Moore-Spence pitchfork solver strategy based on "Phipps" bordering which is the 7-solve modified pitchfork bordering algorithm that uses bordered linear solves. More...

#include <LOCA_Pitchfork_MooreSpence_PhippsBordering.H>

Inheritance diagram for LOCA::Pitchfork::MooreSpence::PhippsBordering:

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Collaboration diagram for LOCA::Pitchfork::MooreSpence::PhippsBordering:

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

virtual	~PhippsBordering ()
	Destructor.

virtual void	setBlocks (const Teuchos::RCP< LOCA::Pitchfork::MooreSpence::AbstractGroup > &group, const Teuchos::RCP< LOCA::Pitchfork::MooreSpence::ExtendedGroup > &pfGroup, const Teuchos::RCP< const NOX::Abstract::MultiVector > &asymMultiVector, const Teuchos::RCP< const NOX::Abstract::Vector > &nullVector, const Teuchos::RCP< const NOX::Abstract::Vector > &JnVector, const Teuchos::RCP< const NOX::Abstract::Vector > &dfdp, const Teuchos::RCP< const NOX::Abstract::Vector > &dJndp)
	Set blocks in extended linear system.

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

Public Member Functions inherited from LOCA::Pitchfork::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_null, const NOX::Abstract::MultiVector::DenseMatrix &input_slack, const NOX::Abstract::MultiVector::DenseMatrix &input_param, NOX::Abstract::MultiVector &result_x, NOX::Abstract::MultiVector &result_null, NOX::Abstract::MultiVector::DenseMatrix &result_slack, NOX::Abstract::MultiVector::DenseMatrix &result_param) 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::Pitchfork::MooreSpence::AbstractGroup >	group
	Underlying group.

Teuchos::RCP< LOCA::Pitchfork::MooreSpence::ExtendedGroup >	pfGroup
	Turning point group.

Teuchos::RCP< const NOX::Abstract::MultiVector >	asymMultiVector
	Antisymmetric vector (psi)

Teuchos::RCP< const NOX::Abstract::Vector >	asymVector
	Antisymmetric vector (psi)

Teuchos::RCP< const NOX::Abstract::Vector >	nullVector
	Null vector.

Teuchos::RCP< const NOX::Abstract::Vector >	JnVector
	Jacobian times null vector.

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

Teuchos::RCP< const NOX::Abstract::Vector >	dJndp
	d(Jn)/dp

Teuchos::RCP< LOCA::BorderedSolver::AbstractStrategy >	borderedSolver
	Bordered solver for solving (n+1)x(n+1) sets of equations.

Teuchos::RCP< NOX::Abstract::MultiVector >	nullMultiVector
	Null vector as a multivector.

Teuchos::RCP< NOX::Abstract::MultiVector >	JnMultiVector
	Jacobian times null vector as a multivector.

double	sigma
	Norm of JnVector.

Detailed Description

Moore-Spence pitchfork solver strategy based on "Phipps" bordering which is the 7-solve modified pitchfork bordering algorithm that uses bordered linear solves.

This class solves the Moore-Spence pitchfork Newton equations:

$\begin{bmatrix} J & 0 & \psi & f_p \\ (Jv)_x & J & 0 & (Jv)_p \\ \psi^T & 0 & 0 & 0 \\ 0 & \phi^T & 0 & 0 \end{bmatrix} \begin{bmatrix} X \\ Y \\ w \\ z \end{bmatrix} = \begin{bmatrix} F \\ G \\ s \\ h \end{bmatrix}$

via the following modified block elimination scheme:

$\begin{split} \begin{bmatrix} J & u \\ v^T & 0 \end{bmatrix} \begin{bmatrix} A & B & C \\ a & b & c \end{bmatrix} &= \begin{bmatrix} F & f_p & \psi \\ 0 & 0 & 0 \end{bmatrix} \\ \begin{bmatrix} J & u \\ v^T & 0 \end{bmatrix} \begin{bmatrix} D & E & K & L \\ d & e & k & l \end{bmatrix} &= \begin{bmatrix} G - (Jv)_x A & (Jv)_p - (Jv)_x B & -(Jv)_x C & -(Jv)_x v \\ 0 & 0 & 0 & 0 \end{bmatrix} \\ \begin{bmatrix} \sigma & 0 & b & c \\ -l & \sigma & e & k \\ \langle v,\psi\rangle & 0 & -\langle B,\psi\rangle & -\langle C,\psi\rangle \\ \phi^T L & \phi^T v & -\phi^T E & -\phi^T K \end{bmatrix} \begin{bmatrix} \alpha \\ \beta \\ z \\ w \end{bmatrix} &= \begin{bmatrix} a \\ d \\ s - \langle A,\psi\rangle h - \phi^T D \end{bmatrix} \\ X &= A - B z - C w + v \alpha \\ Y &= D - E z - K w + L \alpha + v \beta \end{split}$

where $\sigma = \|J v\|$ and $u = J v/\sigma$ . Each bordered solve is implemented by a LOCA::BorderedSolver::AbstractStrategy strategy object.

Constructor & Destructor Documentation

◆ PhippsBordering()

LOCA::Pitchfork::MooreSpence::PhippsBordering::PhippsBordering	(	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. Instantiates a bordered solver for solving the bordeded systems described above. See LOCA::BorderedSolver::Factory for a description of available solvers.

References borderedSolver, globalData, and solverParams.

Member Function Documentation

◆ setBlocks()

void LOCA::Pitchfork::MooreSpence::PhippsBordering::setBlocks	(	const Teuchos::RCP< LOCA::Pitchfork::MooreSpence::AbstractGroup > &	group,
		const Teuchos::RCP< LOCA::Pitchfork::MooreSpence::ExtendedGroup > &	pfGroup,
		const Teuchos::RCP< const NOX::Abstract::MultiVector > &	asymMultiVector,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	nullVector,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	JnVector,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	dfdp,
		const Teuchos::RCP< const NOX::Abstract::Vector > &	dJndp
	)

virtual

Set blocks in extended linear system.

Parameters

group	[in] Underlying group representing J
pfGroup	[in] Pitchfork group representing the pitchfork equations.
asymMultiVector	[in] Multivector representing the asymmetric vector
nullVector	[in] Vector representing v
JnVector	[in] Vector representing Jv
dfdp	[in] Vector representing df/dp
dJndp	[in] Vector representing d(Jv)/dp

Implements LOCA::Pitchfork::MooreSpence::SolverStrategy.

References NOX::DeepCopy, and NOX::Abstract::Vector::TwoNorm.

◆ solve()

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

virtual

Solves the extended system as defined above.

The params argument is the linear solver parameters.

Implements LOCA::Pitchfork::MooreSpence::SolverStrategy.

References LOCA::Pitchfork::MooreSpence::ExtendedMultiVector::getBifParams(), LOCA::Pitchfork::MooreSpence::ExtendedMultiVector::getNullMultiVec(), LOCA::Pitchfork::MooreSpence::ExtendedMultiVector::getSlacks(), LOCA::Pitchfork::MooreSpence::ExtendedMultiVector::getXMultiVec(), and LOCA::Extended::MultiVector::numVectors().

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

LOCA_Pitchfork_MooreSpence_PhippsBordering.H
LOCA_Pitchfork_MooreSpence_PhippsBordering.C

Public Member Functions