Implementation of LOCA::MultiContinuation::ConstraintInterfaceMVDX for computing Hopf bifurcations for the minimally augmented Hopf formulation. More...

#include <LOCA_Hopf_MinimallyAugmented_Constraint.H>

Inheritance diagram for LOCA::Hopf::MinimallyAugmented::Constraint:

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Collaboration diagram for LOCA::Hopf::MinimallyAugmented::Constraint:

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Public Member Functions
	Constraint (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< LOCA::Parameter::SublistParser > &topParams, const Teuchos::RCP< Teuchos::ParameterList > &hpfParams, const Teuchos::RCP< LOCA::Hopf::MinimallyAugmented::AbstractGroup > &g, bool is_symmetric, const NOX::Abstract::Vector &a_real, const NOX::Abstract::Vector &a_imag, const NOX::Abstract::Vector b_real, const NOX::Abstract::Vector b_imag, int bif_param, double freq)
	Constructor.

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

virtual	~Constraint ()
	Destructor.

virtual void	setGroup (const Teuchos::RCP< LOCA::Hopf::MinimallyAugmented::AbstractGroup > &g)
	Set the group pointer. More...

virtual void	setFrequency (double freq)
	Set Hopf frequency.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getLeftNullVecReal () const
	Returns real component of left null vector w.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getLeftNullVecImag () const
	Returns imaginary component of left null vector w.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getRightNullVecReal () const
	Returns real component of right null vector v.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getRightNullVecImag () const
	Returns imaginary component of right null vector v.

virtual double	getSigmaReal () const
	Returns real component of sigma.

virtual double	getSigmaImag () const
	Returns imaginary component of sigma.

virtual NOX::Abstract::Group::ReturnType	computeDOmega (NOX::Abstract::MultiVector::DenseMatrix &domega)
	Compute derivative of sigma w.r.t. frequency omega.

Implementation of LOCA::MultiContinuation::ConstraintInterface
virtual methods
virtual void	copy (const LOCA::MultiContinuation::ConstraintInterface &source)
	Copy.

virtual Teuchos::RCP < LOCA::MultiContinuation::ConstraintInterface >	clone (NOX::CopyType type=NOX::DeepCopy) const
	Cloning function.

virtual int	numConstraints () const
	Return number of constraints.

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

virtual void	setParam (int paramID, double val)
	Sets parameter indexed by paramID.

virtual void	setParams (const std::vector< int > &paramIDs, const NOX::Abstract::MultiVector::DenseMatrix &vals)
	Sets parameters indexed by paramIDs.

virtual NOX::Abstract::Group::ReturnType	computeConstraints ()
	Compute continuation constraint equations.

virtual NOX::Abstract::Group::ReturnType	computeDX ()
	Compute derivative of constraints w.r.t. solution vector x.

virtual NOX::Abstract::Group::ReturnType	computeDP (const std::vector< int > &paramIDs, NOX::Abstract::MultiVector::DenseMatrix &dgdp, bool isValidG)
	Compute derivative of constraints w.r.t. supplied parameters. More...

virtual bool	isConstraints () const
	Return `true` if constraint residuals are valid.

virtual bool	isDX () const
	Return `true` if derivatives of constraints w.r.t. x are valid.

virtual const NOX::Abstract::MultiVector::DenseMatrix &	getConstraints () const
	Return constraint residuals.

virtual const NOX::Abstract::MultiVector *	getDX () const
	Return solution component of constraint derivatives.

virtual bool	isDXZero () const
	Return `true` if solution component of constraint derivatives is zero.

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

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

virtual	~ConstraintInterfaceMVDX ()
	Destructor.

virtual NOX::Abstract::Group::ReturnType	multiplyDX (double alpha, const NOX::Abstract::MultiVector &input_x, NOX::Abstract::MultiVector::DenseMatrix &result_p) const
	Compute result_p = alpha * dg/dx * input_x. More...

virtual NOX::Abstract::Group::ReturnType	addDX (Teuchos::ETransp transb, double alpha, const NOX::Abstract::MultiVector::DenseMatrix &b, double beta, NOX::Abstract::MultiVector &result_x) const
	Compute result_x = alpha * dg/dx^T * op(b) + beta * result_x. More...

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

virtual	~ConstraintInterface ()
	Destructor.

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

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

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

Teuchos::RCP < Teuchos::ParameterList >	hopfParams
	Bifurcation parameter list.

Teuchos::RCP < LOCA::Hopf::MinimallyAugmented::AbstractGroup >	grpPtr
	Pointer to base group that defines .

Teuchos::RCP < NOX::Abstract::MultiVector >	a_vector
	Vector for .

Teuchos::RCP < NOX::Abstract::MultiVector >	b_vector
	Vector for .

Teuchos::RCP < NOX::Abstract::MultiVector >	w_vector
	Stores left null vector.

Teuchos::RCP < NOX::Abstract::MultiVector >	v_vector
	Stores right null vector.

Teuchos::RCP < NOX::Abstract::MultiVector >	Cv_vector
	Stores C*v.

Teuchos::RCP < NOX::Abstract::MultiVector >	sigma_x
	Stores sigma_x.

NOX::Abstract::MultiVector::DenseMatrix	constraints
	Constraint values.

Teuchos::RCP < LOCA::BorderedSolver::AbstractStrategy >	borderedSolver
	Stores bordered solver strategy.

double	dn
	Stores vector length as a double.

double	sigma_scale
	Stores scale factor on sigma.

bool	isSymmetric
	Flag indicating whether Jacobian is symmetric.

bool	isValidConstraints
	Flag indicating whether constraints are valid.

bool	isValidDX
	Flag indicating whether sigma_x is valid.

std::vector< int >	bifParamID
	Stores the bifurcation parameter index.

double	omega
	Stores Hopf frequency.

bool	updateVectorsEveryContinuationStep
	Flag indicating whether to update and every continuation step.

bool	updateVectorsEveryIteration
	Flag indicating whether to update and every nonlinear iteration.

Detailed Description

Implementation of LOCA::MultiContinuation::ConstraintInterfaceMVDX for computing Hopf bifurcations for the minimally augmented Hopf formulation.

This class implements the turning point constraint equation $\sigma(x,p,\omega) = 0$ for the minimally augmented Hopf formulation where $\sigma$ is defined via

$\begin{bmatrix} J+i\omega M & a \\ b^H & 0 \end{bmatrix} \begin{bmatrix} v \\ \sigma_1 \end{bmatrix} = \begin{bmatrix} 0 \\ n \end{bmatrix},$

$\begin{bmatrix} J^T-i\omega M^T & b \\ a^H & 0 \end{bmatrix} \begin{bmatrix} w \\ \sigma_2 \end{bmatrix} = \begin{bmatrix} 0 \\ n \end{bmatrix},$

$\sigma = w^H J+i\omega M v/n$

for any vectors $a$ and $b$ in $\mathbb{C}^n$ . Using these relationships, it is easy to show

$\begin{split} \sigma_x &= (w^H(J+i\omega M)v)_x/n = w^H(J+i\omega M)_x v/n \\ \sigma_p &= (w^H(J+i\omega M)v)_p/n = w^H(J+i\omega M)_p v/n \end{split}$

The class is intialized via the hpfParams parameter list argument to the constructor. The parameters this class recognizes are:

"Update Null Vectors Every Continuation Step" – [bool] (default: true) - Flag indicating whether to update and vectors via and every continuation step
"Update Null Vectors Every Nonlinear Iteration" – [bool] (default: false) - Flag indicating whether to update and vectors via and every nonlinear iteration

Member Function Documentation

NOX::Abstract::Group::ReturnType LOCA::Hopf::MinimallyAugmented::Constraint::computeDP	(	const std::vector< int > &	paramIDs,
		NOX::Abstract::MultiVector::DenseMatrix &	dgdp,
		bool	isValidG
	)

virtual

Compute derivative of constraints w.r.t. supplied parameters.

The first column of dgdp should be filled with the constraint residuals $g$ if isValidG is false. If isValidG is true, then the dgdp contains $g$ on input.

Implements LOCA::MultiContinuation::ConstraintInterface.

References NOX::Abstract::Group::Ok, Teuchos::SerialDenseMatrix< OrdinalType, ScalarType >::scale(), and Teuchos::View.

void LOCA::Hopf::MinimallyAugmented::Constraint::postProcessContinuationStep ( LOCA::Abstract::Iterator::StepStatus stepStatus )

virtual

Perform any postprocessing after a continuation step finishes.

The stepStatus argument indicates whether the step was successful. Here we update the $a$ and $b$ vectors to $w$ and $v$ respectively if requested.

Reimplemented from LOCA::MultiContinuation::ConstraintInterface.

References NOX::Utils::StepperDetails, and LOCA::Abstract::Iterator::Successful.

void LOCA::Hopf::MinimallyAugmented::Constraint::setGroup ( const Teuchos::RCP< LOCA::Hopf::MinimallyAugmented::AbstractGroup > & g )

virtual

Set the group pointer.

This method should be called when ever the constrained group is copied, since we don't explicitly copy the underlying group here.

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

LOCA_Hopf_MinimallyAugmented_Constraint.H
LOCA_Hopf_MinimallyAugmented_Constraint.C

Public Member Functions

Protected Attributes

Detailed Description

Member Function Documentation