Specialization of LOCA::MultiContinuation::ExtendedGroup to pseudo-arclength continuation. More...

#include <LOCA_MultiContinuation_ArcLengthGroup.H>

Inheritance diagram for LOCA::MultiContinuation::ArcLengthGroup:

Collaboration diagram for LOCA::MultiContinuation::ArcLengthGroup:

Public Member Functions
	ArcLengthGroup (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< LOCA::Parameter::SublistParser > &topParams, const Teuchos::RCP< Teuchos::ParameterList > &continuationParams, const Teuchos::RCP< LOCA::MultiContinuation::AbstractGroup > &grp, const Teuchos::RCP< LOCA::MultiPredictor::AbstractStrategy > &pred, const std::vector< int > &paramIDs)
	Constructor. More...

	ArcLengthGroup (const ArcLengthGroup &source, NOX::CopyType type=NOX::DeepCopy)
	Copy constructor.

virtual	~ArcLengthGroup ()
	Destructor.

Implementation of NOX::Abstract::Group virtual methods
virtual NOX::Abstract::Group &	operator= (const NOX::Abstract::Group &source)
	Assignment operator.

virtual Teuchos::RCP < NOX::Abstract::Group >	clone (NOX::CopyType type=NOX::DeepCopy) const
	Clone function.

Implementation of LOCA::MultiContinuation::AbstractStrategy virtual methods
virtual void	copy (const NOX::Abstract::Group &source)
	Copy.

virtual void	scaleTangent ()
	Scales predictor.

virtual double	computeScaledDotProduct (const NOX::Abstract::Vector &x, const NOX::Abstract::Vector &y) const
	Computes a scaled dot product between two continuation vectors.

virtual void	recalculateScaleFactor (double dpds, double thetaOld, double &thetaNew)
	Calculates scale factors.

Public Member Functions inherited from LOCA::MultiContinuation::ExtendedGroup
	ExtendedGroup (const ExtendedGroup &source, NOX::CopyType type=NOX::DeepCopy)
	Copy constructor.

virtual	~ExtendedGroup ()
	Destructor.

virtual void	setX (const NOX::Abstract::Vector &y)
	Set the solution vector to y.

virtual void	computeX (const NOX::Abstract::Group &g, const NOX::Abstract::Vector &d, double step)
	Compute and return solution vector, x, where this.x = grp.x + step * d.

virtual NOX::Abstract::Group::ReturnType	computeF ()
	Compute extended continuation equations.

virtual NOX::Abstract::Group::ReturnType	computeJacobian ()
	Compute extended continuation jacobian.

virtual NOX::Abstract::Group::ReturnType	computeGradient ()
	Gradient is not defined for this system.

virtual NOX::Abstract::Group::ReturnType	computeNewton (Teuchos::ParameterList &params)
	Compute Newton direction for extended continuation system.

virtual NOX::Abstract::Group::ReturnType	applyJacobian (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Applies Jacobian for extended system.

virtual NOX::Abstract::Group::ReturnType	applyJacobianTranspose (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Jacobian transpose not defined for this system.

virtual NOX::Abstract::Group::ReturnType	applyJacobianInverse (Teuchos::ParameterList &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Applies Jacobian inverse for extended system.

virtual NOX::Abstract::Group::ReturnType	applyJacobianMultiVector (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	Applies Jacobian for extended system.

virtual NOX::Abstract::Group::ReturnType	applyJacobianTransposeMultiVector (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	Jacobian transpose not defined for this system.

virtual NOX::Abstract::Group::ReturnType	applyJacobianInverseMultiVector (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	Applies Jacobian inverse for extended system.

virtual bool	isF () const
	Return `true` if extended residual is valid.

virtual bool	isJacobian () const
	Return `true` if the extended Jacobian is valid.

virtual bool	isGradient () const
	Always returns false.

virtual bool	isNewton () const
	Return `true` if the extended Newton direction is valid.

virtual const NOX::Abstract::Vector &	getX () const
	Return extended solution vector.

virtual const NOX::Abstract::Vector &	getF () const
	Return extended residual.

virtual double	getNormF () const
	Return 2-norm of extended residual.

virtual const NOX::Abstract::Vector &	getGradient () const
	Gradient is never valid.

virtual const NOX::Abstract::Vector &	getNewton () const
	Return extended Newton direction.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getXPtr () const
	Return extended solution vector.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getFPtr () const
	Return extended residual.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getGradientPtr () const
	Gradient is never valid.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getNewtonPtr () const
	Return extended Newton direction.

virtual double	getNormNewtonSolveResidual () const
	Returns 2-norm of extended Newton solve residual.

virtual Teuchos::RCP< const LOCA::MultiContinuation::AbstractGroup >	getUnderlyingGroup () const
	Return underlying group.

virtual Teuchos::RCP < LOCA::MultiContinuation::AbstractGroup >	getUnderlyingGroup ()
	Return underlying group.

virtual int	getNumParams () const
	Returns number of parameters.

virtual void	preProcessContinuationStep (LOCA::Abstract::Iterator::StepStatus stepStatus)
	Perform any preprocessing before a continuation step starts. More...

virtual void	postProcessContinuationStep (LOCA::Abstract::Iterator::StepStatus stepStatus)
	Perform any postprocessing after a continuation step finishes. More...

virtual NOX::Abstract::Group::ReturnType	computePredictor ()
	Compute predictor directions.

virtual bool	isPredictor () const
	Is Predictor valid.

virtual void	setPredictorTangentDirection (const LOCA::MultiContinuation::ExtendedVector &v, int i)
	Sets tangent to predictor. More...

virtual const LOCA::MultiContinuation::ExtendedMultiVector &	getPredictorTangent () const
	Returns tangent to predictor.

virtual const LOCA::MultiContinuation::ExtendedMultiVector &	getScaledPredictorTangent () const
	Returns scaled tangent to predictor.

virtual void	setPrevX (const NOX::Abstract::Vector &y)
	Set the previous solution vector y.

virtual const LOCA::MultiContinuation::ExtendedVector &	getPrevX () const
	Gets the previous solution vector.

virtual void	setStepSize (double deltaS, int i=0)
	Set step size for continuation constraint equation i.

virtual double	getStepSize (int i=0) const
	Get step size for continuation constraint equation i.

virtual void	setContinuationParameter (double val, int i=0)
	Sets the value for continuation parameter i.

virtual double	getContinuationParameter (int i=0) const
	Returns the value for continuation parameter i.

virtual int	getContinuationParameterID (int i=0) const
	Get the continuation parameter id for parameter i.

virtual const std::vector< int > &	getContinuationParameterIDs () const
	Get the continuation parameter ids.

virtual std::string	getContinuationParameterName (int i=0) const
	Get the continuation parameter id for parameter i.

virtual double	getStepSizeScaleFactor (int i=0) const
	Returns step size scale factor for constraint equation i.

virtual void	printSolution () const
	Prints the group.

virtual int	projectToDrawDimension () const
	Returns dimension of project to draw array.

virtual void	projectToDraw (const LOCA::MultiContinuation::ExtendedVector &x, double *px) const
	Fills the project to draw array.

virtual int	getBorderedWidth () const
	Return the total width of the bordered rows/columns.

virtual Teuchos::RCP< const NOX::Abstract::Group >	getUnborderedGroup () const
	Get bottom-level unbordered group.

virtual bool	isCombinedAZero () const
	Indicates whether combined A block is zero.

virtual bool	isCombinedBZero () const
	Indicates whether combined B block is zero.

virtual bool	isCombinedCZero () const
	Indicates whether combined C block is zero.

virtual void	extractSolutionComponent (const NOX::Abstract::MultiVector &v, NOX::Abstract::MultiVector &v_x) const

virtual void	extractParameterComponent (bool use_transpose, const NOX::Abstract::MultiVector &v, NOX::Abstract::MultiVector::DenseMatrix &v_p) const

virtual void	loadNestedComponents (const NOX::Abstract::MultiVector &v_x, const NOX::Abstract::MultiVector::DenseMatrix &v_p, NOX::Abstract::MultiVector &v) const

virtual void	fillA (NOX::Abstract::MultiVector &A) const
	Fill the combined A block as described above.

virtual void	fillB (NOX::Abstract::MultiVector &B) const
	Fill the combined B block as described above.

virtual void	fillC (NOX::Abstract::MultiVector::DenseMatrix &C) const
	Fill the combined C block as described above.

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

virtual	~AbstractStrategy ()
	Destructor.

Public Member Functions inherited from LOCA::Extended::MultiAbstractGroup
	MultiAbstractGroup ()
	Default constructor.

virtual	~MultiAbstractGroup ()
	Destructor.

virtual Teuchos::RCP< const LOCA::MultiContinuation::AbstractGroup >	getBaseLevelUnderlyingGroup () const
	Return base-level underlying group. More...

virtual Teuchos::RCP < LOCA::MultiContinuation::AbstractGroup >	getBaseLevelUnderlyingGroup ()
	Return base-level underlying group. More...

Public Member Functions inherited from NOX::Abstract::Group
	Group ()
	Constructor. More...

virtual	~Group ()
	Destructor.

virtual NOX::Abstract::Group::ReturnType	applyRightPreconditioning (bool useTranspose, Teuchos::ParameterList &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Apply right preconditiong to the given input vector. More...

virtual NOX::Abstract::Group::ReturnType	applyRightPreconditioningMultiVector (bool useTranspose, Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	applyRightPreconditioning for multiple right-hand sides More...

virtual const NOX::Abstract::Vector &	getScaledX () const

virtual void	logLastLinearSolveStats (NOX::SolverStats &stats) const
	Adds statistics from last linear solve to the SovlerStats object.

virtual NOX::Abstract::Group::ReturnType	getNormLastLinearSolveResidual (double &residual) const
	Return the norm of the last linear solve residual as the result of either a call to computeNewton() or applyJacobianInverse(). More...

Public Member Functions inherited from LOCA::BorderedSystem::AbstractGroup
	AbstractGroup ()
	Constructor.

virtual	~AbstractGroup ()
	Destructor.

Protected Attributes
std::vector< double >	theta
	Stores scaling factor for each arclength equation.

bool	doArcLengthScaling
	Flag indicating whether to do arc-length scaling.

double	gGoal
	Goal value of dp/ds squared.

double	gMax
	Minimum value for dp/ds for which rescaling is applied.

double	thetaMin
	Maximum value of scale factor.

bool	isFirstRescale
	Flag indicating whether this is the first rescaling of predictor.

Protected Attributes inherited from LOCA::MultiContinuation::ExtendedGroup
Teuchos::RCP< LOCA::GlobalData >	globalData
	Pointer LOCA global data object.

Teuchos::RCP < LOCA::Parameter::SublistParser >	parsedParams
	Parsed top-level parameters.

Teuchos::RCP < Teuchos::ParameterList >	continuationParams
	Continuation parameter list.

Teuchos::RCP < LOCA::MultiContinuation::AbstractGroup >	grpPtr
	Pointer to underlying group.

Teuchos::RCP < LOCA::MultiPredictor::AbstractStrategy >	predictor
	Pointer to predictor object.

Teuchos::RCP < LOCA::MultiContinuation::ConstrainedGroup >	conGroup
	Pointer to constrained group implementation.

int	numParams
	Number of parameters.

LOCA::MultiContinuation::ExtendedMultiVector	tangentMultiVec
	Stores the tangent to the predictor.

LOCA::MultiContinuation::ExtendedMultiVector	scaledTangentMultiVec
	Stores the scaled tangent to the predictor.

LOCA::MultiContinuation::ExtendedVector	prevXVec
	Stores the previous extended solution vector.

std::vector< int >	conParamIDs
	integer id of continuation parameters

std::vector< double >	stepSize
	continuation step size

std::vector< double >	stepSizeScaleFactor
	step size scale factors

bool	isValidPredictor
	Is Predictor vector valid.

bool	baseOnSecant
	Flag indicating whether to base predictor direction on secant.

Additional Inherited Members
Public Types inherited from NOX::Abstract::Group
enum	ReturnType { Ok, NotDefined, BadDependency, NotConverged, Failed }
	The computation of, say, the Newton direction in computeNewton() may fail in many different ways, so we have included a variety of return codes to describe the failures. Of course, we also have a code for success. More...

Protected Member Functions inherited from LOCA::MultiContinuation::ExtendedGroup
	ExtendedGroup (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< LOCA::Parameter::SublistParser > &topParams, const Teuchos::RCP< Teuchos::ParameterList > &continuationParams, const Teuchos::RCP< LOCA::MultiContinuation::AbstractGroup > &grp, const Teuchos::RCP< LOCA::MultiPredictor::AbstractStrategy > &pred, const std::vector< int > &paramIDs)
	Constructor used by derived classes.

virtual void	setConstraints (const Teuchos::RCP< LOCA::MultiContinuation::ConstraintInterface > &constraints, bool skip_dfdp)
	Set constraint object. More...

Detailed Description

Specialization of LOCA::MultiContinuation::ExtendedGroup to pseudo-arclength continuation.

Pseudo arc-length continuation corresponds to a continuation equation $g(x,p,x_0,p_0,x^\ast,p^\ast,v,\Delta s)=0$ with $g$ given by

$g(x,p,x_0,p_0,x^\ast,p^\ast,v,\Delta s)= (x-x^\ast)^Tv_x + (p-p^\ast) v_p - \Delta s$

where $v_x$ , $v_p$ are the solution and parameter components of the predictor direction $v$ respectively. This corresponds geometrically to constraining the nonlinear solver steps used in calculating $F(x,p)=0$ to be orthogonal to the predictor direction $v$ . The arclength constraint $g$ is represented by a LOCA::MultiContinuation::ArcLengthConstraint object.

This class also reimplements the scaleTangent() and computeScaledDotProduct() methods to implement a scaling method that tries to ensure the solution and parameter contributions to the arc-length equation are of the same order. Specifically, the arc-length equation is replaced by

$(x-x^\ast)^Tv_x + \theta^2(p-p^\ast) v_p - \Delta s = 0$

where $\theta$ is chosen so that $\theta^2 v_p$ is equal to a target value, 0.5 by default. Parameters for this scaling method are passed through the continuationParams argument to the constructor and are:

"Enable Arc Length Scaling" – [bool] (default: true)
"Initial Scale Factor" – double
"Goal Arc Length Parameter Contribution" – double
"Max Arc Length Parameter Contribution" – double
"Min Scale Factor" – double

Whether this scaling method is used is determined by the "Enable Arc Length Scaling", and the initial value for $\theta$ is given by "Initial Scale Factor". A new value of $\theta$ is chosen only if $\theta^2 v_p$ is larger than the value given by "Max Arc Length Parameter Contribution" and "Min Scale Factor" provides a minimum value for $\theta$ .

Constructor & Destructor Documentation

LOCA::MultiContinuation::ArcLengthGroup::ArcLengthGroup	(	const Teuchos::RCP< LOCA::GlobalData > &	global_data,
		const Teuchos::RCP< LOCA::Parameter::SublistParser > &	topParams,
		const Teuchos::RCP< Teuchos::ParameterList > &	continuationParams,
		const Teuchos::RCP< LOCA::MultiContinuation::AbstractGroup > &	grp,
		const Teuchos::RCP< LOCA::MultiPredictor::AbstractStrategy > &	pred,
		const std::vector< int > &	paramIDs
	)

Constructor.

Parameters

global_data	[in] Global data object
topParams	[in] Parsed top-level parameter list.
continuationParams	[in] Continuation parameters as described above.
grp	[in] Group representing .
pred	[in] Predictor strategy.
paramIDs	[in] Parameter IDs of continuation parameters.

References doArcLengthScaling, Teuchos::ParameterList::get(), gGoal, LOCA::MultiContinuation::ExtendedGroup::globalData, gMax, LOCA::MultiContinuation::ExtendedGroup::numParams, Teuchos::rcp(), LOCA::MultiContinuation::ExtendedGroup::setConstraints(), theta, and thetaMin.

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

LOCA_MultiContinuation_ArcLengthGroup.H
LOCA_MultiContinuation_ArcLengthGroup.C

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation