Sparse matrix vector multiplication for augmented Lagrangian-based preconditioners. More...

#include <Teko_ALOperator.hpp>

Inheritance diagram for Teko::NS::ALOperator:

Public Member Functions
	ALOperator (const std::vector< std::vector< int > > &vars, const Teuchos::RCP< Epetra_Operator > &content, LinearOp pressureMassMatrix, double gamma=0.05, const std::string &label="<ANYM>")
	ALOperator (const std::vector< std::vector< int > > &vars, const Teuchos::RCP< Epetra_Operator > &content, double gamma=0.05, const std::string &label="<ANYM>")
void	setPressureMassMatrix (LinearOp pressureMassMatrix)
const LinearOp &	getPressureMassMatrix () const
void	setGamma (double gamma)
const double &	getGamma () const
void	augmentRHS (const Epetra_MultiVector &b, Epetra_MultiVector &bAugmented)
int	getNumberOfBlockRows () const
virtual void	RebuildOps ()
const Teuchos::RCP< const Epetra_Operator >	GetBlock (int i, int j) const
Protected Member Functions
void	checkDim (const std::vector< std::vector< int > > &vars)
void	BuildALOperator ()
Protected Attributes
Teuchos::RCP < Thyra::LinearOpBase< double > >	alOperator_
Teuchos::RCP < Thyra::LinearOpBase< double > >	alOperatorRhs_
LinearOp	pressureMassMatrix_
LinearOp	invPressureMassMatrix_
double	gamma_
int	dim_
int	numBlockRows_

Detailed Description

Sparse matrix vector multiplication for augmented Lagrangian-based preconditioners.

This class implements sparse matrix vector multiplication for augmented Lagrangian-based preconditioners. Details can be found in the following papers:

[1] M. Benzi and M. A. Olshanskii, An Augmented Lagrangian-Based Approach to the Oseen Problem, SIAM J. Scientific Computing, 28 (2006), pp. 2095-2113.

[2] Benzi, M. A. Olshanskii and Z. Wang, Modified Augmented Lagrangian Preconditioners for the Incompressible Navier-Stokes Equations, International Journal for Numerical Methods in Fluids, 66 (2011), pp. 486-508.

Suppose we are solving the following linear system:

$\left[ \begin{array}{cc} A & B^T \\ B & -C \end{array} \right] \left[ \begin{array}{c} u \\ p \end{array} \right] = \left[ \begin{array}{c} f \\ g \end{array} \right].$

The equivalent augmented Lagrangian formulation is:

$\left[ \begin{array}{cc} A + \gamma B^T W^{-1} B & B^T - \gamma B^T W^{-1} C \\ B & -C \end{array} \right] \left[ \begin{array}{c} u \\ p \end{array} \right] = \left[ \begin{array}{c} f + \gamma B^T W^{-1} g \\ g \end{array} \right]$

or

$\widehat{\mathcal{A}} x = \hat{b}.$

Here $ W $ can be take as the diagonal of the pressure mass matrix and $\gamma$ is a positive number.

This class implements the matrix vector product with $\widehat{\mathcal{A}}$ .

Definition at line 83 of file Teko_ALOperator.hpp.

Constructor & Destructor Documentation

Teko::NS::ALOperator::ALOperator	(	const std::vector< std::vector< int > > &	vars,
		const Teuchos::RCP< Epetra_Operator > &	content,
		LinearOp	pressureMassMatrix,
		double	gamma = `0.05`,
		const std::string &	label = `"<ANYM>"`
	)

Build an augmented Lagrangian operator based on a vector of vector of global IDs.

Parameters:

[in]	vars	Vector of vectors of global ids specifying how the operator is to be blocked.
[in]	content	Operator to be blocked
[in]	pressureMassMatrix	Pressure mass matrix
[in]	gamma	Augmentation parameter
[in]	label	Label for name the operator

Definition at line 34 of file Teko_ALOperator.cpp.

Teko::NS::ALOperator::ALOperator	(	const std::vector< std::vector< int > > &	vars,
		const Teuchos::RCP< Epetra_Operator > &	content,
		double	gamma = `0.05`,
		const std::string &	label = `"<ANYM>"`
	)

Build a modified augmented Lagrangian operator based on a vector of vector of global IDs.

