operator implementation of the local Schur complement More...

#include <feti.h>

Inheritance diagram for ug::LocalSchurComplement< TAlgebra >:

Classes
struct	StepConv

Public Types
typedef TAlgebra	algebra_type

typedef TAlgebra::matrix_type	matrix_type

typedef TAlgebra::vector_type	vector_type

Public Types inherited from ug::ILinearOperator< TAlgebra::vector_type, 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::IOperator< X, Y >
typedef Y	codomain_function_type
	Range space.

typedef X	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 void	apply (vector_type &f, const vector_type &u)

virtual void	apply_sub (vector_type &f, const vector_type &u)
	solves the system

void	clear_total_itercnt_of_inner_solvers ()

int	get_total_itercnt_of_inner_solvers ()

virtual void	init ()
	initializes the solver for operator A

void	init (const vector_type &u)
	implementation of the operator for the solution dependent initialization.

	LocalSchurComplement ()
	constructor

virtual const char *	name () const
	name of solver

void	print_statistic_of_inner_solver (bool bPrintOnlyAverages)
	prints some convergence statistic of inner solvers

void	set_dirichlet_solver (SmartPtr< ILinearOperatorInverse< vector_type > > dirichletSolver)
	sets a sequential Dirichlet solver

void	set_feti_layouts (FetiLayouts< algebra_type > &fetiLayouts)
	sets the primal layouts

void	set_matrix (SmartPtr< MatrixOperator< matrix_type, vector_type > > A)
	set original matrix from which the local Schur complement is constructed

void	set_statistic_type (std::string type)
	sets statistic slot where next iterate should be counted

virtual	~LocalSchurComplement ()

Public Member Functions inherited from ug::ILinearOperator< TAlgebra::vector_type, TAlgebra::vector_type >
virtual void	prepare (TAlgebra::vector_type &u)
	default implementation for IOperator interface

virtual	~ILinearOperator ()
	virtual destructor

Public Member Functions inherited from ug::IOperator< X, Y >
virtual void	apply (Y &d, const X &u)=0
	computes the nonlinear mapping d := N(u)

virtual void	prepare (X &u)=0
	prepares domain and codomain functions for application

virtual	~IOperator ()
	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 Attributes
int	m_applyCnt

std::map< std::string, std::vector< StepConv > >	m_mvStepConv

matrix_type *	m_pDirichletMatrix

FetiLayouts< algebra_type > *	m_pFetiLayouts

matrix_type *	m_pMatrix

SmartPtr< MatrixOperator< matrix_type, vector_type > >	m_spDirichletOperator

SmartPtr< ILinearOperatorInverse< vector_type > >	m_spDirichletSolver

SmartPtr< MatrixOperator< matrix_type, vector_type > >	m_spOperator

std::string	m_statType

int	m_totalIterCntOfInnerSolvers

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.

Additional Inherited Members
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)

Detailed Description

template<typename TAlgebra>
class ug::LocalSchurComplement< TAlgebra >

operator implementation of the local Schur complement

This operator is the application of the local Schur complement \(S_{\Delta}^{i}\). The underlying matrix must have at least two layouts. The first layout, layout level 0, will be used to describe subdomain internal interfaces (i.e. "pure" processor interfaces), all other layouts are used to identify the boundary, layout level 1: \( \Delta \) (edges of subdomains), layout level 2: \( \Pi \) (vertices of subdomains, a.k.a. "cross points") - will be constructed here, and the Schur complement is build w.r.t. to these variables.

Member Typedef Documentation

◆ algebra_type

template<typename TAlgebra >

typedef TAlgebra ug::LocalSchurComplement< TAlgebra >::algebra_type

◆ matrix_type

template<typename TAlgebra >

typedef TAlgebra::matrix_type ug::LocalSchurComplement< TAlgebra >::matrix_type

◆ vector_type

template<typename TAlgebra >

typedef TAlgebra::vector_type ug::LocalSchurComplement< TAlgebra >::vector_type

Constructor & Destructor Documentation

◆ LocalSchurComplement()

template<typename TAlgebra >

ug::LocalSchurComplement< TAlgebra >::LocalSchurComplement ( )

constructor

References new().

◆ ~LocalSchurComplement()

template<typename TAlgebra >

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

inlinevirtual

Member Function Documentation

◆ apply()

template<typename TAlgebra >

void ug::LocalSchurComplement< TAlgebra >::apply	(	vector_type &	f,
		const vector_type &	u
	)

virtual

applies the Schur complement built from matrix operator set via 'set_matrix()' to 'u' and returns the result 'f := S times u'

Implements ug::ILinearOperator< TAlgebra::vector_type, TAlgebra::vector_type >.

References FETI_PROFILE_BEGIN, ug::LocalSchurComplement< TAlgebra >::StepConv::lastDef3b, name, ug::LocalSchurComplement< TAlgebra >::StepConv::numIter3b, pcl::ProcRank(), ug::PST_ADDITIVE, ug::PST_CONSISTENT, SPNULL, UG_LOG_ALL_PROCS, and UG_THROW.

◆ apply_sub()

template<typename TAlgebra >

void ug::LocalSchurComplement< TAlgebra >::apply_sub	(	vector_type &	f,
		const vector_type &	u
	)

virtual

solves the system

Implements ug::ILinearOperator< TAlgebra::vector_type, TAlgebra::vector_type >.

References FETI_PROFILE_BEGIN.

◆ clear_total_itercnt_of_inner_solvers()

template<typename TAlgebra >

void ug::LocalSchurComplement< TAlgebra >::clear_total_itercnt_of_inner_solvers ( )

inline

References ug::LocalSchurComplement< TAlgebra >::m_totalIterCntOfInnerSolvers.

Referenced by ug::FETISolver< TAlgebra >::print_statistic_of_inner_solver().

◆ get_total_itercnt_of_inner_solvers()

template<typename TAlgebra >

int ug::LocalSchurComplement< TAlgebra >::get_total_itercnt_of_inner_solvers ( )

inline

References ug::LocalSchurComplement< TAlgebra >::m_totalIterCntOfInnerSolvers.

Referenced by ug::FETISolver< TAlgebra >::print_statistic_of_inner_solver().

◆ init() [1/2]

template<typename TAlgebra >

void ug::LocalSchurComplement< TAlgebra >::init ( )

virtual

initializes the solver for operator A

This method must be called, before the apply() method can be invoked. It has to be called each time, when the matrix has been replaced. A deep copy of the matrix is then constructed and in this copy the rows belonging to the \(\Delta\) and \(\Pi\) unknowns are set to identity rows. This matrix is used in the solution of the local dirichlet problem.

Implements ug::ILinearOperator< TAlgebra::vector_type, TAlgebra::vector_type >.

References UG_THROW.

◆ init() [2/2]

template<typename TAlgebra >

void ug::LocalSchurComplement< TAlgebra >::init ( const vector_type & u )

inlinevirtual

implementation of the operator for the solution dependent initialization.

Implements ug::ILinearOperator< TAlgebra::vector_type, TAlgebra::vector_type >.

References ug::LocalSchurComplement< TAlgebra >::init().

Referenced by ug::LocalSchurComplement< TAlgebra >::init().

◆ name()

template<typename TAlgebra >

virtual const char * ug::LocalSchurComplement< TAlgebra >::name ( ) const

inlinevirtual

name of solver

◆ print_statistic_of_inner_solver()

template<typename TAlgebra >

void ug::LocalSchurComplement< TAlgebra >::print_statistic_of_inner_solver ( bool bPrintOnlyAverages )

prints some convergence statistic of inner solvers

References pcl::ProcessCommunicator::allreduce(), pcl::NumProcs(), PCL_DT_DOUBLE, PCL_DT_INT, PCL_RO_MAX, PCL_RO_MIN, PCL_RO_SUM, and UG_LOG.

Referenced by ug::FETISolver< TAlgebra >::print_statistic_of_inner_solver().

◆ set_dirichlet_solver()

template<typename TAlgebra >

void ug::LocalSchurComplement< TAlgebra >::set_dirichlet_solver ( SmartPtr< ILinearOperatorInverse< vector_type > > dirichletSolver )

inline

sets a sequential Dirichlet solver

This method sets the Dirichlet Solver that is used to invert the inner matrix \(A_{II}\)

References ug::LocalSchurComplement< TAlgebra >::m_spDirichletSolver.

◆ set_feti_layouts()

template<typename TAlgebra >

void ug::LocalSchurComplement< TAlgebra >::set_feti_layouts ( FetiLayouts< algebra_type > & fetiLayouts )

inline

sets the primal layouts

References ug::LocalSchurComplement< TAlgebra >::m_pFetiLayouts.

◆ set_matrix()

template<typename TAlgebra >

void ug::LocalSchurComplement< TAlgebra >::set_matrix ( SmartPtr< MatrixOperator< matrix_type, vector_type > > A )

inline

set original matrix from which the local Schur complement is constructed

Using this method, the original matrix A is set. Given the matrix in the form \( A = \sum\limits_{p=1}^{N} A^{(p)}\) in additive form, with

\begin{align*} A^{(p)} \begin{pmatrix} A_{II}^{(p)} & A_{I \Delta}^{(p)} & A_{I \Pi}^{(p)} \\ A_{\Delta I}^{(p)} & A_{\Delta \Delta}^{(p)} & A_{\Delta \Pi}^{(p)} \\ A_{\Pi I}^{(p)} & A_{\Pi \Delta}^{(p)} & A_{\Pi \Pi}^{(p)} \end{pmatrix} \end{align*}

the local Schur complement is the processwise application of the operator

\begin{align*} S_{\Delta \Delta} = A_{\Delta \Delta} - \begin{pmatrix} A_{I \Delta}^T & A_{\Pi \Delta}^T \end{pmatrix} \begin{pmatrix} A_{II} & A_{I \Pi} \\ A_{\Pi I} & A_{\Pi \Pi} \end{pmatrix}^{-1} \begin{pmatrix} A_{I \Delta} \\ A_{\Pi \Delta} \end{pmatrix} * \end{align*}

References ug::LocalSchurComplement< TAlgebra >::m_spOperator.

◆ set_statistic_type()

template<typename TAlgebra >

void ug::LocalSchurComplement< TAlgebra >::set_statistic_type ( std::string type )

inline

sets statistic slot where next iterate should be counted

References ug::LocalSchurComplement< TAlgebra >::m_statType.

Member Data Documentation

◆ m_applyCnt

template<typename TAlgebra >

int ug::LocalSchurComplement< TAlgebra >::m_applyCnt

protected

◆ m_mvStepConv

template<typename TAlgebra >

std::map<std::string, std::vector<StepConv> > ug::LocalSchurComplement< TAlgebra >::m_mvStepConv

protected

◆ m_pDirichletMatrix

template<typename TAlgebra >

matrix_type* ug::LocalSchurComplement< TAlgebra >::m_pDirichletMatrix

protected

◆ m_pFetiLayouts

template<typename TAlgebra >

FetiLayouts<algebra_type>* ug::LocalSchurComplement< TAlgebra >::m_pFetiLayouts

protected

Referenced by ug::LocalSchurComplement< TAlgebra >::set_feti_layouts().

◆ m_pMatrix

template<typename TAlgebra >

matrix_type* ug::LocalSchurComplement< TAlgebra >::m_pMatrix

protected

◆ m_spDirichletOperator

template<typename TAlgebra >

SmartPtr<MatrixOperator<matrix_type, vector_type> > ug::LocalSchurComplement< TAlgebra >::m_spDirichletOperator

protected

◆ m_spDirichletSolver

template<typename TAlgebra >

SmartPtr<ILinearOperatorInverse<vector_type> > ug::LocalSchurComplement< TAlgebra >::m_spDirichletSolver

protected

Referenced by ug::LocalSchurComplement< TAlgebra >::set_dirichlet_solver().

◆ m_spOperator

template<typename TAlgebra >

SmartPtr<MatrixOperator<matrix_type,vector_type> > ug::LocalSchurComplement< TAlgebra >::m_spOperator

protected

Referenced by ug::LocalSchurComplement< TAlgebra >::set_matrix().

◆ m_statType

template<typename TAlgebra >

std::string ug::LocalSchurComplement< TAlgebra >::m_statType

protected

Referenced by ug::LocalSchurComplement< TAlgebra >::set_statistic_type().

◆ m_totalIterCntOfInnerSolvers

template<typename TAlgebra >

int ug::LocalSchurComplement< TAlgebra >::m_totalIterCntOfInnerSolvers

protected

Referenced by ug::LocalSchurComplement< TAlgebra >::clear_total_itercnt_of_inner_solvers(), and ug::LocalSchurComplement< TAlgebra >::get_total_itercnt_of_inner_solvers().

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

ugbase/lib_algebra/operator/linear_solver/feti.h
ugbase/lib_algebra/operator/linear_solver/feti.cpp

Classes

Public Types

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ algebra_type

◆ matrix_type

◆ vector_type

Constructor & Destructor Documentation

◆ LocalSchurComplement()

◆ ~LocalSchurComplement()

Member Function Documentation

◆ apply()

◆ apply_sub()

◆ clear_total_itercnt_of_inner_solvers()

◆ get_total_itercnt_of_inner_solvers()

◆ init() [1/2]

◆ init() [2/2]

◆ name()

◆ print_statistic_of_inner_solver()

◆ set_dirichlet_solver()

◆ set_feti_layouts()

◆ set_matrix()

◆ set_statistic_type()

Member Data Documentation

◆ m_applyCnt

◆ m_mvStepConv

◆ m_pDirichletMatrix

◆ m_pFetiLayouts

◆ m_pMatrix

◆ m_spDirichletOperator

◆ m_spDirichletSolver

◆ m_spOperator

◆ m_statType

◆ m_totalIterCntOfInnerSolvers