Constraint space information for the potential prolongator. More...

#include <MueLu_Constraint_decl.hpp>

Inheritance diagram for MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >:

Public Member Functions
RCP< const CrsGraph >	GetPattern () const

Public Member Functions inherited from MueLu::BaseClass
virtual	~BaseClass ()
	Destructor. More...

Public Member Functions inherited from MueLu::VerboseObject
VerbLevel	GetVerbLevel () const
	Get the verbosity level. More...

void	SetVerbLevel (const VerbLevel verbLevel)
	Set the verbosity level of this object. More...

int	GetProcRankVerbose () const
	Get proc rank used for printing. Do not use this information for any other purpose. More...

int	SetProcRankVerbose (int procRank) const
	Set proc rank used for printing. More...

bool	IsPrint (MsgType type, int thisProcRankOnly=-1) const
	Find out whether we need to print out information for a specific message type. More...

Teuchos::FancyOStream &	GetOStream (MsgType type, int thisProcRankOnly=0) const
	Get an output stream for outputting the input message type. More...

Teuchos::FancyOStream &	GetBlackHole () const

	VerboseObject ()

virtual	~VerboseObject ()
	Destructor. More...

Public Member Functions inherited from Teuchos::VerboseObject< VerboseObject >
	VerboseObject (const EVerbosityLevel verbLevel=VERB_DEFAULT, const RCP< FancyOStream > &oStream=Teuchos::null)

virtual const VerboseObject &	setVerbLevel (const EVerbosityLevel verbLevel) const

virtual const VerboseObject &	setOverridingVerbLevel (const EVerbosityLevel verbLevel) const

virtual EVerbosityLevel	getVerbLevel () const

TEUCHOSPARAMETERLIST_LIB_DLL_EXPORT RCP< const ParameterList >	getValidVerboseObjectSublist ()

TEUCHOSPARAMETERLIST_LIB_DLL_EXPORT void	setupVerboseObjectSublist (ParameterList *paramList)

TEUCHOSPARAMETERLIST_LIB_DLL_EXPORT void	readVerboseObjectSublist (ParameterList paramList, RCP< FancyOStream > oStream, EVerbosityLevel *verbLevel)

void	readVerboseObjectSublist (ParameterList paramList, VerboseObject< ObjectType > verboseObject)

Public Member Functions inherited from Teuchos::VerboseObjectBase
virtual	~VerboseObjectBase ()

	VerboseObjectBase (const RCP< FancyOStream > &oStream=Teuchos::null)

virtual const VerboseObjectBase &	setOStream (const RCP< FancyOStream > &oStream) const

virtual const VerboseObjectBase &	setOverridingOStream (const RCP< FancyOStream > &oStream) const

virtual VerboseObjectBase &	setLinePrefix (const std::string &linePrefix)

virtual RCP< FancyOStream >	getOStream () const

virtual RCP< FancyOStream >	getOverridingOStream () const

virtual std::string	getLinePrefix () const

virtual OSTab	getOSTab (const int tabs=1, const std::string &linePrefix="") const

Public Member Functions inherited from MueLu::Describable
virtual	~Describable ()
	Destructor. More...

virtual std::string	ShortClassName () const
	Return the class name of the object, without template parameters and without namespace. More...

virtual void	describe (Teuchos::FancyOStream &out_arg, const VerbLevel verbLevel=Default) const

virtual std::string	description () const
	Return a simple one-line description of this object. More...

void	describe (Teuchos::FancyOStream &out, const Teuchos::EVerbosityLevel verbLevel=Teuchos::Describable::verbLevel_default) const
	Print the object with some verbosity level to an FancyOStream object. More...

Public Member Functions inherited from Teuchos::Describable
void	describe (std::ostream &out, const EVerbosityLevel verbLevel=verbLevel_default) const

	LabeledObject ()

virtual	~LabeledObject ()

virtual void	setObjectLabel (const std::string &objectLabel)

virtual std::string	getObjectLabel () const

DescribableStreamManipulatorState	describe (const Describable &describable, const EVerbosityLevel verbLevel=Describable::verbLevel_default)

std::ostream &	operator<< (std::ostream &os, const DescribableStreamManipulatorState &d)

Private Attributes
RCP< MultiVector >	X_
	Overlapped coarse nullspace. More...

RCP< const CrsGraph >	Ppattern_
	Nonzero sparsity pattern. More...

ArrayRCP < Teuchos::SerialDenseMatrix < LO, SC > >	XXtInv_
	Array storing \((Q_i Q_i^H)^{-1}\). More...

Setup methods.
void	Setup (const MultiVector &B, const MultiVector &Bc, RCP< const CrsGraph > Ppattern)

Apply methods.
void	Apply (const Matrix &P, Matrix &Projected) const
	Apply constraint. More...

Additional Inherited Members
Static Public Member Functions inherited from MueLu::VerboseObject
static void	SetMueLuOStream (const Teuchos::RCP< Teuchos::FancyOStream > &mueluOStream)

static Teuchos::RCP < Teuchos::FancyOStream >	GetMueLuOStream ()

static void	SetDefaultVerbLevel (const VerbLevel defaultVerbLevel)
	Set the default (global) verbosity level. More...

static VerbLevel	GetDefaultVerbLevel ()
	Get the default (global) verbosity level. More...