Parameters:

[in]	vars	Vector of vectors of global ids specifying how the operator is to be blocked.
[in]	content	Operator to be blocked
[in]	gamma	Augmentation parameter
[in]	label	Name of the operator

Definition at line 46 of file Teko_ALOperator.cpp.

Member Function Documentation

void Teko::NS::ALOperator::setPressureMassMatrix ( LinearOp pressureMassMatrix )

Set the pressure mass matrix.

Parameters:

[in] pressureMassMatrix Pressure mass matrix.

Definition at line 58 of file Teko_ALOperator.cpp.

const LinearOp& Teko::NS::ALOperator::getPressureMassMatrix ( ) const [inline]

Returns:: Pressure mass matrix that can be used to construct preconditioner.

Definition at line 143 of file Teko_ALOperator.hpp.

void Teko::NS::ALOperator::setGamma ( double gamma )

Set gamma.

Parameters:

[in] gamma Augmentation parameter.

Definition at line 67 of file Teko_ALOperator.cpp.

const double& Teko::NS::ALOperator::getGamma ( ) const [inline]

Returns:: Gamma Augmentation parameter.

Definition at line 161 of file Teko_ALOperator.hpp.

void Teko::NS::ALOperator::augmentRHS	(	const Epetra_MultiVector &	b,
		Epetra_MultiVector &	bAugmented
	)

Parameters:

[in]	b	Right-hand side.
[out]	bAugmented	Augmented right-hand side.

Definition at line 215 of file Teko_ALOperator.cpp.

int Teko::NS::ALOperator::getNumberOfBlockRows ( ) const [inline]

Returns:: Number of rows.

Definition at line 179 of file Teko_ALOperator.hpp.

virtual void Teko::NS::ALOperator::RebuildOps ( ) [inline, virtual]

Force a rebuild of the blocked operator from the stored content operator.

Reimplemented from Teko::Epetra::BlockedEpetraOperator.

Definition at line 189 of file Teko_ALOperator.hpp.

const Teuchos::RCP< const Epetra_Operator > Teko::NS::ALOperator::GetBlock	(	int	i,
		int	j
	)		const

Get the (i,j) block of the original (non-augmented) operator.

Parameters:

[in]	i	Row index.
[in]	j	Column index.

Reimplemented from Teko::Epetra::BlockedEpetraOperator.

Definition at line 74 of file Teko_ALOperator.cpp.

void Teko::NS::ALOperator::checkDim ( const std::vector< std::vector< int > > & vars ) [protected]

Check dimension. Only implemente for 2D and 3D problems.

Definition at line 84 of file Teko_ALOperator.cpp.

void Teko::NS::ALOperator::BuildALOperator ( ) [protected]

Build AL operator.

Definition at line 91 of file Teko_ALOperator.cpp.

Member Data Documentation

Teuchos::RCP<Thyra::LinearOpBase<double> > Teko::NS::ALOperator::alOperator_ [protected]

AL operator.

Definition at line 209 of file Teko_ALOperator.hpp.

Teuchos::RCP<Thyra::LinearOpBase<double> > Teko::NS::ALOperator::alOperatorRhs_ [protected]

Operator for augmenting the right-hand side.

Definition at line 214 of file Teko_ALOperator.hpp.

LinearOp Teko::NS::ALOperator::pressureMassMatrix_ [protected]

Pressure mass matrix and its inverse.

Definition at line 219 of file Teko_ALOperator.hpp.

LinearOp Teko::NS::ALOperator::invPressureMassMatrix_ [protected]

Inverse of the pressure mass matrix.

Definition at line 224 of file Teko_ALOperator.hpp.

double Teko::NS::ALOperator::gamma_ [protected]

Augmentation parameter.

Definition at line 229 of file Teko_ALOperator.hpp.

int Teko::NS::ALOperator::dim_ [protected]

Dimension of the problem.

Definition at line 234 of file Teko_ALOperator.hpp.

int Teko::NS::ALOperator::numBlockRows_ [protected]

Number of block rows.

Definition at line 239 of file Teko_ALOperator.hpp.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation