A group representing the minimally augemented turning point equations. More...

#include <LOCA_TurningPoint_MinimallyAugmented_ExtendedGroup.H>

Inheritance diagram for LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup:

Collaboration diagram for LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup:

Public Member Functions
	ExtendedGroup (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)
	Constructor with initial data passed through parameter lists.

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

virtual	~ExtendedGroup ()
	Destructor.

double	getBifParam () const
	Get bifurcation parameter.

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

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

Teuchos::RCP< const NOX::Abstract::Vector >	getAVec () const
	Returns "A" vector.

Teuchos::RCP< const NOX::Abstract::Vector >	getBVec () const
	Returns "B".

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
	Cloning function.

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

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

virtual NOX::Abstract::Group::ReturnType	computeF ()
	Compute the turning point equation residual . More...

virtual NOX::Abstract::Group::ReturnType	computeJacobian ()
	Compute the blocks of the Jacobian derivative of . More...

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

virtual NOX::Abstract::Group::ReturnType	computeNewton (Teuchos::ParameterList &params)
	Compute Newton direction using applyJacobianInverse().

virtual NOX::Abstract::Group::ReturnType	applyJacobian (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Computes the extended Jacobian vector product.

virtual NOX::Abstract::Group::ReturnType	applyJacobianTranspose (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Computes the extended Jacobian transpose vector product.

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

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 for extended 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 the 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 equation residual .

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

virtual const NOX::Abstract::Vector &	getGradient () const
	Vector returned is not valid.

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

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

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

virtual Teuchos::RCP< const NOX::Abstract::Vector >	getGradientPtr () const
	Vector returned is not valid.

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

virtual double	getNormNewtonSolveResidual () const
	Return the norm of the Newton solve residual.

Implementation of LOCA::Extended::MultiAbstractGroup
virtual methods
virtual Teuchos::RCP< const LOCA::MultiContinuation::AbstractGroup >	getUnderlyingGroup () const
	Return underlying group.

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

Implementation of LOCA::MultiContinuation::AbstractGroup
virtual methods
virtual void	copy (const NOX::Abstract::Group &source)
	Assignment operator.

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

virtual void	setParams (const ParameterVector &p)
	Set the parameter vector in the group to p.

virtual void	setParam (std::string paramID, double val)
	Set parameter indexed by paramID.

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

virtual const ParameterVector &	getParams () const
	Return a const reference to the paramter vector owned by the group.

virtual double	getParam (int paramID) const
	Return copy of parameter indexed by paramID.

virtual double	getParam (std::string paramID) const
	Return copy of parameter indexed by paramID.

virtual NOX::Abstract::Group::ReturnType	computeDfDpMulti (const std::vector< int > &paramIDs, NOX::Abstract::MultiVector &dfdp, bool isValidF)

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 void	projectToDraw (const NOX::Abstract::Vector &x, double *px) const
	Projects solution to a few scalars for multiparameter continuation.

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

virtual void	printSolution (const double conParam) const
	Function to print out extended solution and continuation parameter after successful continuation step. More...

virtual void	printSolution (const NOX::Abstract::Vector &x_, const double conParam) const
	Function to print out extended solution and continuation parameter after successful continuation step. More...

Implementation of
LOCA::BorderedSystem::AbstractGroup virtual methods
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.

Implementation of LOCA::Abstract::TransposeSolveGroup
virtual methods
virtual NOX::Abstract::Group::ReturnType	applyJacobianTransposeInverse (Teuchos::ParameterList &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Solve Jacobian-tranpose system.

virtual NOX::Abstract::Group::ReturnType	applyJacobianTransposeInverseMultiVector (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	Solve Jacobian-tranpose system with multiple right-hand sides.

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

virtual	~MultiAbstractGroup ()
	Destructor.

virtual Teuchos::RCP < NOX::Abstract::Group >	getNestedGroup ()
	Override from NOX::Abstract::Group base class. Calls getUnderlyingGroup() from this class.

virtual Teuchos::RCP< const NOX::Abstract::Group >	getNestedGroup () const
	Override from NOX::Abstract::Group base class. Calls getUnderlyingGroup() from this class.

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::MultiContinuation::AbstractGroup
	AbstractGroup ()
	Default constructor.

virtual	~AbstractGroup ()
	Destructor.

virtual double	computeScaledDotProduct (const NOX::Abstract::Vector &a, const NOX::Abstract::Vector &b) const
	Compute a scaled dot product. More...

virtual void	scaleVector (NOX::Abstract::Vector &x) const
	Scales a vector using scaling vector. More...

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

virtual	~AbstractGroup ()
	Destructor.

Public Member Functions inherited from LOCA::Abstract::TransposeSolveGroup
	TransposeSolveGroup ()
	Constructor.

virtual	~TransposeSolveGroup ()
	Destructor.

Protected Member Functions
void	setBifParam (double param)
	Set bifurcation parameter.

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 < LOCA::TurningPoint::MinimallyAugmented::Constraint >	constraint
	Pointer to the constraint equation.

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

int	bifParamID
	Stores the bifurcation parameter index.

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...

Detailed Description

A group representing the minimally augemented turning point equations.

The LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup is a concrete implementation of the NOX::Abstract::Group, LOCA::MultiContinuation::AbstractGroup and LOCA::Extended::MultiAbstractGroup that defines the following extended set of equations that are regular at a generic turning point:

$G(z) = \left[ \begin{array}{c} F(x,p) \\ \sigma \end{array} \right] = 0$

where $z = [x, p]\in\Re^{n+1}$ , $x$ is the solution vector, $p$ is the bifurcation parameter, $J$ is the Jacobian of $F$ , and $\sigma\in\Re$ is a measure of the singularity of $F$ and 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 group stores an underlying group of type LOCA::TurningPoint::MinimallyAugmented::AbstractGroup to represent the equations $F(x,p) = 0$ and to manipulate the underlying Jacobian $J$ . This interface defines methods for computing the derivatives $(w^T J v)_x$ and $(w^T J v)_p$ as well.

This class implements all of the NOX::Abstract::Group, LOCA::MultiContinuation::AbstractGroup, and LOCA::Extended::MultiAbstractGroup methods for this extended set of equations and therefore is a complete group which can be passed to most NOX solvers to locate a single turning point or to the LOCA::Stepper to compute a family of turning points in a second parameter.

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

"Bifurcation Parameter" – [string] (Must be supplied) - Name of the bifurcation parameter
"Bordered Solver Method" – [string] (default "Bordering") Method for solving bordered systems of equations. See LOCA::BorderedSolver::Factory for a description.
"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
"Constraint Method" – [string] (default: "Default") - Type of constraint method to use. Valid choices are
- "Default" (LOCA::TurningPoint::MinimallyAugmented::Constraint) Default method described above.
- "Modified" (LOCA::TurningPoint::MinimallyAugmented::ModifiedConstraint) A modified method that computes updates to the null vectors every nonlinear interation, instead of directly solving for them
"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 $a$ and $b$ are set to 1.0
"Null Vector Scaling Method" – [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 Function Documentation

NOX::Abstract::Group::ReturnType LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::computeDfDpMulti	(	const std::vector< int > &	paramIDs,
		NOX::Abstract::MultiVector &	dfdp,
		bool	isValidF
	)

virtual

Compute $\partial F/\partial p$ for each parameter $p$ indexed by paramIDs. The first column of dfdp holds F, which is valid if isValidF is true. Otherwise F must be computed.

Implements LOCA::MultiContinuation::AbstractGroup.

NOX::Abstract::Group::ReturnType LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::computeF ( )

virtual

Compute the turning point equation residual $G$ .

This method fills the extended residual

$G(z) = \left[ \begin{array}{c} F(x,p) \\ \sigma \end{array} \right].$

Implements NOX::Abstract::Group.

NOX::Abstract::Group::ReturnType LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::computeJacobian ( )

virtual

Compute the blocks of the Jacobian derivative of $G$ .

This method computes the $J$ , $F_p$ , $\sigma_x$ and $\sigma_p$ blocks of the extended Jacobian:

$D_z G(z) = \begin{bmatrix} J & F_p \\ \sigma_x & \sigma_p \end{bmatrix}$

Reimplemented from NOX::Abstract::Group.

void LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::extractParameterComponent	(	bool	use_transpose,
		const NOX::Abstract::MultiVector &	v,
		NOX::Abstract::MultiVector::DenseMatrix &	v_p
	)		const

virtual

Given the vector v, extract the parameter components of all of the nested subvectors in v down to the solution component for the unbordered group.

Implements LOCA::BorderedSystem::AbstractGroup.

void LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::extractSolutionComponent	(	const NOX::Abstract::MultiVector &	v,
		NOX::Abstract::MultiVector &	v_x
	)		const

virtual

Given the vector v, extract the underlying solution component corresponding to the unbordered group.

Implements LOCA::BorderedSystem::AbstractGroup.

void LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::loadNestedComponents	(	const NOX::Abstract::MultiVector &	v_x,
		const NOX::Abstract::MultiVector::DenseMatrix &	v_p,
		NOX::Abstract::MultiVector &	v
	)		const

virtual

Given the solution component v_x and combined parameter components v_p, distribute these components through the nested sub-vectors in v.

Implements LOCA::BorderedSystem::AbstractGroup.

void LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::postProcessContinuationStep ( LOCA::Abstract::Iterator::StepStatus stepStatus )

virtual

Perform any postprocessing after a continuation step finishes.

The stepStatus argument indicates whether the step was successful.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

void LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::preProcessContinuationStep ( LOCA::Abstract::Iterator::StepStatus stepStatus )

virtual

Perform any preprocessing before a continuation step starts.

The stepStatus argument indicates whether the previous step was successful.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

void LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::printSolution ( const double conParam ) const

virtual

Function to print out extended solution and continuation parameter after successful continuation step.

This method prints the solution, null-vector, and parameter components of the extended solution vector using the printSolution method of the underlying group.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

References NOX::Utils::StepperDetails.

void LOCA::TurningPoint::MinimallyAugmented::ExtendedGroup::printSolution	(	const NOX::Abstract::Vector &	x_,
		const double	conParam
	)		const

virtual

Function to print out extended solution and continuation parameter after successful continuation step.

This method prints the solution, null-vector, and parameter components of the extended solution vector using the printSolution method of the underlying group.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

References LOCA::Extended::Vector::getScalar(), LOCA::MultiContinuation::ExtendedVector::getXVec(), and NOX::Utils::StepperDetails.

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

LOCA_TurningPoint_MinimallyAugmented_ExtendedGroup.H
LOCA_TurningPoint_MinimallyAugmented_ExtendedGroup.C

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation