra_type

typedef IPreconditioner< TAlgebra >	base_type
	Base type.

typedef IPreconditioner< TAlgebra >::matrix_operator_type	matrix_operator_type
	Matrix Operator type.

typedef TAlgebra::matrix_type	matrix_type

typedef IOrderingAlgorithm< TAlgebra, ordering_container_type >	ordering_algo_type

typedef std::vector< size_t >	ordering_container_type
	Ordering type.

typedef TAlgebra::vector_type	vector_type

Public Types inherited from ug::IPreconditioner< TAlgebra >
typedef TAlgebra	algebra_type
	Algebra type.

typedef MatrixOperator< matrix_type, vector_type >	matrix_operator_type
	Matrix Operator type.

typedef TAlgebra::matrix_type	matrix_type
	Matrix type.

typedef TAlgebra::vector_type	vector_type
	Vector type.

Public Types inherited from ug::ILinearIterator< TAlgebra::vector_type >
typedef TAlgebra::vector_type	codomain_function_type
	Range space.

typedef TAlgebra::vector_type	domain_function_type
	Domain space.

Public Types inherited from ug::DebugWritingObject< TAlgebra >
typedef TAlgebra	algebra_type
	type of algebra

typedef TAlgebra::matrix_type	matrix_type
	type of matrix

typedef TAlgebra::vector_type	vector_type
	type of vector

Public Types inherited from ug::VectorDebugWritingObject< TAlgebra::vector_type >
typedef TAlgebra::vector_type	vector_type
	type of vector

Public Member Functions
virtual SmartPtr< ILinearIterator< vector_type > >	clone ()
	Clone.

	ProjGaussSeidel ()

	ProjGaussSeidel (const ProjGaussSeidel< TDomain, TAlgebra > &parent)
	copy constructor

virtual void	step (const matrix_type &mat, vector_type &c, const vector_type &d, const number relax)
	computes a new correction c = B*d and projects on the underlying constraint

Public Member Functions inherited from ug::IProjGaussSeidel< TDomain, TAlgebra >
void	add_obstacle_constraint (SmartPtr< IObstacleConstraint< TDomain, TAlgebra > > spObsCons)
	adds the obstacle constraint function c(u)

virtual bool	apply (vector_type &c, const vector_type &d)
	Compute new correction c = B*d.

virtual bool	apply_update_defect (vector_type &c, vector_type &d)
	Compute new correction c = Bd and return new defect d := d - Ac.

virtual bool	init (SmartPtr< ILinearOperator< vector_type > > J, const vector_type &u)
	Prepare for Operator J(u) and linearization point u (current solution)

	IProjGaussSeidel ()
	constructor

	IProjGaussSeidel (const IProjGaussSeidel< TDomain, TAlgebra > &parent)
	clone constructor

void	project_correction (value_type &c_i, const size_t i)
	projects the correction on the underlying constraints set by the obstacleConstraints

	~IProjGaussSeidel ()
	Destructor.

Public Member Functions inherited from ug::GaussSeidelBase< TAlgebra >
void	enable_consistent_interfaces (bool enable)
	activates the new parallelization approach (disabled by default)

void	enable_overlap (bool enable)

	GaussSeidelBase ()

	GaussSeidelBase (const GaussSeidelBase< TAlgebra > &parent)
	clone constructor

void	set_ordering_algorithm (SmartPtr< ordering_algo_type > ordering_algo)
	sets an ordering algorithm

void	set_sor_relax (number relaxFactor)
	set relaxation parameter to define a SOR-method

Public Member Functions inherited from ug::IPreconditioner< TAlgebra >
virtual bool	apply (vector_type &c, const vector_type &d)
	compute new correction c = B*d

virtual bool	apply_update_defect (vector_type &c, vector_type &d)
	compute new correction c = Bd and update defect d:= d - Lc

SmartPtr< MatrixOperator< matrix_type, vector_type > >	approx_operator ()
	underlying matrix based operator used for the preconditioner

SmartPtr< MatrixOperator< matrix_type, vector_type > >	defect_operator ()
	underlying matrix based operator for calculation of defect

virtual bool	init (SmartPtr< ILinearOperator< vector_type > > J, const vector_type &u)
	implements the ILinearIterator-interface for matrix based preconditioner

bool	init (SmartPtr< ILinearOperator< vector_type > > L)
	implements the ILinearIterator-interface for matrix based preconditioner

bool	init (SmartPtr< MatrixOperator< matrix_type, vector_type > > Op)
	initializes the preconditioner for a matrix based operator

	IPreconditioner ()
	default constructor

	IPreconditioner (const IPreconditioner< TAlgebra > &parent)
	clone constructor

	IPreconditioner (SmartPtr< IDebugWriter< algebra_type > > spDebugWriter)
	constructor setting debug writer

virtual void	set_approximation (SmartPtr< MatrixOperator< matrix_type, vector_type > > approx)

virtual	~IPreconditioner ()
	virtual destructor

Public Member Functions inherited from ug::ILinearIterator< TAlgebra::vector_type >
virtual std::string	config_string () const

SmartPtr< IDamping< TAlgebra::vector_type, TAlgebra::vector_type > >	damping ()
	returns the scaling

	ILinearIterator ()
	constructor

	ILinearIterator (const ILinearIterator< TAlgebra::vector_type, TAlgebra::vector_type > &parent)
	copy constructor

virtual bool	init (SmartPtr< ILinearOperator< TAlgebra::vector_type, TAlgebra::vector_type > > J, const TAlgebra::vector_type &u)=0
	initialize for operator J(u) and linearization point u

virtual bool	init (SmartPtr< ILinearOperator< TAlgebra::vector_type, TAlgebra::vector_type > > L)=0
	initialize for linear operator L

void	set_damp (number factor)
	sets the damping to a constant factor

void	set_damp (SmartPtr< IDamping< TAlgebra::vector_type, TAlgebra::vector_type > > spScaling)
	sets a scaling for the correction

virtual	~ILinearIterator ()
	virtual destructor

Public Member Functions inherited from ug::DebugWritingObject< TAlgebra >
SmartPtr< IDebugWriter< algebra_type > >	debug_writer ()
	returns the debug writer

ConstSmartPtr< IDebugWriter< algebra_type > >	debug_writer () const

bool	debug_writer_valid () const
	returns true if the debug writer is set

	DebugWritingObject ()

	DebugWritingObject (const DebugWritingObject< algebra_type > &parent)
	clone constructor

	DebugWritingObject (SmartPtr< IDebugWriter< algebra_type > > spDebugWriter)

virtual void	set_debug (SmartPtr< IDebugWriter< algebra_type > > spDebugWriter)
	set debug writer

virtual	~DebugWritingObject ()
	virtual destructor

Public Member Functions inherited from ug::VectorDebugWritingObject< TAlgebra::vector_type >
virtual void	set_debug (SmartPtr< IVectorDebugWriter< vector_type > > spDebugWriter)
	set debug writer

SmartPtr< IVectorDebugWriter< vector_type > >	vector_debug_writer ()
	returns the debug writer

ConstSmartPtr< IVectorDebugWriter< vector_type > >	vector_debug_writer () const

bool	vector_debug_writer_valid () const
	returns true if the debug writer is set

	VectorDebugWritingObject ()

