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

Public Member Functions inherited from Teko::Epetra::BlockedEpetraOperator
	BlockedEpetraOperator (const std::vector< std::vector< int > > &vars, const Teuchos::RCP< const Epetra_Operator > &content, const std::string &label="<ANYM>")

virtual void	SetContent (const std::vector< std::vector< int > > &vars, const Teuchos::RCP< const Epetra_Operator > &content)

void	Reorder (const BlockReorderManager &brm)

void	RemoveReording ()
	Remove any reordering on this object. More...

virtual void	WriteBlocks (const std::string &prefix) const

bool	testAgainstFullOperator (int count, double tol) const
	Helps perform sanity checks. More...

Public Member Functions inherited from Teko::Epetra::EpetraOperatorWrapper
const RCP< const Thyra::LinearOpBase< double > >	getThyraOp () const
	Return the thyra operator associated with this wrapper. More...

const RCP< const MappingStrategy >	getMapStrategy () const
	Get the mapping strategy for this wrapper (translate between Thyra and Epetra) More...

virtual int	GetBlockRowCount ()
	Get the number of block rows in this operator. More...

virtual int	GetBlockColCount ()
	Get the number of block columns in this operator. More...

Teuchos::RCP< const Epetra_Operator >	GetBlock (int i, int j) const
	Grab the i,j block. More...

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 ( )

inlinevirtual

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.

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