Block elimination strategy for solving a block upper-triangular system. More...

#include <LOCA_BorderedSolver_UpperTriangularBlockElimination.H>

Public Member Functions
	UpperTriangularBlockElimination (const Teuchos::RCP< LOCA::GlobalData > &global_data)
	Constructor.

virtual	~UpperTriangularBlockElimination ()
	Destructor.

NOX::Abstract::Group::ReturnType	solve (Teuchos::ParameterList &params, const LOCA::BorderedSolver::AbstractOperator &op, const NOX::Abstract::MultiVector A, const NOX::Abstract::MultiVector::DenseMatrix &C, 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 described above.

NOX::Abstract::Group::ReturnType	solveTranspose (Teuchos::ParameterList &params, const LOCA::BorderedSolver::AbstractOperator &op, const NOX::Abstract::MultiVector A, const NOX::Abstract::MultiVector::DenseMatrix &C, 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 using the tranpose of J and C as described above.

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

Detailed Description

Block elimination strategy for solving a block upper-triangular system.

This class solves the extended system of equations

$\begin{bmatrix} op(J) & A \\ 0 & op(C) \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} F \\ G \end{bmatrix}$

via block elimination:

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

where represents either the identity operation or the transpose. must be nonzero, while , or may be zero. The solve for the non-transposed system is implemented by the solve() method, while the solve for the transposed system is implemented by the solveTranspose() method.

Constructor & Destructor Documentation

◆ UpperTriangularBlockElimination()

LOCA::BorderedSolver::UpperTriangularBlockElimination::UpperTriangularBlockElimination ( const Teuchos::RCP< LOCA::GlobalData > & global_data )

Constructor.

Parameters

global_data [in] Global data object

Member Function Documentation

◆ solve()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::UpperTriangularBlockElimination::solve	(	Teuchos::ParameterList &	params,
		const LOCA::BorderedSolver::AbstractOperator &	op,
		const NOX::Abstract::MultiVector *	A,
		const NOX::Abstract::MultiVector::DenseMatrix &	C,
		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 described above.

Either A, F, or G may be zero by passing NULL.

References LOCA::BorderedSolver::AbstractOperator::applyInverse(), NOX::Abstract::MultiVector::clone(), NOX::DeepCopy, NOX::Abstract::Group::Failed, NOX::Abstract::MultiVector::init(), and NOX::Abstract::Group::Ok.

Referenced by LOCA::BorderedSolver::EpetraAugmented::applyInverse(), LOCA::BorderedSolver::EpetraHouseholder::applyInverse(), LOCA::BorderedSolver::TpetraHouseholder::applyInverse(), and LOCA::BorderedSolver::Bordering::applyInverse().

◆ solveTranspose()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::UpperTriangularBlockElimination::solveTranspose	(	Teuchos::ParameterList &	params,
		const LOCA::BorderedSolver::AbstractOperator &	op,
		const NOX::Abstract::MultiVector *	A,
		const NOX::Abstract::MultiVector::DenseMatrix &	C,
		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 using the tranpose of J and C as described above.

Either A, F, or G may be zero by passing NULL.

References LOCA::BorderedSolver::AbstractOperator::applyInverseTranspose(), NOX::Abstract::MultiVector::clone(), NOX::DeepCopy, NOX::Abstract::Group::Failed, NOX::Abstract::MultiVector::init(), and NOX::Abstract::Group::Ok.

Referenced by LOCA::BorderedSolver::EpetraHouseholder::applyInverseTranspose(), LOCA::BorderedSolver::TpetraHouseholder::applyInverseTranspose(), and LOCA::BorderedSolver::Bordering::applyInverseTranspose().

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

LOCA_BorderedSolver_UpperTriangularBlockElimination.H
LOCA_BorderedSolver_UpperTriangularBlockElimination.C