	VectorDebugWritingObject (SmartPtr< IVectorDebugWriter< vector_type > > spDebugWriter)

void	write_debug (const vector_type &vec, const char *filename)
	writing debug output for a vector (if debug writer set)

virtual	~VectorDebugWritingObject ()
	virtual destructor

Protected Member Functions
virtual const char *	name () const
	name

Protected Member Functions inherited from ug::GaussSeidelBase< TAlgebra >
virtual bool	postprocess ()
	cleans the operator

virtual bool	preprocess (SmartPtr< MatrixOperator< matrix_type, vector_type > > pOp)
	initializes the preconditioner

virtual void	step (const matrix_type &A, vector_type &c, const vector_type &d, const number relax)=0

virtual bool	step (SmartPtr< MatrixOperator< matrix_type, vector_type > > pOp, vector_type &c, const vector_type &d)
	computes a new correction c = B*d

virtual bool	supports_parallel () const
	returns if parallel solving is supported

Protected Member Functions inherited from ug::DebugWritingObject< TAlgebra >
void	enter_debug_writer_section (const char *secDir)
	enters a debugging section

void	enter_debug_writer_section (std::string secDir)
	enters a debugging section

void	leave_debug_writer_section ()
	leaves a debugging section

void	write_debug (const matrix_type &mat, const char *filename)
	write debug output for a matrix (if debug writer set)

void	write_debug (const matrix_type &mat, std::string name)
	write debug output for a matrix (if debug writer set)

Protected Member Functions inherited from ug::VectorDebugWritingObject< TAlgebra::vector_type >
void	enter_vector_debug_writer_section (const char *secDir)
	enters a debugging section

void	enter_vector_debug_writer_section (std::string secDir)
	enters a debugging section

void	leave_vector_debug_writer_section ()
	leaves a debugging section

void	print_debugger_message (const char *msg)
	prints a debugger message (listing all the sections)

void	print_debugger_message (std::string msg)
	prints a debugger message (listing all the sections)

virtual void	write_debug (const vector_type &vec, std::string name)
	writing debug output for a vector (if debug writer set)

Additional Inherited Members
Protected Attributes inherited from ug::IProjGaussSeidel< TDomain, TAlgebra >
vector< SmartPtr< IObstacleConstraint< TDomain, TAlgebra > > >	m_spvObsConstraint
	obstacle constraint

Protected Attributes inherited from ug::GaussSeidelBase< TAlgebra >
matrix_type	m_A

bool	m_bConsistentInterfaces

vector_type	m_oC

vector_type	m_oD
	for overlaps only

number	m_relax
	relaxation parameter

SmartPtr< ordering_algo_type >	m_spOrderingAlgo
	for ordering algorithms

bool	m_useOverlap

Protected Attributes inherited from ug::IPreconditioner< TAlgebra >
bool	m_bInit
	init flag indicating if init has been called

bool	m_bOtherApproxOperator

SmartPtr< MatrixOperator< matrix_type, vector_type > >	m_spApproxOperator
	underlying matrix based operator used for the preconditioner

SmartPtr< ILinearOperator< vector_type > >	m_spDefectOperator
	underlying matrix based operator for calculation of defect

Protected Attributes inherited from ug::ILinearIterator< TAlgebra::vector_type >
SmartPtr< IDamping< TAlgebra::vector_type, TAlgebra::vector_type > >	m_spDamping
	the scaling

Protected Attributes inherited from ug::DebugWritingObject< TAlgebra >
SmartPtr< IDebugWriter< algebra_type > >	m_spDebugWriter
	Debug Writer.

Protected Attributes inherited from ug::VectorDebugWritingObject< TAlgebra::vector_type >
SmartPtr< IVectorDebugWriter< vector_type > >	m_spVectorDebugWriter
	Debug Writer.

Detailed Description

template<typename TDomain, typename TAlgebra>
class ug::ProjGaussSeidel< TDomain, TAlgebra >

Projected GaussSeidel (SOR) -method.

The projected GaussSeidel method can be applied to problems of the form

A * u >= b        (I)
c(u) >= 0       (II)
c(u)^T * [A*u - b] = 0, (III)

where u, b are vectors and A is a matrix. '*' denotes componentwise multiplication. c(u) denotes an obstacle-function, which depends on the solution vector u. One possible example for such an obstacle-function could be the scalar obstacle function

u >= 0.

