Construct a preconditioner using a LDU dcomposition of a block 2x2 matrix. More...

#include <Teko_LU2x2PreconditionerFactory.hpp>

Inheritance diagram for Teko::LU2x2PreconditionerFactory:

Public Member Functions
LinearOp	buildPreconditionerOperator (BlockedLinearOp &blo, BlockPreconditionerState &state) const
	Create the LU 2x2 preconditioner operator.
virtual void	initializeFromParameterList (const Teuchos::ParameterList &settings)
	This function builds the internals of the preconditioner factory from a parameter list.
virtual Teuchos::RCP < Teuchos::ParameterList >	getRequestedParameters () const
	Request the additional parameters this preconditioner factory needs.
virtual bool	updateRequestedParameters (const Teuchos::ParameterList &pl)
	Update this object with the fields from a parameter list.
virtual bool	useFullLDU () const
	Determine the type of inverse operator to build.
virtual void	setFullLDU (bool value)
	Set the type of inverse operation to use.
Constructors.
	LU2x2PreconditionerFactory (LinearOp &invA00, LinearOp &invS)
	Build a simple static LU2x2 preconditioner.
	LU2x2PreconditionerFactory (LinearOp &hatInvA00, LinearOp &tildeInvA00, LinearOp &invS)
	Build a simple static LU2x2 preconditioner.
	LU2x2PreconditionerFactory (const Teuchos::RCP< LU2x2Strategy > &strategy)
	Constructor that permits the most generality in building $A_{00}^{-1}$ and $S^{-1}$ .
	LU2x2PreconditionerFactory ()
	Default constructor for use with AutoClone.
Static Public Member Functions
static RCP< LU2x2Strategy >	buildStrategy (const std::string &name, const Teuchos::ParameterList &settings, const RCP< const InverseLibrary > &invLib, const RCP< RequestHandler > &rh)
	Builder function for creating strategies.
static void	addStrategy (const std::string &name, const RCP< Cloneable > &clone)
	Add a strategy to the builder. This is done using the clone pattern.
Protected Attributes
Teuchos::RCP< LU2x2Strategy >	invOpsStrategy_
	some members
bool	useFullLDU_

Detailed Description

Construct a preconditioner using a LDU dcomposition of a block 2x2 matrix.

This produces a preconditioner using the block-LDU decomposition of the matrix. The general assumption made is that the matrix is 2x2 and the block factorization can be constructed (i.e. assumptions about the invertability of some blocks). The pattern used, and the one you should follow if you want to use this software is

$A = \left[ \begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array} \right] = \left[ \begin{array}{cc} I & 0 \\ A_{10} A_{00}^{-1} & I \end{array} \right] \left[ \begin{array}{cc} A_{00} & 0 \\ 0 & -S \end{array} \right] \left[ \begin{array}{cc} I & A_{00}^{-1} A_{01} \\ 0 & I \end{array} \right]$

where the Schur complement is $S=-A_{11}+A_{10} A_{00}^{-1} A_{01}$ .

To use an LDU approximation 2 evaluations of $A_{00}^{-1}$ and a single evalution of $S^{-1}$ are needed. For increased flexibility both evaluations of $A_{00}^{-1}$ can be specified independently. For righthand side vector $[f, g]^T$ and solution vector $[u,v]^T$ the two inverses ( $A$ -hat and $A$ -tilde) are needed to evaluate

$\hat{A}_{00} u^* = f$ ,

$\tilde{A}_{00} v = A_{01} v$

where $u^*$ is an intermediate step.

In order to facilate using this class in a nonlinear solve (or for a time-dependent problem) the additional abstraction of a ``Strategy'' has been added. This strategy, abstractly represented as the LU2x2Strategy, provides the $A_{00}^{-1}$ and $S^{-1}$ operators. Typical usage for this class is to build a LU2x2Strategy and pass it into the primary constructor. Additional constructors are provided both for convenience and to ease adoption. Underneath the hood all these constructors do is invoke the corresponding strategy object.

For example, assume that you have the particularly nice case that your approximations of $A_{00}^{-1}$ and $S^{-1}$ are independent of the source operator. Then, one way to instantiate a LU2x2PreconditionerFactory is

RCP<LinearOpBase<double> > invA00 = buildInvA00(...); RCP<LinearOpBase<double> > invS = buildInvS(...); RCP<LU2x2PreconditionerFactory> precFact = rcp(new LU2x2PreconditionerFactory(invA00,invS));

Now using the strategy constructor, an entirely equivalent factory object can be constructed by

RCP<LinearOpBase<double> > invA00 = buildInvA00(...); RCP<LinearOpBase<double> > invS = buildInvS(...); RCP<LU2x2Strateghy> precStrat = rcp(new StaticLU2x2Strategy(invA00,invS)); RCP<LU2x2PreconditionerFactory> precFact = rcp(new LU2x2PreconditionerFactory(precStrat));

Notice that the StaticLU2x2Strategy takes the same objects as the original constructor, it acts as an intermediary to tell the LU2x2PreconditionerFactory what those operators are.

Definition at line 141 of file Teko_LU2x2PreconditionerFactory.hpp.

Constructor & Destructor Documentation

Teko::LU2x2PreconditionerFactory::LU2x2PreconditionerFactory	(	LinearOp &	invA00,
		LinearOp &	invS
	)

Build a simple static LU2x2 preconditioner.

Definition at line 63 of file Teko_LU2x2PreconditionerFactory.cpp.

Teko::LU2x2PreconditionerFactory::LU2x2PreconditionerFactory	(	LinearOp &	hatInvA00,
		LinearOp &	tildeInvA00,
		LinearOp &	invS
	)

Build a simple static LU2x2 preconditioner.

Definition at line 68 of file Teko_LU2x2PreconditionerFactory.cpp.

Teko::LU2x2PreconditionerFactory::LU2x2PreconditionerFactory ( const Teuchos::RCP< LU2x2Strategy > & strategy )

Constructor that permits the most generality in building $A_{00}^{-1}$ and $S^{-1}$ .

Parameters:

[in] strategy Strategy object that takes a 2x2 block matrix and and constructs the $A_{00}^{-1}$ and $S^{-1}$ objects.

Teko::LU2x2PreconditionerFactory::LU2x2PreconditionerFactory ( )

Default constructor for use with AutoClone.

Default constructor for use with AutoClone

Definition at line 76 of file Teko_LU2x2PreconditionerFactory.cpp.

Member Function Documentation

LinearOp Teko::LU2x2PreconditionerFactory::buildPreconditionerOperator	(	BlockedLinearOp &	blo,
		BlockPreconditionerState &	state
	)		const `[virtual]`

Create the LU 2x2 preconditioner operator.

This method breaks apart the BlockLinearOp and builds a block LU preconditioner. This will require two applications of the inverse of the (0,0) block and one application of the inverse Schur complement.

Implements Teko::BlockPreconditionerFactory.

Definition at line 84 of file Teko_LU2x2PreconditionerFactory.cpp.

void Teko::LU2x2PreconditionerFactory::initializeFromParameterList ( const Teuchos::ParameterList & settings ) [virtual]

This function builds the internals of the preconditioner factory from a parameter list.

This function builds the internals of the preconditioner factory from a parameter list. Furthermore, it allows a preconditioner factory developer to easily add a factory to the build system. This function is required for building a preconditioner from a parameter list.

Parameters:

[in] settings Parmaeter list to use as the internal settings

Note:: The default implementation does nothing.

Reimplemented from Teko::PreconditionerFactory.

Definition at line 114 of file Teko_LU2x2PreconditionerFactory.cpp.

Teuchos::RCP< Teuchos::ParameterList > Teko::LU2x2PreconditionerFactory::getRequestedParameters ( ) const [virtual]

Request the additional parameters this preconditioner factory needs.

Request the additonal parameters needed by this preconditioner factory. The parameter list will have a set of fields that can be filled with the requested values. These fields include all requirements, even those of the sub-solvers if there are any. Once correctly filled the object can be updated by calling the updateRequestedParameters with the filled parameter list.

Returns:: A parameter list with the requested parameters.

Note:: The default implementation returns Teuchos::null.

Reimplemented from Teko::PreconditionerFactory.

Definition at line 144 of file Teko_LU2x2PreconditionerFactory.cpp.

bool Teko::LU2x2PreconditionerFactory::updateRequestedParameters ( const Teuchos::ParameterList & pl ) [virtual]

Update this object with the fields from a parameter list.

Update the requested fields using a parameter list. This method is expected to pair with the getRequestedParameters method (i.e. the fields requested are going to be update using this method).

Parameters:

[in] pl Parameter list containing the requested parameters.

Returns:: If the method succeeded (found all its required parameters) this method returns true, otherwise it returns false.

Note:: The default implementation returns true (it does nothing!).

Reimplemented from Teko::PreconditionerFactory.

Definition at line 163 of file Teko_LU2x2PreconditionerFactory.cpp.

virtual bool Teko::LU2x2PreconditionerFactory::useFullLDU ( ) const [inline, virtual]

Determine the type of inverse operator to build.

Determine the type of inverse operator to build. If true use the full LDU decomposition. If false only the upper triangular solve should be used. Motivation for doing this can be found in Murphy, Golub and Wathen, SISC 2000.

Returns:: A boolean indicating the type of inverse operator to use.

Note:: Default behavior for this class is to return true.

Definition at line 236 of file Teko_LU2x2PreconditionerFactory.hpp.

virtual void Teko::LU2x2PreconditionerFactory::setFullLDU ( bool value ) [inline, virtual]

Set the type of inverse operation to use.

Set the type of inverse operator to use. If true use the full LDU decomposition. If false only the upper triangular solve should be used. Motivation for doing this can be found in Murphy, Golub and Wathen, SISC 2000.

Parameters:

[in] value Boolean indicating type of inverse operator to build.

Definition at line 248 of file Teko_LU2x2PreconditionerFactory.hpp.

RCP< LU2x2Strategy > Teko::LU2x2PreconditionerFactory::buildStrategy	(	const std::string &	name,
		const Teuchos::ParameterList &	settings,
		const RCP< const InverseLibrary > &	invLib,
		const RCP< RequestHandler > &	rh
	)		`[static]`

Builder function for creating strategies.

Parameters:

[in]	name	String name of strategy to build
[in]	settings	Parameter list describing the parameters for the strategy to build
[in]	invLib	Inverse library for the strategy to use.

Returns:: If the name is associated with a strategy a pointer is returned, otherwise Teuchos::null is returned.

Definition at line 188 of file Teko_LU2x2PreconditionerFactory.cpp.

void Teko::LU2x2PreconditionerFactory::addStrategy	(	const std::string &	name,
		const RCP< Cloneable > &	clone
	)		`[static]`

Add a strategy to the builder. This is done using the clone pattern.

Add a strategy to the builder. This is done using the clone pattern. If your class does not support the Cloneable interface then you can use the AutoClone class to construct your object.