Bordered system solver strategy based on bordering. More...

#include <LOCA_BorderedSolver_Bordering.H>

Inheritance diagram for LOCA::BorderedSolver::Bordering:

Collaboration diagram for LOCA::BorderedSolver::Bordering:

Public Member Functions
	Bordering (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< LOCA::Parameter::SublistParser > &topParams, const Teuchos::RCP< Teuchos::ParameterList > &solverParams)
	Constructor.

virtual	~Bordering ()
	Destructor.

virtual void	setMatrixBlocks (const Teuchos::RCP< const LOCA::BorderedSolver::AbstractOperator > &op, const Teuchos::RCP< const NOX::Abstract::MultiVector > &blockA, const Teuchos::RCP< const LOCA::MultiContinuation::ConstraintInterface > &blockB, const Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix > &blockC)
	Set blocks.

virtual NOX::Abstract::Group::ReturnType	initForSolve ()
	Intialize solver for a solve.

virtual NOX::Abstract::Group::ReturnType	initForTransposeSolve ()
	Intialize solver for a transpose solve.

virtual NOX::Abstract::Group::ReturnType	apply (const NOX::Abstract::MultiVector &X, const NOX::Abstract::MultiVector::DenseMatrix &Y, NOX::Abstract::MultiVector &U, NOX::Abstract::MultiVector::DenseMatrix &V) const
	Computed extended matrix-multivector product.

virtual NOX::Abstract::Group::ReturnType	applyTranspose (const NOX::Abstract::MultiVector &X, const NOX::Abstract::MultiVector::DenseMatrix &Y, NOX::Abstract::MultiVector &U, NOX::Abstract::MultiVector::DenseMatrix &V) const
	Computed extended matrix transpose-multivector product.

virtual NOX::Abstract::Group::ReturnType	applyInverse (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector F, const NOX::Abstract::MultiVector::DenseMatrix G, NOX::Abstract::MultiVector &X, NOX::Abstract::MultiVector::DenseMatrix &Y) const
	Solves the extended system as defined above using bordering.

virtual NOX::Abstract::Group::ReturnType	applyInverseTranspose (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector F, const NOX::Abstract::MultiVector::DenseMatrix G, NOX::Abstract::MultiVector &X, NOX::Abstract::MultiVector::DenseMatrix &Y) const
	Solves the transpose of the extended system as defined above using bordering.

Public Member Functions inherited from LOCA::BorderedSolver::AbstractStrategy
	AbstractStrategy ()
	Constructor.

virtual	~AbstractStrategy ()
	Destructor.

virtual void	setMatrixBlocksMultiVecConstraint (const Teuchos::RCP< const LOCA::BorderedSolver::AbstractOperator > &op, const Teuchos::RCP< const NOX::Abstract::MultiVector > &blockA, const Teuchos::RCP< const NOX::Abstract::MultiVector > &blockB, const Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix > &blockC)
	Set blocks with multivector constraint.

Protected Member Functions
NOX::Abstract::Group::ReturnType	solveFZero (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector AA, const LOCA::MultiContinuation::ConstraintInterface BB, const NOX::Abstract::MultiVector::DenseMatrix CC, const NOX::Abstract::MultiVector::DenseMatrix G, NOX::Abstract::MultiVector &X, NOX::Abstract::MultiVector::DenseMatrix &Y) const
	Solves the extended system when F = 0.

NOX::Abstract::Group::ReturnType	solveContiguous (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector AA, const LOCA::MultiContinuation::ConstraintInterface BB, const NOX::Abstract::MultiVector::DenseMatrix CC, std::vector< int > &indexF, std::vector< int > &indexA, const NOX::Abstract::MultiVector F, const NOX::Abstract::MultiVector::DenseMatrix *G, NOX::Abstract::MultiVector &X, NOX::Abstract::MultiVector::DenseMatrix &Y) const
	Solves the extended system when F and A are contiguous.

NOX::Abstract::Group::ReturnType	solveFZeroTrans (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector AA, const NOX::Abstract::MultiVector BB, const NOX::Abstract::MultiVector::DenseMatrix CC, const NOX::Abstract::MultiVector::DenseMatrix G, NOX::Abstract::MultiVector &X, NOX::Abstract::MultiVector::DenseMatrix &Y) const
	Solves the transpose of the extended system when F = 0.

NOX::Abstract::Group::ReturnType	solveContiguousTrans (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector AA, const NOX::Abstract::MultiVector BB, const NOX::Abstract::MultiVector::DenseMatrix CC, std::vector< int > &indexF, std::vector< int > &indexA, const NOX::Abstract::MultiVector F, const NOX::Abstract::MultiVector::DenseMatrix *G, NOX::Abstract::MultiVector &X, NOX::Abstract::MultiVector::DenseMatrix &Y) const
	Solves the transpose of the extended system when F and B are contiguous.

Protected Attributes
Teuchos::RCP< LOCA::GlobalData >	globalData
	Global data object.

Teuchos::RCP< Teuchos::ParameterList >	solverParams
	Solver parameters.

Teuchos::RCP< const LOCA::BorderedSolver::AbstractOperator >	op
	Pointer to operator.

Teuchos::RCP< const NOX::Abstract::MultiVector >	A
	Pointer to A block.

Teuchos::RCP< const LOCA::MultiContinuation::ConstraintInterface >	B
	Pointer to B block.

Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix >	C
	Pointer to C block.

bool	isZeroA
	flag indicating whether A block is zero

bool	isZeroB
	flag indicating whether B block is zero

bool	isZeroC
	flag indicating whether C block is zero

bool	isZeroF
	flag indicating whether F block is zero

bool	isZeroG
	flag indicating whether G block is zero

Detailed Description

Bordered system solver strategy based on bordering.

This class solves the extended system of equations

$\begin{bmatrix} J & A \\ B^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} F \\ G \end{bmatrix}$

via bordering (block elimination):

$\begin{aligned} X_1 &= J^{-1} F \\ X_2 &= J^{-1} A \\ Y &= (C-B^T X_2)^{-1}(G-B^T X_1) \\ X &= X_1 - X_2 Y \end{aligned}$

It takes advantage of any of the matrix blocks being zero and concatenates and into a contiguous multivector to compute and in one block solve.

To solve the transpose of the system, a similar bordering algorithm is implemented. Note however that for the transpose, the constraint object representing must implement the LOCA::MultiContinuation::ConstraintInterfaceMVDX since appears on the right-hand-side of a linear system.

Constructor & Destructor Documentation

◆ Bordering()

LOCA::BorderedSolver::Bordering::Bordering	(	const Teuchos::RCP< LOCA::GlobalData > &	global_data,
		const Teuchos::RCP< LOCA::Parameter::SublistParser > &	topParams,
		const Teuchos::RCP< Teuchos::ParameterList > &	solverParams
	)

Constructor.

Parameters

global_data	[in] Global data object
topParams	[in] Parsed top-level parameter list
solverParams	[in] Bordered solver parameters. Currently none are referenced.

Member Function Documentation

◆ apply()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::Bordering::apply	(	const NOX::Abstract::MultiVector &	X,
		const NOX::Abstract::MultiVector::DenseMatrix &	Y,
		NOX::Abstract::MultiVector &	U,
		NOX::Abstract::MultiVector::DenseMatrix &	V
	)		const

virtual

Computed extended matrix-multivector product.

Computes

$\begin{bmatrix} U \\ V \end{bmatrix} = \begin{bmatrix} J & A \\ B^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} J*X + A*Y \\ B^T*X + C*Y \end{bmatrix}.$

Implements LOCA::BorderedSolver::AbstractStrategy.

References NOX::Abstract::Group::Failed, NOX::Abstract::MultiVector::multiply(), and NOX::Abstract::MultiVector::update().

◆ applyInverse()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::Bordering::applyInverse	(	Teuchos::ParameterList &	params,
		const NOX::Abstract::MultiVector *	F,
		const NOX::Abstract::MultiVector::DenseMatrix *	G,
		NOX::Abstract::MultiVector &	X,
		NOX::Abstract::MultiVector::DenseMatrix &	Y
	)		const

virtual

Solves the extended system as defined above using bordering.

The params argument is the linear solver parameters. If isZeroF or isZeroG is true, than the corresponding F or G pointers may be NULL.

Implements LOCA::BorderedSolver::AbstractStrategy.

References NOX::Abstract::MultiVector::clone(), NOX::Abstract::MultiVector::numVectors(), LOCA::BorderedSolver::LowerTriangularBlockElimination::solve(), and LOCA::BorderedSolver::UpperTriangularBlockElimination::solve().

◆ applyInverseTranspose()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::Bordering::applyInverseTranspose	(	Teuchos::ParameterList &	params,
		const NOX::Abstract::MultiVector *	F,
		const NOX::Abstract::MultiVector::DenseMatrix *	G,
		NOX::Abstract::MultiVector &	X,
		NOX::Abstract::MultiVector::DenseMatrix &	Y
	)		const

virtual

Solves the transpose of the extended system as defined above using bordering.

The params argument is the linear solver parameters. If isZeroF or isZeroG is true, than the corresponding F or G pointers may be NULL. Note that for the transpose solve B must be of type LOCA::MultiContinuation::ConstraintInterfaceMVDX.

Implements LOCA::BorderedSolver::AbstractStrategy.

References NOX::Abstract::MultiVector::clone(), NOX::Abstract::MultiVector::numVectors(), LOCA::BorderedSolver::LowerTriangularBlockElimination::solveTranspose(), and LOCA::BorderedSolver::UpperTriangularBlockElimination::solveTranspose().

◆ applyTranspose()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::Bordering::applyTranspose	(	const NOX::Abstract::MultiVector &	X,
		const NOX::Abstract::MultiVector::DenseMatrix &	Y,
		NOX::Abstract::MultiVector &	U,
		NOX::Abstract::MultiVector::DenseMatrix &	V
	)		const

virtual

Computed extended matrix transpose-multivector product.

Computes

$\begin{bmatrix} U \\ V \end{bmatrix} = \begin{bmatrix} J^T & B \\ A^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} J^T*X + B*Y \\ A^T*X + C^T*Y \end{bmatrix}.$

Implements LOCA::BorderedSolver::AbstractStrategy.

References NOX::Abstract::Group::Failed, and NOX::Abstract::MultiVector::multiply().

◆ initForSolve()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::Bordering::initForSolve ( )

virtual

Intialize solver for a solve.

This should be called after setMatrixBlocks(), but before applyInverse().

Implements LOCA::BorderedSolver::AbstractStrategy.

References NOX::Abstract::Group::Ok.

◆ initForTransposeSolve()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::Bordering::initForTransposeSolve ( )

virtual

Intialize solver for a transpose solve.

This should be called after setMatrixBlocks(), but before applyInverseTranspose().

Implements LOCA::BorderedSolver::AbstractStrategy.

References NOX::Abstract::Group::Ok.

◆ setMatrixBlocks()

void LOCA::BorderedSolver::Bordering::setMatrixBlocks	(	const Teuchos::RCP< const LOCA::BorderedSolver::AbstractOperator > &	op,
		const Teuchos::RCP< const NOX::Abstract::MultiVector > &	blockA,
		const Teuchos::RCP< const LOCA::MultiContinuation::ConstraintInterface > &	blockB,
		const Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix > &	blockC
	)

virtual

Set blocks.

The blockA or blockC pointer may be null if either is zero. Whether block B is zero will be determined by querying blockB via ConstraintInterface::isConstraintDerivativesXZero.

Implements LOCA::BorderedSolver::AbstractStrategy.

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

LOCA_BorderedSolver_Bordering.H
LOCA_BorderedSolver_Bordering.C

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Bordering()

Member Function Documentation

◆ apply()

◆ applyInverse()

◆ applyInverseTranspose()

◆ applyTranspose()

◆ initForSolve()

◆ initForTransposeSolve()

◆ setMatrixBlocks()