The obstacle function c(u) is defined by creating an instance of IObstacleConstraint, which is passed to the projected preconditioner by the method 'IProjPreconditioner::set_obstacle_constraint'.

Similar problems, which e.g. only differ in the sign in (I) and/or (II) can be equivalently treated by the method.

Note: Due to (II) the old solution needs to be stored within this method. This is a difference to the classical smoothers/preconditioners, which usually work on the correction and the defect only.

By calling 'set_sor_damp(number)' one gets the successive overrelaxation-version of the projected preconditioners of GaussSeidel type.

References:

A. Brandt and C. W. Cryer. Multigrid algorithms for the solution of linear
complementarity problems arising from free boundary problems. SIAM J. SCI. STAT. COMPUT. Vol. 4, No. 4 (1983)

Template Parameters

TAlgebra Algebra type

Member Typedef Documentation

◆ algebra_type

template<typename TDomain , typename TAlgebra >

typedef TAlgebra ug::ProjGaussSeidel< TDomain, TAlgebra >::algebra_type

Algebra type.

◆ base_type

template<typename TDomain , typename TAlgebra >

typedef IProjGaussSeidel<TDomain,TAlgebra> ug::ProjGaussSeidel< TDomain, TAlgebra >::base_type

Base class type.

◆ matrix_type

template<typename TDomain , typename TAlgebra >

typedef algebra_type::matrix_type ug::ProjGaussSeidel< TDomain, TAlgebra >::matrix_type

Matrix type.

◆ vector_type

template<typename TDomain , typename TAlgebra >

typedef algebra_type::vector_type ug::ProjGaussSeidel< TDomain, TAlgebra >::vector_type

Vector type.

Constructor & Destructor Documentation

◆ ProjGaussSeidel() [1/2]

template<typename TDomain , typename TAlgebra >

ug::ProjGaussSeidel< TDomain, TAlgebra >::ProjGaussSeidel ( )

inline

◆ ProjGaussSeidel() [2/2]

template<typename TDomain , typename TAlgebra >

ug::ProjGaussSeidel< TDomain, TAlgebra >::ProjGaussSeidel ( const ProjGaussSeidel< TDomain, TAlgebra > & parent )

inline

copy constructor

Member Function Documentation

◆ clone()

template<typename TDomain , typename TAlgebra >

virtual SmartPtr< ILinearIterator< vector_type > > ug::ProjGaussSeidel< TDomain, TAlgebra >::clone ( )

inlinevirtual

Clone.

Implements ug::ILinearIterator< TAlgebra::vector_type >.

References make_sp().

◆ name()

template<typename TDomain , typename TAlgebra >

virtual const char * ug::ProjGaussSeidel< TDomain, TAlgebra >::name ( ) const

inlineprotectedvirtual

name

Implements ug::IProjGaussSeidel< TDomain, TAlgebra >.

◆ step()

template<typename TDomain , typename TAlgebra >

void ug::ProjGaussSeidel< TDomain, TAlgebra >::step	(	const matrix_type &	mat,
		vector_type &	c,
		const vector_type &	d,
		const number	relax
	)

virtual

computes a new correction c = B*d and projects on the underlying constraint

Implements ug::IProjGaussSeidel< TDomain, TAlgebra >.

References ug::forward_gs_step().

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

ugbase/lib_algebra/operator/preconditioner/projected_gauss_seidel/proj_gauss_seidel.h
ugbase/lib_algebra/operator/preconditioner/projected_gauss_seidel/proj_gauss_seidel_impl.h

Public Types

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ algebra_type

◆ base_type

◆ matrix_type

◆ vector_type

Constructor & Destructor Documentation

◆ ProjGaussSeidel() [1/2]

◆ ProjGaussSeidel() [2/2]

Member Function Documentation

◆ clone()

◆ name()

◆ step()