MueLu Version of the Day
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Constraint space information for the potential prolongator. More...
#include <MueLu_Constraint_decl.hpp>
Apply methods. | |
RCP< MultiVector > | X_ |
Overlapped coarse nullspace. | |
RCP< const CrsGraph > | Ppattern_ |
Nonzero sparsity pattern. | |
ArrayRCP< Teuchos::SerialDenseMatrix< LO, SC > > | XXtInv_ |
Array storing \((Q_i Q_i^H)^{-1}\). | |
void | Apply (const Matrix &P, Matrix &Projected) const |
Apply constraint. | |
RCP< const CrsGraph > | GetPattern () const |
Setup methods. | |
void | Setup (const MultiVector &B, const MultiVector &Bc, RCP< const CrsGraph > Ppattern) |
Additional Inherited Members | |
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virtual | ~BaseClass () |
Destructor. | |
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VerboseObject () | |
virtual | ~VerboseObject () |
Destructor. | |
VerbLevel | GetVerbLevel () const |
Get the verbosity level. | |
void | SetVerbLevel (const VerbLevel verbLevel) |
Set the verbosity level of this object. | |
int | GetProcRankVerbose () const |
Get proc rank used for printing. Do not use this information for any other purpose. | |
int | SetProcRankVerbose (int procRank) const |
Set proc rank used for printing. | |
bool | IsPrint (MsgType type, int thisProcRankOnly=-1) const |
Find out whether we need to print out information for a specific message type. | |
Teuchos::FancyOStream & | GetOStream (MsgType type, int thisProcRankOnly=0) const |
Get an output stream for outputting the input message type. | |
Teuchos::FancyOStream & | GetBlackHole () const |
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virtual | ~Describable () |
Destructor. | |
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. | |
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. | |
virtual std::string | ShortClassName () const |
Return the class name of the object, without template parameters and without namespace. | |
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static void | SetDefaultVerbLevel (const VerbLevel defaultVerbLevel) |
Set the default (global) verbosity level. | |
static VerbLevel | GetDefaultVerbLevel () |
Get the default (global) verbosity level. | |
static void | SetMueLuOStream (const Teuchos::RCP< Teuchos::FancyOStream > &mueluOStream) |
static void | SetMueLuOFileStream (const std::string &filename) |
static Teuchos::RCP< Teuchos::FancyOStream > | GetMueLuOStream () |
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 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.
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
\f[P = P - Q^H(QQ^H)^{-1}QP.\f]
Because of the block diagonal form of Q, this can be done row-by-row.
\[(QQ^H)^{-1}\]
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.
void Constraint::Setup | ( | const MultiVector & | B, |
const MultiVector & | Bc, | ||
RCP< const CrsGraph > | Ppattern ) |
Setup constraint.
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.
void Constraint::Apply | ( | const Matrix & | P, |
Matrix & | Projected ) const |
Apply constraint.
Definition at line 137 of file MueLu_Constraint_def.hpp.
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inline |
Definition at line 136 of file MueLu_Constraint_decl.hpp.
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private |
Overlapped coarse nullspace.
Definition at line 141 of file MueLu_Constraint_decl.hpp.
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private |
Nonzero sparsity pattern.
Definition at line 142 of file MueLu_Constraint_decl.hpp.
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Array storing \((Q_i Q_i^H)^{-1}\).
Definition at line 143 of file MueLu_Constraint_decl.hpp.