Moore-Spence Hopf solver strategy based on "Salinger" bordering. This is the classic 5-solve Hopf bordering method. More...

#include <LOCA_Hopf_MooreSpence_SalingerBordering.H>

Inheritance diagram for LOCA::Hopf::MooreSpence::SalingerBordering:

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Collaboration diagram for LOCA::Hopf::MooreSpence::SalingerBordering:

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

virtual	~SalingerBordering ()
	Destructor.

virtual void	setBlocks (const Teuchos::RCP< LOCA::Hopf::MooreSpence::AbstractGroup > &group, const Teuchos::RCP< LOCA::Hopf::MooreSpence::ExtendedGroup > &hopfGroup, const Teuchos::RCP< const NOX::Abstract::Vector > &yVector, const Teuchos::RCP< const NOX::Abstract::Vector > &zVector, const Teuchos::RCP< const NOX::Abstract::Vector > &CeRealVector, const Teuchos::RCP< const NOX::Abstract::Vector > &CeImagVector, const Teuchos::RCP< const NOX::Abstract::Vector > &dfdp, const Teuchos::RCP< const NOX::Abstract::Vector > &dCedpReal, const Teuchos::RCP< const NOX::Abstract::Vector > &dCedpImag, const Teuchos::RCP< const NOX::Abstract::Vector > &ByVector, const Teuchos::RCP< const NOX::Abstract::Vector > &mBzVector, double w)
	Set blocks in extended linear system.

virtual NOX::Abstract::Group::ReturnType	solve (Teuchos::ParameterList &params, const LOCA::Hopf::MooreSpence::ExtendedMultiVector &input, LOCA::Hopf::MooreSpence::ExtendedMultiVector &result) const
	Solves the extended system as defined above.

Public Member Functions inherited from LOCA::Hopf::MooreSpence::SolverStrategy
	SolverStrategy ()
	Constructor.

virtual	~SolverStrategy ()
	Destructor.

Protected Member Functions
NOX::Abstract::Group::ReturnType	solveContiguous (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input_x, const NOX::Abstract::MultiVector &input_y, const NOX::Abstract::MultiVector &input_z, const NOX::Abstract::MultiVector::DenseMatrix &input_w, const NOX::Abstract::MultiVector::DenseMatrix &input_p, NOX::Abstract::MultiVector &result_x, NOX::Abstract::MultiVector &result_y, NOX::Abstract::MultiVector &result_z, NOX::Abstract::MultiVector::DenseMatrix &result_w, NOX::Abstract::MultiVector::DenseMatrix &result_p) const
	Solves equations with contiguous arguments.

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

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

Teuchos::RCP< LOCA::Hopf::MooreSpence::AbstractGroup >	group
	Underlying group.

Teuchos::RCP< LOCA::Hopf::MooreSpence::ExtendedGroup >	hopfGroup
	Hopf group.

Teuchos::RCP< const NOX::Abstract::Vector >	yVector
	Real component of eigenvector.

Teuchos::RCP< const NOX::Abstract::Vector >	zVector
	Imaginary component of eigenvector.

Teuchos::RCP< const NOX::Abstract::Vector >	CeRealVector
	Jy-wBz vector.

Teuchos::RCP< const NOX::Abstract::Vector >	CeImagVector
	Jz+wBy vector.

Teuchos::RCP< const NOX::Abstract::Vector >	dfdp
	df/dp vector

Teuchos::RCP< const NOX::Abstract::Vector >	dCedpReal
	d(Jy-wBz)/dp vector

Teuchos::RCP< const NOX::Abstract::Vector >	dCedpImag
	d(Jz+wBy)/dp vector

Teuchos::RCP< const NOX::Abstract::Vector >	ByVector
	By vector.

Teuchos::RCP< const NOX::Abstract::Vector >	minusBzVector
	-Bz vector

double	w
	Frequency w.

Detailed Description

Moore-Spence Hopf solver strategy based on "Salinger" bordering. This is the classic 5-solve Hopf bordering method.

This class solves the Moore-Spence Hopf Newton equations:

$\begin{bmatrix} J & 0 & 0 & 0 & f_p \\ (Jy-wBz)_x & J & -wB & -Bz & (Jy-wBz)_p \\ (Jz+wBy)_x & wB & J & By & (Jz+wBy)_p \\ 0 & \phi^T & 0 & 0 & 0 \\ 0 & 0 & \phi^T & 0 & 0 \end{bmatrix} \begin{bmatrix} X \\ Y \\ Z \\ \omega \\ \lambda \end{bmatrix} = \begin{bmatrix} F \\ G \\ H \\ u \\ v \end{bmatrix}.$

via the following block elimination scheme:

$\begin{split} J [A \; b] &= [F \; f_p] \\ \begin{bmatrix} J & -wB \\ wB & J \end{bmatrix} \begin{bmatrix} C & e & g \\ D & f & h \end{bmatrix} &= \begin{bmatrix} G - (Jy-wBz)_x A & (Jy-wBz)_p - (Jy-wBz)_x b & -Bz \\ H - (Jz+wBy)_x A & (Jz+wBy)_p - (Jy-wBz)_x b & By \end{bmatrix} \\ \lambda &= \frac{(\phi^T h)(\phi^T C-u)-(\phi^T g)(\phi^T D-v)} {(\phi^T h)(\phi^T e)-(\phi^T g)(\phi^T f)} \\ \omega &= \frac{\phi^T D - v - (\phi^T f)\lambda}{\phi^T h} \\ X &= A - b \lambda \\ \begin{bmatrix} Y \\ Z \end{bmatrix} &= \begin{bmatrix} C \\ D \end{bmatrix} - \begin{bmatrix} e \\ f \end{bmatrix}\lambda - \begin{bmatrix} g \\ h \end{bmatrix}\omega \end{split}$

Constructor & Destructor Documentation

◆ SalingerBordering()

LOCA::Hopf::MooreSpence::SalingerBordering::SalingerBordering	(	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

◆ setBlocks()

void LOCA::Hopf::MooreSpence::SalingerBordering::setBlocks	(	const Teuchos::RCP< LOCA::Hopf::MooreSpence::AbstractGroup > &	group,
		const Teuchos::RCP< LOCA::Hopf::MooreSpence::ExtendedGroup > &	hopfGroup,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	yVector,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	zVector,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	CeRealVector,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	CeImagVector,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	dfdp,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	dCedpReal,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	dCedpImag,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	ByVector,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	mBzVector,
		double	w
	)

virtual

Set blocks in extended linear system.

Parameters

group	[in] Underlying group representing J
hopfGroup	[in] Hopf group representing the Hopf equations.
yVector	[in] Vector representing y
zVector	[in] Vector representing z
CeRealVector	[in] Vector representing Jy-wBz
CeImagVector	[in] Vector representing Jz+wBy
dfdp	[in] Vector representing df/dp
dCedpReal	[in] Vector representing d(Jy-wBz)/dp
dCedpImag	[in] Vector representing d(Jz+wBy)/dp
ByVector	[in] Vector representing By
mBzVector	[in] Vector representing -Bz
w	[in] Bifurcation frequency w

Implements LOCA::Hopf::MooreSpence::SolverStrategy.

◆ solve()

NOX::Abstract::Group::ReturnType LOCA::Hopf::MooreSpence::SalingerBordering::solve	(	Teuchos::ParameterList &	params,
		const LOCA::Hopf::MooreSpence::ExtendedMultiVector &	input,
		LOCA::Hopf::MooreSpence::ExtendedMultiVector &	result
	)		const

virtual

Solves the extended system as defined above.

The params argument is the linear solver parameters.

Implements LOCA::Hopf::MooreSpence::SolverStrategy.

References LOCA::Hopf::MooreSpence::ExtendedMultiVector::getBifParams(), LOCA::Hopf::MooreSpence::ExtendedMultiVector::getFrequencies(), LOCA::Hopf::MooreSpence::ExtendedMultiVector::getImagEigenMultiVec(), LOCA::Hopf::MooreSpence::ExtendedMultiVector::getRealEigenMultiVec(), LOCA::Hopf::MooreSpence::ExtendedMultiVector::getXMultiVec(), and LOCA::Extended::MultiVector::numVectors().

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

LOCA_Hopf_MooreSpence_SalingerBordering.H
LOCA_Hopf_MooreSpence_SalingerBordering.C

Public Member Functions