Static Public Member Functions inherited from Teuchos::VerboseObject< VerboseObject >
static void	setDefaultVerbLevel (const EVerbosityLevel defaultVerbLevel)

static EVerbosityLevel	getDefaultVerbLevel ()

Static Public Member Functions inherited from Teuchos::VerboseObjectBase
static void	setDefaultOStream (const RCP< FancyOStream > &defaultOStream)

static RCP< FancyOStream >	getDefaultOStream ()

Static Public Attributes inherited from Teuchos::Describable
static const EVerbosityLevel	verbLevel_default

Protected Member Functions inherited from Teuchos::VerboseObject< VerboseObject >
void	initializeVerboseObject (const EVerbosityLevel verbLevel=VERB_DEFAULT, const RCP< FancyOStream > &oStream=Teuchos::null)

Protected Member Functions inherited from Teuchos::VerboseObjectBase
void	initializeVerboseObjectBase (const RCP< FancyOStream > &oStream=Teuchos::null)

virtual void	informUpdatedVerbosityState () const

Detailed Description

template<class Scalar = double, class LocalOrdinal = int, class GlobalOrdinal = LocalOrdinal, class Node = KokkosClassic::DefaultNode::DefaultNodeType>
class MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >

Constraint space information for the potential prolongator.

This class implements an idea of the constrained space. In energy minimization, constrained space is used simultaneously with the iterative method to construct the final prolongator. The space has two different constraints.

Nonzero pattern constraint

Nonzero pattern constraint means that the final prolongator must have the provided nonzero pattern. This is achieved on each step of the iterative method by restricting the graph of the temporary prolongator to the desired pattern. It is implemented in the Apply function.

Note: We do not update the graph of the provided temporary prolongator as this is a very expensive procedure. Rather, we extract its values and replace some of the values of the matrix with the correct graph.

Coarse space approximation constraint

Generally, the coarse space constraint is presented by some matrix (X or Q) (see, for instance, the article by Mandel, Brezina and Vanek '99. It is well known that this matrix can be permuted to have a block diagonal form, where each block corresponds to a row in the prolongator. Specifically, let P be the prolongator, and Q be the constraint matrix. Then the constraint is generally written as \(Q P = B,\) where B is the fine nullspace multivector. Q is a block diagonal matrix, \(Q = diag(Q_1, ..., Q_n)\), where n is the number of rows in P. Each block Q_i is of size NSDim x nnz_i, where NSDim is the number of fine nullspace vectors, and nnz_i is the number of nonzero elements in the i-th row of P.

To constrain the potential prolongator (with correct sparsity pattern, i.e. after the application of the nonzero pattern constraint), one updates its values as

\[P = P - Q^H(QQ^H)^{-1}QP.\]

Because of the block diagonal form of Q, this can be done row-by-row.

Note: For efficiency reasons, we store
\[(QQ^H)^{-1}\]
in the XXtInv_ array. These matrices are dense, but have small size (NSDim x NSDim).

Definition at line 106 of file MueLu_Constraint_decl.hpp.

Member Function Documentation

template<class Scalar , class LocalOrdinal , class GlobalOrdinal , class Node >

void Constraint::Setup	(	const MultiVector &	B,
		const MultiVector &	Bc,
		RCP< const CrsGraph >	Ppattern
	)

Setup constraint.

Parameters

B	– Fine nullspace vectors
Bc	– Coarse nullspace vectors
Ppattern	– Nonzero sparsity pattern for the prolongator

Definition at line 70 of file MueLu_Constraint_def.hpp.

template<class Scalar , class LocalOrdinal , class GlobalOrdinal , class Node >

void Constraint::Apply	(	const Matrix &	P,
		Matrix &	Projected
	)		const

Apply constraint.

Note: We assume that the graph of Projected is the same as Ppattern_

Definition at line 137 of file MueLu_Constraint_def.hpp.

template<class Scalar = double, class LocalOrdinal = int, class GlobalOrdinal = LocalOrdinal, class Node = KokkosClassic::DefaultNode::DefaultNodeType>

RCP<const CrsGraph> MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >::GetPattern ( ) const

inline

Definition at line 136 of file MueLu_Constraint_decl.hpp.

Member Data Documentation

template<class Scalar = double, class LocalOrdinal = int, class GlobalOrdinal = LocalOrdinal, class Node = KokkosClassic::DefaultNode::DefaultNodeType>

RCP<MultiVector> MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >::X_

private

Overlapped coarse nullspace.

Definition at line 141 of file MueLu_Constraint_decl.hpp.

template<class Scalar = double, class LocalOrdinal = int, class GlobalOrdinal = LocalOrdinal, class Node = KokkosClassic::DefaultNode::DefaultNodeType>

RCP<const CrsGraph> MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >::Ppattern_

private

Nonzero sparsity pattern.

Definition at line 142 of file MueLu_Constraint_decl.hpp.

template<class Scalar = double, class LocalOrdinal = int, class GlobalOrdinal = LocalOrdinal, class Node = KokkosClassic::DefaultNode::DefaultNodeType>

ArrayRCP<Teuchos::SerialDenseMatrix<LO,SC> > MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >::XXtInv_

private

Array storing \((Q_i Q_i^H)^{-1}\).

Definition at line 143 of file MueLu_Constraint_decl.hpp.

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

Public Member Functions

Private Attributes

Setup methods.

Apply methods.

Additional Inherited Members

Detailed Description

template<class Scalar = double, class LocalOrdinal = int, class GlobalOrdinal = LocalOrdinal, class Node = KokkosClassic::DefaultNode::DefaultNodeType> class MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >

Nonzero pattern constraint

Coarse space approximation constraint

Member Function Documentation

Member Data Documentation

template<class Scalar = double, class LocalOrdinal = int, class GlobalOrdinal = LocalOrdinal, class Node = KokkosClassic::DefaultNode::DefaultNodeType>
class MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >