Modified augmented Lagrangian-based preconditioner for incompressible Navier-Stokes equations. More...

#include <Teko_ModALPreconditionerFactory.hpp>

Inheritance diagram for Teko::NS::ModALPreconditionerFactory:

Public Member Functions
void	setPressureMassMatrix (const LinearOp &pressureMassMatrix)

void	setGamma (double gamma)

virtual LinearOp	buildPreconditionerOperator (BlockedLinearOp &alOp, BlockPreconditionerState &state) const

virtual Teuchos::RCP < PreconditionerState >	buildPreconditionerState () const

Public Member Functions inherited from Teko::BlockPreconditionerFactory
RCP< BlockPreconditionerState >	buildBlockPreconditionerState () const
	Function that constructs a BlockPreconditionerState object. More...

virtual LinearOp	buildPreconditionerOperator (LinearOp &blo, PreconditionerState &state) const
	Function that is called to build the preconditioner for the linear operator that is passed in. More...

bool	isCompatible (const Thyra::LinearOpSourceBase< double > &fwdOpSrc) const
	is this operator compatiable with the preconditioner factory? More...

Public Member Functions inherited from Teko::PreconditionerFactory
void	setInverseLibrary (const Teuchos::RCP< const InverseLibrary > &il)
	Set the inverse library used by this preconditioner factory. More...

Teuchos::RCP< const InverseLibrary >	getInverseLibrary () const
	Get the inverse library used by this preconditioner factory. More...

void	setRequestHandler (const Teuchos::RCP< RequestHandler > &rh)
	Set the request handler with pointers to the appropriate callbacks. More...

Teuchos::RCP< RequestHandler >	getRequestHandler () const
	Get the request handler with pointers to the appropriate callbacks. More...

virtual void	initializeFromParameterList (const Teuchos::ParameterList &)
	This function builds the internals of the preconditioner factory from a parameter list. More...

virtual Teuchos::RCP < Teuchos::ParameterList >	getRequestedParameters () const
	Request the additional parameters this preconditioner factory needs. More...

virtual bool	updateRequestedParameters (const Teuchos::ParameterList &)
	Update this object with the fields from a parameter list. More...

bool	isCompatible (const Thyra::LinearOpSourceBase< double > &fwdOpSrc) const
	is this operator compatiable with the preconditioner factory? More...

Teuchos::RCP < Thyra::PreconditionerBase < double > >	createPrec () const
	create an instance of the preconditioner More...

void	initializePrec (const Teuchos::RCP< const Thyra::LinearOpSourceBase< double > > &fwdOpSrc, const Teuchos::RCP< const Thyra::MultiVectorBase< double > > &solnVec, Thyra::PreconditionerBase< double > *precOp, const Thyra::ESupportSolveUse supportSolveUse) const
	initialize a newly created preconditioner object More...

void	initializePrec (const Teuchos::RCP< const Thyra::LinearOpSourceBase< double > > &fwdOpSrc, Thyra::PreconditionerBase< double > *precOp, const Thyra::ESupportSolveUse supportSolveUse) const
	initialize a newly created preconditioner object More...

void	uninitializePrec (Thyra::PreconditionerBase< double > prec, Teuchos::RCP< const Thyra::LinearOpSourceBase< double > > fwdOpSrc, Thyra::ESupportSolveUse *supportSolveUse) const
	wipe clean a already initialized preconditioner object More...

void	setParameterList (const Teuchos::RCP< Teuchos::ParameterList > &paramList)
	Set parameters from a parameter list and return with default values. More...

Teuchos::RCP < Teuchos::ParameterList >	getNonconstParameterList ()
	Get the parameter list that was set using setParameterList(). More...

Teuchos::RCP < Teuchos::ParameterList >	unsetParameterList ()
	Unset the parameter list that was set using setParameterList(). More...

Additional Inherited Members
Static Public Member Functions inherited from Teko::PreconditionerFactory
static Teuchos::RCP < PreconditionerFactory >	buildPreconditionerFactory (const std::string &name, const Teuchos::ParameterList &settings, const Teuchos::RCP< const InverseLibrary > &invLib=Teuchos::null)
	Builder function for creating preconditioner factories (yes this is a factory factory). More...

static void	addPreconditionerFactory (const std::string &name, const Teuchos::RCP< Cloneable > &clone)
	Add a preconditioner factory to the builder. This is done using the clone pattern. More...

static void	getPreconditionerFactoryNames (std::vector< std::string > &names)
	Get the names of the block preconditioner factories. More...

Protected Attributes inherited from Teko::PreconditionerFactory
Teuchos::RCP < Teuchos::ParameterList >	paramList_
	for ParameterListAcceptor More...

Teuchos::RCP< RequestHandler >	callbackHandler_
	For handling requests and send requests back to the user. More...

Detailed Description

Modified augmented Lagrangian-based preconditioner for incompressible Navier-Stokes equations.

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

[1] 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.

[2] M. Benzi and Z. Wang, Analysis of Augmented Lagrangian-Based Preconditioners for the Steady Incompressible Navier-Stokes Equations, SIAM J. Scientific Computing, 33 (2011), pp. 2761-2784.

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 (AL) formulation is:

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

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

If $A = (A_{11}, A_{12}; A_{21}, A_{22}) \quad \mathrm{and} \quad B = (B_1, B_2)$ ,

then the modified AL preconditioner is defined as

$\left[ \begin{array}{ccc} A_{11} + \gamma B_1^T W^{-1} B_1^T & A_{12} + \gamma B_1^T W^{-1} B_2^T & B_1^T - \gamma B_1^T W^{-1} C \\ 0 & A_{22} + \gamma B_2^T W^{-1} B_2^T & B_1^T - \gamma B_2^T W^{-1} C \\ 0 & 0 & S \end{array} \right].$