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.
	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.
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.

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] (default: 1.0)
"Goal Arc Length Parameter Contribution" -- [double] (default: 0.5)
"Max Arc Length Parameter Contribution" -- [double] (default: 0.8)
"Min Scale Factor" -- [double] (default: 1.0e-3)

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

Detailed Description

Constructor & Destructor Documentation