Constraint space information for the potential prolongator. More...
#include <MueLu_Constraint_decl.hpp>
Public Types | |
| using | MagnitudeType = typename Teuchos::ScalarTraits< Scalar >::magnitudeType |
Apply methods. | |
| RCP< MultiVector > | B_ |
| RCP< MultiVector > | Bc_ |
| 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 RCP< MultiVector > &B, const RCP< MultiVector > &Bc, RCP< const CrsGraph > Ppattern) |
| MagnitudeType | ResidualNorm (const RCP< const Matrix > P) const |
Additional Inherited Members | |
 Public Member Functions inherited from MueLu::BaseClass | |
| virtual | ~BaseClass () |
| Destructor. | |
| Public Member Functions inherited from MueLu::VerboseObject | |
| 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 |
| Public Member Functions inherited from MueLu::Describable | |
| 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. | |
| Static Public Member Functions inherited from MueLu::VerboseObject | |
| 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 () |
Detailed Description
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
\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.
- 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 Typedef Documentation
◆ MagnitudeType
| using MueLu::Constraint< Scalar, LocalOrdinal, GlobalOrdinal, Node >::MagnitudeType = typename Teuchos::ScalarTraits<Scalar>::magnitudeType |
Definition at line 78 of file MueLu_Constraint_decl.hpp.
Member Function Documentation
◆ Setup()
| void Constraint::Setup | ( | const RCP< MultiVector > & | B, |
| const RCP< 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.
◆ ResidualNorm()
| Teuchos::ScalarTraits< Scalar >::magnitudeType Constraint::ResidualNorm | ( | const RCP< const Matrix > | P | ) | const |
Definition at line 103 of file MueLu_Constraint_def.hpp.
◆ Apply()
| 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 120 of file MueLu_Constraint_def.hpp.
◆ GetPattern()
|
inline |
Definition at line 102 of file MueLu_Constraint_decl.hpp.
Member Data Documentation
◆ B_
|
private |
Definition at line 107 of file MueLu_Constraint_decl.hpp.
◆ Bc_
|
private |
Definition at line 108 of file MueLu_Constraint_decl.hpp.
◆ X_
|
private |
Overlapped coarse nullspace.
Definition at line 109 of file MueLu_Constraint_decl.hpp.
◆ Ppattern_
|
private |
Nonzero sparsity pattern.
Definition at line 110 of file MueLu_Constraint_decl.hpp.
◆ XXtInv_
|
private |
Array storing \((Q_i Q_i^H)^{-1}\).
Definition at line 111 of file MueLu_Constraint_decl.hpp.
The documentation for this class was generated from the following files:
