Jacobi-Iteration. More...

#include <jacobi.h>

Inheritance diagram for ug::Jacobi< TAlgebra >:

Public Types
typedef TAlgebra	algebra_type
	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
	Matrix type.

typedef TAlgebra::vector_type	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.

	Jacobi ()
	default constructor

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

	Jacobi (number damp)
	constructor setting the damping parameter

void	set_block (bool b)
	sets if blocked jacobi is used (inverting block-diagonal), or plain (scalar) diagonal if false

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

virtual	~Jacobi ()
	Destructor.

Public Member Functions inherited from ug::IPreconditioner< TAlgebra >
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 Types
typedef block_traits< typenamematrix_type::value_type >::inverse_type	inverse_type
	type of block-inverse

Protected Member Functions
virtual bool	apply (vector_type &c, const vector_type &d)
	compute new correction c = B*d

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

virtual const char *	name () const
	Name of preconditioner.

virtual bool	postprocess ()
	Postprocess routine.

virtual bool	preprocess (SmartPtr< MatrixOperator< matrix_type, vector_type > > pOp)
	Preprocess routine.

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

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)

Protected Attributes
bool	m_bBlock

std::vector< inverse_type >	m_diagInv
	storage of the inverse diagonal in parallel

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 TAlgebra>
class ug::Jacobi< TAlgebra >

Jacobi-Iteration.

Here, the Jacobi-iteration is described for solving the linear equation

\f$ A * x = b.      A \in R^{nxn}, x \in R^n, b \in R^n \f$.

Most of the common linear iteration-methods base on the decomposition of A into its diagonal (D) and strict-upper(-U) and strict-lower part (-L),

\( A = D - L - U \).

Among others, W. Hackbusch ('Iterative Loesung grosser Gleichungssysteme'), distinguishes three different forms for describing a linear iteration scheme. The general 'first normal-form' of a linear iteration scheme takes the form

\( x^{m+1} = M * x^m + N * b \),

with some Matrices \( M \) and \( N \in R^{nxn} \). m denotes the iteration index. The general 'second normal-form' of a linear iteration scheme takes the form

\( x^{m+1} = x^m - N * (A * x^m - b) \).

Those linear iteration schemes, which can be represented by the second normal-form are the linear, consistent iteration schemes.

Introducing the correction \( c{m+1} := x^{m+1} - x^m \) and the defect \( d^m := b - A * x^m \) the second normal-form can be rewritten as

\( c = N * d \).

The matrix of the second normal-form for the Jacobi-method takes the simple form

\( N = D^{-1} \). .

References:

W. Hackbusch. Iterative Loesung grosser Gleichungssysteme

Jacobi Preconditioner

Member Typedef Documentation

◆ algebra_type

template<typename TAlgebra >

typedef TAlgebra ug::Jacobi< TAlgebra >::algebra_type

Algebra type.

◆ base_type

template<typename TAlgebra >

typedef IPreconditioner<TAlgebra> ug::Jacobi< TAlgebra >::base_type

Base type.

◆ inverse_type

template<typename TAlgebra >

typedef block_traits<typenamematrix_type::value_type>::inverse_type ug::Jacobi< TAlgebra >::inverse_type

protected

type of block-inverse

◆ matrix_operator_type

template<typename TAlgebra >

typedef IPreconditioner<TAlgebra>::matrix_operator_type ug::Jacobi< TAlgebra >::matrix_operator_type

Matrix Operator type.

◆ matrix_type

template<typename TAlgebra >

typedef TAlgebra::matrix_type ug::Jacobi< TAlgebra >::matrix_type

Matrix type.

◆ vector_type

template<typename TAlgebra >

typedef TAlgebra::vector_type ug::Jacobi< TAlgebra >::vector_type

Vector type.

Constructor & Destructor Documentation

◆ Jacobi() [1/3]

template<typename TAlgebra >

ug::Jacobi< TAlgebra >::Jacobi ( )

inline

default constructor

References ug::Jacobi< TAlgebra >::m_bBlock, and ug::ILinearIterator< TAlgebra::vector_type >::set_damp().

◆ Jacobi() [2/3]

template<typename TAlgebra >

ug::Jacobi< TAlgebra >::Jacobi ( number damp )

inline

constructor setting the damping parameter

References ug::Jacobi< TAlgebra >::m_bBlock, and ug::ILinearIterator< TAlgebra::vector_type >::set_damp().

◆ Jacobi() [3/3]

template<typename TAlgebra >

ug::Jacobi< TAlgebra >::Jacobi ( const Jacobi< TAlgebra > & parent )

inline

clone constructor

References ug::Jacobi< TAlgebra >::m_bBlock, and ug::Jacobi< TAlgebra >::set_block().

◆ ~Jacobi()

template<typename TAlgebra >

virtual ug::Jacobi< TAlgebra >::~Jacobi ( )

inlinevirtual

Destructor.

Member Function Documentation

◆ apply()

template<typename TAlgebra >

virtual bool ug::Jacobi< TAlgebra >::apply	(	vector_type &	c,
		const vector_type &	d
	)

inlineprotectedvirtual

compute new correction c = B*d

This method implements the virtual method of the ILinearIterator-interface. Basically, besides some common checks the request is forwarded to the (virtual) 'step'-method.

Parameters