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MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node > Class Template Reference

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

#include <MueLu_Constraint_decl.hpp>

Inheritance diagram for MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >:
MueLu::BaseClass MueLu::VerboseObject MueLu::Describable Teuchos::VerboseObject< VerboseObject > Teuchos::Describable Teuchos::VerboseObjectBase Teuchos::LabeledObject

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 void SetMueLuOFileStream (const std::string &filename)
 
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 = DefaultScalar, class LocalOrdinal = DefaultLocalOrdinal, class GlobalOrdinal = DefaultGlobalOrdinal, class Node = DefaultNode>
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 69 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 33 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 100 of file MueLu_Constraint_def.hpp.

template<class Scalar = DefaultScalar, class LocalOrdinal = DefaultLocalOrdinal, class GlobalOrdinal = DefaultGlobalOrdinal, class Node = DefaultNode>
RCP<const CrsGraph> MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >::GetPattern ( ) const
inline

Definition at line 98 of file MueLu_Constraint_decl.hpp.

Member Data Documentation

template<class Scalar = DefaultScalar, class LocalOrdinal = DefaultLocalOrdinal, class GlobalOrdinal = DefaultGlobalOrdinal, class Node = DefaultNode>
RCP<MultiVector> MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >::X_
private

Overlapped coarse nullspace.

Definition at line 103 of file MueLu_Constraint_decl.hpp.

template<class Scalar = DefaultScalar, class LocalOrdinal = DefaultLocalOrdinal, class GlobalOrdinal = DefaultGlobalOrdinal, class Node = DefaultNode>
RCP<const CrsGraph> MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >::Ppattern_
private

Nonzero sparsity pattern.

Definition at line 104 of file MueLu_Constraint_decl.hpp.

template<class Scalar = DefaultScalar, class LocalOrdinal = DefaultLocalOrdinal, class GlobalOrdinal = DefaultGlobalOrdinal, class Node = DefaultNode>
ArrayRCP<Teuchos::SerialDenseMatrix<LO, SC> > MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >::XXtInv_
private

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

Definition at line 105 of file MueLu_Constraint_decl.hpp.

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