LOCA::Bifurcation::TPBord::ExtendedGroup Class Reference

LOCA's generic turning point group. Implements the bordering algorithm to solve turning point equations. More...

#include <LOCA_Bifurcation_TPBord_ExtendedGroup.H>

Inheritance diagram for LOCA::Bifurcation::TPBord::ExtendedGroup:

[legend]Collaboration diagram for LOCA::Bifurcation::TPBord::ExtendedGroup:[legend]List of all members.


Public Member Functions
	ExtendedGroup (LOCA::Bifurcation::TPBord::AbstractGroup &g, NOX::Parameter::List &bifParamList)
	Constructor with initial data passed through parameter lists.
	ExtendedGroup (LOCA::Bifurcation::TPBord::AbstractGroup &g, const NOX::Abstract::Vector &lenVec, const NOX::Abstract::Vector &nullVec, int paramId)
	Constructor to set the base group, length normalization vector , initial guess for the null vector , and bifurcation paramter id (integer).
	ExtendedGroup (const LOCA::Bifurcation::TPBord::AbstractGroup &g, const NOX::Abstract::Vector &lenVec, const NOX::Abstract::Vector &nullVec, int paramId)
	Constructor to set the base group, length normalization vector , initial guess for the null vector , and bifurcation paramter id (integer).
	ExtendedGroup (const ExtendedGroup &source, NOX::CopyType type=NOX::DeepCopy)
	Copy constructor.
virtual	~ExtendedGroup ()
	Destructor.
virtual ExtendedGroup &	operator= (const ExtendedGroup &source)
	Assignment operator.
double	getBifParam () const
	Get bifurcation parameter.
Implementation of NOX::Abstract::Group virtual methods
virtual NOX::Abstract::Group &	operator= (const NOX::Abstract::Group &source)
	Assignment operator.
virtual 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	setX (const LOCA::Bifurcation::TPBord::ExtendedVector &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 void	computeX (const LOCA::Bifurcation::TPBord::ExtendedGroup &g, const LOCA::Bifurcation::TPBord::ExtendedVector &d, double step)
	Compute this.x = grp.x + step * d.
virtual NOX::Abstract::Group::ReturnType	computeF ()
	Compute the turning point equation residual .
virtual NOX::Abstract::Group::ReturnType	computeJacobian ()
	Compute the blocks of the Jacobian derivative of .
virtual NOX::Abstract::Group::ReturnType	computeGradient ()
	Gradient computation is not defined for this group.
virtual NOX::Abstract::Group::ReturnType	computeNewton (NOX::Parameter::List &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
	Jacobian transpose product is not defined by this group.
virtual NOX::Abstract::Group::ReturnType	applyJacobianInverse (NOX::Parameter::List &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Applies the inverse of the extended Jacobian matrix using the bordering algorithm.
virtual NOX::Abstract::Group::ReturnType	applyRightPreconditioning (bool useTranspose, NOX::Parameter::List &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Applies the extended right preconditioner.
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 double	getNormNewtonSolveResidual () const
	Return the norm of the Newton solve residual.
Implementation of LOCA::Continuation::AbstractGroup virtual methods
virtual LOCA::Continuation::AbstractGroup &	operator= (const LOCA::Continuation::AbstractGroup &source)
	Assignment operator.
virtual void	setParams (const ParameterVector &p)
	Set the parameter vector in the group to p.
virtual const ParameterVector &	getParams () const
	Return a const reference to the paramter vector owned by the group.
virtual void	setParam (int paramID, double val)
	Set parameter indexed by paramID.
virtual double	getParam (int paramID) const
	Return copy of parameter indexed by paramID.
virtual void	setParam (string paramID, double val)
	Set parameter indexed by paramID.
virtual double	getParam (string paramID) const
	Return copy of parameter indexed by paramID.
virtual NOX::Abstract::Group::ReturnType	computeDfDp (int paramID, NOX::Abstract::Vector &result)
	Compute parameter derivative $dG/d\lambda$ for the extended system.
virtual NOX::Abstract::Group::ReturnType	applyJacobianInverseMulti (NOX::Parameter::List &params, const NOX::Abstract::Vector const inputs, NOX::Abstract::Vector **results, int nVecs) const
	applyJacobian for multiple right-hand sides Applies the inverse of the extended Jacobian matrix using the bordering algorithm for multiple right-hand sides.
virtual void	printSolution (const double conParam) const
	Function to print out extended solution and continuation parameter after successful continuation step.
Implementation of LOCA::Extended::AbstractGroup virtual methods
virtual LOCA::Extended::AbstractGroup &	operator= (const LOCA::Extended::AbstractGroup &source)
	Assignment operator.
virtual const LOCA::Continuation::AbstractGroup &	getUnderlyingGroup () const
	Return underlying group.
virtual LOCA::Continuation::AbstractGroup &	getUnderlyingGroup ()
	Return underlying group.
Protected Member Functions
void	init (bool perturbSoln=false, double perturbSize=0.0)
	Initializes group.
void	setBifParam (double param)
	Set bifurcation parameter.
double	lTransNorm (const NOX::Abstract::Vector &n) const
	Defines null vector normalization .
Protected Attributes
LOCA::Bifurcation::TPBord::AbstractGroup *	grpPtr
	Stores the underlying group, which stores the solution vector, jacobian, and solution residual.
LOCA::Bifurcation::TPBord::ExtendedVector	tpXVec
	Stores the turning point solution vector.
LOCA::Bifurcation::TPBord::ExtendedVector	tpFVec
	Stores the turning point residual vector.
LOCA::Bifurcation::TPBord::ExtendedVector	tpNewtonVec
	Stores the turning point Newton vector.
NOX::Abstract::Vector *	lengthVecPtr
	Stores the constant length vector.
int	bifParamId
	Stores the bifurcation parameter index.
NOX::Abstract::Vector *	derivResidualParamPtr
	Stores the derivative of the solution residual w.r.t. bifparam.
NOX::Abstract::Vector *	derivNullResidualParamPtr
	Stores the derivative of the null vector residual w.r.t. bifparam.
bool	ownsGroup
	Flag indicating whether we have our own copy of the underlying grp.
bool	isValidF
	Is residual vector valid.
bool	isValidJacobian
	Is Jacobian matrix valid.
bool	isValidNewton
	Is Newton vector valid.

Detailed Description

LOCA's generic turning point group. Implements the bordering algorithm to solve turning point equations.

The LOCA::Bifurcation::TPBord::Group is a concrete implementation of the NOX::Abstract::Group, LOCA::Continuation::AbstractGroup and LOCA::Extended::AbstractGroup that defines the following extended set of equations that are regular at a generic turning point:

$G(z) = \left[ \begin{array}{c} F(x,p) \\ Jn \\ l^Tn-1 \end{array} \right] = 0$

where $z = [x, n, p]\in\Re^{2n+1}$ , $x$ is the solution vector, $n$ is the null vector, $l$ is the length normalization vector and $J$ is the Jacobian of F.

The group stores an underlying group of type LOCA::Bifurcation::TPBord::AbstractGroup to represent the equations $F(x,p) = 0$ and to manipulate the underlying Jacobian $J$ . Note that the entire extended Jacobian $D_z G$ is not stored in memory, rather a block-elimination algorithm (bordering algorithm) is used to compute linear solves of the extended Jacobian (see LOCA::Bifurcation::TPBord::ExtendedGroup::applyJacobianInverse(), LOCA::Bifurcation::TPBord::ExtendedGroup::applyJacobianInverseMulti() for more details).

This class implements all of the NOX::Abstract::Group, LOCA::Continuation::AbstractGroup, and LOCA::Extended::AbstractGroup 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.

However, Jacobian-tranpose operations and gradient calculations cannot be implemented efficiently and therefore gradient-base nonlinear solvers such as steepest descent and Trust region methods cannot be used to solve the extended turning point equations.

Constructor & Destructor Documentation

LOCA::Bifurcation::TPBord::ExtendedGroup::ExtendedGroup ( LOCA::Bifurcation::TPBord::AbstractGroup & g,

const NOX::Abstract::Vector & lenVec,

const NOX::Abstract::Vector & nullVec,

int paramId

)

Constructor to set the base group, length normalization vector $l$ , initial guess for the null vector $n$ , and bifurcation paramter id (integer).
The initial guess to the null vector is re-scaled so that the normalization condition $l^Tn = 1$ is satisfied.
In this version of the constructor, a non-const reference to the underlying group g is passed and therefore the group will not be copied.

LOCA::Bifurcation::TPBord::ExtendedGroup::ExtendedGroup ( const LOCA::Bifurcation::TPBord::AbstractGroup & g,

const NOX::Abstract::Vector & lenVec,

const NOX::Abstract::Vector & nullVec,

int paramId

)

Constructor to set the base group, length normalization vector $l$ , initial guess for the null vector $n$ , and bifurcation paramter id (integer).
The initial guess to the null vector is re-scaled so that the normalization condition $l^Tn = 1$ is satisfied.
In this version of the constructor, a const reference to the underlying group g is passed and therefore the group will be copied.

Member Function Documentation

NOX::Abstract::Group::ReturnType LOCA::Bifurcation::TPBord::ExtendedGroup::applyJacobian ( const NOX::Abstract::Vector & input,

NOX::Abstract::Vector & result

) const [virtual]

Computes the extended Jacobian vector product.
This method computes the extended Jacobian vector product
$\begin{bmatrix} J & 0 & \frac{\partial F}{\partial p} \\ \frac{\partial Jn}{\partial x} & J & \frac{\partial Jn}{\partial p} \\ 0 & l^T & 0 \end{bmatrix} \begin{bmatrix} a \\ b \\ c \end{bmatrix} = \begin{bmatrix} Ja + \frac{\partial F}{\partial p}c \\ \frac{\partial Jn}{\partial x}a + Jb + \frac{\partial Jn}{\partial p}c \\ l^T b \end{bmatrix}$
using the applyJacobian and computeDJnDxa methods of the underlying group where $a$ , $b$ , and $c$ are the solution, null-vector, and paramter components of the given vector input. Vectors input and result must be of type LOCA::Bifurcation::TPBord::ExtendedVector, otherwise an error is thrown.
Reimplemented from NOX::Abstract::Group.

NOX::Abstract::Group::ReturnType LOCA::Bifurcation::TPBord::ExtendedGroup::applyJacobianInverse ( NOX::Parameter::List & params,

const NOX::Abstract::Vector & input,

NOX::Abstract::Vector & result

) const [virtual]

Applies the inverse of the extended Jacobian matrix using the bordering algorithm.
This method is a special case of applyJacobianInverseMulti() for a single right-hand-side.
Reimplemented from NOX::Abstract::Group.
Reimplemented in LOCA::Bifurcation::TPBord::ModifiedBorderingGroup, and LOCA::Bifurcation::TPBord::NicDayModifiedBorderingGroup.

NOX::Abstract::Group::ReturnType LOCA::Bifurcation::TPBord::ExtendedGroup::applyJacobianInverseMulti ( NOX::Parameter::List & params,

const NOX::Abstract::Vector *const * inputs,

NOX::Abstract::Vector ** results,

int nVecs

) const [virtual]

applyJacobian for multiple right-hand sides Applies the inverse of the extended Jacobian matrix using the bordering algorithm for multiple right-hand sides.
This method performs the following multiple right-hand-side linear solve of the extended Jacobian matrix:
$\begin{bmatrix} J & 0 & \frac{\partial F}{\partial p} \\ \frac{\partial Jn}{\partial x} & J & \frac{\partial Jn}{\partial p} \\ 0 & l^T & 0 \end{bmatrix} \begin{bmatrix} U \\ V \\ w^T \end{bmatrix} = \begin{bmatrix} X \\ Y \\ z^T \end{bmatrix}$
where $U$ , $V$ , $X$ , and $Y$ each have nVecs columns and $w$ , and $z$ each have nVecs components (i.e., each column of $X$ , $Y$ , and $z^T$ have the solution, null-vector, and parameter components of one right-hand-side). The solution components $U$ , $V$ , and $w$ are computed using a multiple right-hand-side block elimination (bordering) algorithm:
$\begin{split} J\begin{bmatrix} A & b \end{bmatrix} &= \begin{bmatrix} X & \frac{\partial F}{\partial p} \end{bmatrix} \\ J\begin{bmatrix} C & d \end{bmatrix} &= \begin{bmatrix} Y & \frac{\partial Jn}{\partial p} \end{bmatrix} - \frac{\partial Jn}{\partial x} \begin{bmatrix} A & b \end{bmatrix} \\ w &= \frac{C^Tl - z}{l^Td} \\ U &= A - b w^T \\ V &= C - d w^T \end{split}$
which requires $2(\text{nVecs} + 1)$ solves of the underlying Jacobian $J$ calculated by 2 calls to the applyJacobianInverseMulti method of the underlying group.
Each vector in the arrays inputs and outputs must be of type LOCA::Bifurcation::TPBord::ExtendedVector, otherwise an error is thrown.
Reimplemented from LOCA::Continuation::AbstractGroup.
Reimplemented in LOCA::Bifurcation::TPBord::ModifiedBorderingGroup.

NOX::Abstract::Group::ReturnType LOCA::Bifurcation::TPBord::ExtendedGroup::applyRightPreconditioning ( bool useTranspose,

NOX::Parameter::List & params,

const NOX::Abstract::Vector & input,

NOX::Abstract::Vector & result

) const [virtual]

Applies the extended right preconditioner.
This method is implemented using a similar bordering algorithm to applyJacobianInverse(), except calls to the underlying group's applyJacobianInvese method are replaced by applyRightPreconditioning.
Reimplemented from NOX::Abstract::Group.

NOX::Abstract::Group::ReturnType LOCA::Bifurcation::TPBord::ExtendedGroup::computeDfDp ( int paramID,

NOX::Abstract::Vector & result

) [virtual]

Compute parameter derivative $dG/d\lambda$ for the extended system.
For a given parameter $\lambda$ , this method computes the derivative
$\frac{\partial G(z,\lambda)}{\partial\lambda} = \left[ \begin{array}{c} \frac{\partial F(x,p,\lambda)}{\partial\lambda} \\ \frac{\partial Jn}{\partial\lambda} \\ 0 \end{array} \right].$

Implements LOCA::Continuation::AbstractGroup.

NOX::Abstract::Group::ReturnType LOCA::Bifurcation::TPBord::ExtendedGroup::computeF ( ) [virtual]

Compute the turning point equation residual $G$ .
This method fills the extended residual
$G(z) = \left[ \begin{array}{c} F(x,p) \\ Jn \\ l^Tn-1 \end{array} \right].$
The solution component residual $F(x,p)$ and the null-vector residual $Jn$ are calculated via the computeF and applyJacobian methods of the underlying group.
Implements NOX::Abstract::Group.

NOX::Abstract::Group::ReturnType LOCA::Bifurcation::TPBord::ExtendedGroup::computeJacobian ( ) [virtual]

Compute the blocks of the Jacobian derivative of $G$ .
This method computes the $J$ , $\partial F/\partial p$ , and $\partial Jn/\partial p$ blocks of the extended Jacobian:
$D_z G(z) = \begin{bmatrix} J & 0 & \frac{\partial F}{\partial p} \\ \frac{\partial Jn}{\partial x} & J & \frac{\partial Jn}{\partial p} \\ 0 & l^T & 0 \end{bmatrix}$
by calling the computeJacobian, computeDfDp, and computeDJnDp methods of the underlying group. The second derivative matrix $\partial Jn/\partial x$ is not calculated since only its action on vectors is needed for linear solves using the bordering algorithm.
Reimplemented from NOX::Abstract::Group.

void LOCA::Bifurcation::TPBord::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::Continuation::AbstractGroup.

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

LOCA_Bifurcation_TPBord_ExtendedGroup.H
LOCA_Bifurcation_TPBord_ExtendedGroup.C

Generated on Thu Sep 18 12:43:29 2008 for NOX by

1.3.9.1

LOCA::Bifurcation::TPBord::ExtendedGroup Class Reference

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation