Implementation of LOCA::MultiContinuation::ConstraintInterfaceMVDX for computing turning points for the minimally augmented turning point formulation. More...

#include <LOCA_TurningPoint_MinimallyAugmented_Constraint.H>

Inheritance diagram for LOCA::TurningPoint::MinimallyAugmented::Constraint:

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Collaboration diagram for LOCA::TurningPoint::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 > &tpParams, const Teuchos::RCP< LOCA::TurningPoint::MinimallyAugmented::AbstractGroup > &g, int bif_param)
	Constructor.

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

virtual	~Constraint ()
	Destructor.

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

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getLeftNullVec () const
	Returns left null vector w.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getRightNullVec () const
	Returns right null vector v.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getAVec () const
	Returns a vector.

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getBVec () const
	Returns b vector.

virtual double	getSigma () const
	Returns sigma.

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 Types
enum	NullVectorScaling { NVS_None, NVS_OrderOne, NVS_OrderN }
	Enumerated type determining type of scaling. More...

Protected Member Functions
virtual void	scaleNullVectors (NOX::Abstract::Vector &a, NOX::Abstract::Vector &b)
	Scale a & b vectors.

virtual void	getInitialVectors (NOX::Abstract::Vector &a, NOX::Abstract::Vector &b)
	Get initial a & b vectors.

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 >	turningPointParams
	Bifurcation parameter list.

Teuchos::RCP < LOCA::TurningPoint::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 >	Jv_vector
	Stores J*v.

Teuchos::RCP < NOX::Abstract::MultiVector >	Jtw_vector
	Stores J^T*w.

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.

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

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

NullVectorScaling	nullVecScaling
	Null vector scaling method.

bool	multiplyMass
	Multiply null vectors by mass matrix.

Teuchos::RCP < LOCA::TimeDependent::AbstractGroup >	tdGrp
	Time dependent group interface for multiplying by mass matrix.

Teuchos::RCP < NOX::Abstract::Vector >	tmp_mass
	Temporary vector for mulplying null vectors by mass matrix.

Detailed Description

Implementation of LOCA::MultiContinuation::ConstraintInterfaceMVDX for computing turning points for the minimally augmented turning point formulation.

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

$\begin{bmatrix} J & a \\ b^T & 0 \end{bmatrix} \begin{bmatrix} v \\ \sigma_1 \end{bmatrix} = \begin{bmatrix} 0 \\ n \end{bmatrix},$

$\begin{bmatrix} J^T & b \\ a^T & 0 \end{bmatrix} \begin{bmatrix} w \\ \sigma_2 \end{bmatrix} = \begin{bmatrix} 0 \\ n \end{bmatrix},$

$\sigma = -w^T J v/n$

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

$\begin{split} \sigma_x &= -(w^T J v)_x/n = -w^T J_x v/n \\ \sigma_p &= -(w^T J v)_p/n = -w^T J_p v/n \end{split}$

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

"Symmetric Jacobian" – [bool] (default: false) - Flag indicating whether Jacobian matrix is symmetric, in which case we force and therefore the second tranpose solve for is unnecessary
"Initial Null Vector Compuation" – [string] (default: "User Provided") - Method to compute initial and vectors. Valid choices are:
- "User Provided" - Initial vectors are provided in the parameter list, in which case the following parameters are relevant:
  - "Initial A Vector" – [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied) - Vector storing initial value for vector
  - "Initial B Vector" – [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied for nonsymmetric Jacobians) - Vector storing initial value for vector
- "Solve df/dp" - Compute $a = J^{-T}df/dp$ and $b = J^{-1} df/dp$ where is the bifurcation parameter.
- "Constant" - Entries of and are set to 1.0
"Null Vector Scaling" – [string] (default: "Order N") - Method to scale and . This determines the norm of these vectors and the scaling of . Valid choices are:
- "None" – Use initial scaling
- "Order 1" – Scale to unit norm
- "Order N" – Use vector length scaling
"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
"Multiply Null Vectors by Mass Matrix" – [bool] (default: false) - Flag indicating whether to multiply and vectors by the mass matrix $M = \partial f/\partial\dot{x}$ at the strart of a turning point calculation, and each time and are updated. This can improve the scaling of these vectors, and may orthogonalize them against structural null spaces (i.e., pressure null space for incompressible Navier-Stokes).

Member Enumeration Documentation

enum LOCA::TurningPoint::MinimallyAugmented::Constraint::NullVectorScaling

protected

Enumerated type determining type of scaling.

Enumerator

NVS_OrderOne

No scaling.

NVS_OrderN

Scale to O(1)

Scale to O(N) when N is the vector length

Member Function Documentation

NOX::Abstract::Group::ReturnType LOCA::TurningPoint::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.