iMSTK: imstk::NewtonSolver< SystemMatrix > Class Template Reference

Newton method. This version of the newton method is based on the work by Tim Kelly and others at NC State University. The algorithm is globally convergent in the sense that for any initial iterate the iteration either converge to a root of F or fails. Global convergence is achieved using a line search sub-process and the Armijo rule. More...

#include <imstkNewtonSolver.h>

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Public Types
using	LinearSolverType = LinearSolver< SystemMatrix >

Public Types inherited from imstk::NonLinearSolver< SystemMatrix >
using	JacobianType = std::function< const SystemMatrix &(const Vectord &)>

using	UpdateIterateType = std::function< void(const Vectord &, Vectord &)>

using	FunctionType = NonLinearSystem< SparseMatrixd >::VectorFunctionType

Public Member Functions
	NewtonSolver (const NewtonSolver &other)=delete
	Dissallow copy & move.

	NewtonSolver (const NewtonSolver &&other)=delete

NewtonSolver &	operator= (const NewtonSolver &other)=delete

NewtonSolver &	operator= (const NewtonSolver &&other)=delete

void	solveGivenState (Vectord &x) override
	Solve the non linear system of equations G(x)=0 using Newton's method. More...

void	solve () override

void	updateForcingTerm (const double ratio, const double stopTolerance, const double fnorm)
	Update forcing term according to Eisenstat-Walker criteria. More...

void	setLinearSolver (std::shared_ptr< LinearSolverType > newLinearSolver)
	Set LinearSolver. More...

auto	getLinearSolver () const -> std::shared_ptr< LinearSolverType >
	Get LinearSolver.

double	updateJacobian (const Vectord &x)
	Update jacobians. More...

void	setAbsoluteTolerance (const double aTolerance)
	Get JacobianMatrix. Returns jacobian matrix. More...

double	getAbsoluteTolerance () const
	Get AbsoluteTolerance. Returns current tolerance value.

void	setRelativeTolerance (const double newRelativeTolerance)
	Set RelativeTolerance. More...

double	getRelativeTolerance () const
	Get RelativeTolerance. Returns current relative tolerance value.

void	setGamma (const double newGamma)
	Set Gamma. Sets the gamma parameter used to update the forcing term. More...

double	getGamma () const
	Get Gamma. Returns current gamma value.

void	setEtaMax (const double newEtaMax)
	Set EtaMax. Maximum error tolerance for residual in inner iteration. The inner iteration terminates when the relative linear residual is smaller than eta*\| F(x_c) \|. eta is determined by the modified Eisenstat-Walker formula if etamax > 0. If etamax < 0, then eta = \|etamax\| for the entire iteration. More...

double	getEtaMax () const
	Get EtaMax. Returns current etaMax value.

void	setMaxIterations (const size_t newMaxIterations)
	Set MaxIterations. The maximum number of nonlinear iterations.

size_t	getMaxIterations () const
	Get MaxIterations. Returns current maximum nonlinear iterations.

void	setUseArmijo (const bool value)
	Set the useArmijo flag. If useArmijo is true a line search is performed using the Armijo-Goldstein condition.

bool	getUseArmijo () const
	Get MaxIterations. Returns current maximum nonlinear iterations.

void	setForcingTerm (const double value)
	Set the useArmijo flag. If useArmijo is true a line search is performed using the Armijo-Goldstein condition.

double	getForcingTerm () const
	Get MaxIterations. Returns current maximum nonlinear iterations.

void	setToFullyImplicit () override
	Set the Newton solver to be fully implicit.

void	setToSemiImplicit () override
	Set the Newton solver to be fully implicit.

Public Member Functions inherited from imstk::NonLinearSolver< SystemMatrix >
double	armijo (const Vectord &dx, Vectord &x, const double previousFnorm)
	Backtracking line search method based on the Armijo-Goldstein condition. More...

void	parabolicModel (const std::array< double, 3 > &fnorm, std::array< double, 3 > &lambda)
	Three-point safeguarded parabolic model for a line search. Upon return lambda[0] will contain the new value of lambda given by the parabolic model. More...

void	setSigma (const std::array< double, 2 > &newSigma)
	Set/Get Sigma. Safeguard parameter for the the line search method. More...

const std::array< double, 2 > &	getSigma () const

void	setAlpha (const double newAlpha)
	Set/Get Alpha. Parameter to measure sufficient decrease in the line search. More...

double	getAlpha () const

void	setArmijoMax (const size_t newArmijoMax)
	Set/Get ArmijoMax. Maximum number of step length reductions. More...

size_t	getArmijoMax () const

void	setSystem (std::shared_ptr< NonLinearSystem< SystemMatrix >> newSystem)
	Sets the system. System of nonlinear equations. More...

std::shared_ptr< NonLinearSystem< SystemMatrix > >	getSystem () const

void	setUpdateIterate (const UpdateIterateType &newUpdateIterate)
	Set a customized iterate update function. More...

Additional Inherited Members
Public Attributes inherited from imstk::SolverBase
std::shared_ptr< DataTracker >	m_dataTracker

Protected Attributes inherited from imstk::NonLinearSolver< SystemMatrix >
std::array< double, 2 >	m_sigma
	Safeguarding bounds for the line search.

double	m_alpha
	Parameter to measure decrease.

size_t	m_armijoMax
	Maximum number of step length reductions.

std::shared_ptr< NonLinearSystem< SystemMatrix > >	m_nonLinearSystem
	System of non-linear equations.

UpdateIterateType	m_updateIterate
	Update iteration function.

bool	m_isSemiImplicit = false
	Semi-Implicit solver.

Detailed Description

template<typename SystemMatrix>
class imstk::NewtonSolver< SystemMatrix >

Definition at line 24 of file imstkNewtonSolver.h.

Member Function Documentation

◆ setAbsoluteTolerance()

template<typename SystemMatrix >

void imstk::NewtonSolver< SystemMatrix >::setAbsoluteTolerance ( const double aTolerance )

Get JacobianMatrix. Returns jacobian matrix.

Set AbsoluteTolerance

Parameters

aTolerance New absolute tolerance value

Definition at line 196 of file imstkNewtonSolver.cpp.

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◆ setEtaMax()

template<typename SystemMatrix >

void imstk::NewtonSolver< SystemMatrix >::setEtaMax ( const double newEtaMax )

inline

Set EtaMax. Maximum error tolerance for residual in inner iteration. The inner iteration terminates when the relative linear residual is smaller than eta*| F(x_c) |. eta is determined by the modified Eisenstat-Walker formula if etamax > 0. If etamax < 0, then eta = |etamax| for the entire iteration.

See also: updateForcingTerm()

Definition at line 135 of file imstkNewtonSolver.h.

◆ setGamma()

template<typename SystemMatrix >

void imstk::NewtonSolver< SystemMatrix >::setGamma ( const double newGamma )

inline

Set Gamma. Sets the gamma parameter used to update the forcing term.

Parameters

newGamma New gamma value

Definition at line 120 of file imstkNewtonSolver.h.

◆ setLinearSolver()

template<typename SystemMatrix >

void imstk::NewtonSolver< SystemMatrix >::setLinearSolver ( std::shared_ptr< LinearSolverType > newLinearSolver )

inline

Set LinearSolver.

Parameters

newLinearSolver Linear solver pointer

Definition at line 65 of file imstkNewtonSolver.h.

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◆ setRelativeTolerance()

template<typename SystemMatrix >

void imstk::NewtonSolver< SystemMatrix >::setRelativeTolerance ( const double newRelativeTolerance )

inline

Set RelativeTolerance.

Parameters

newRelativeTolerance New relative tolerance value

Definition at line 105 of file imstkNewtonSolver.h.

◆ solveGivenState()

template<typename SystemMatrix >

void imstk::NewtonSolver< SystemMatrix >::solveGivenState ( Vectord & x )

overridevirtual

Solve the non linear system of equations G(x)=0 using Newton's method.

Parameters

x	Current iterate

Implements imstk::NonLinearSolver< SystemMatrix >.

Definition at line 44 of file imstkNewtonSolver.cpp.

◆ updateForcingTerm()

template<typename SystemMatrix >

void imstk::NewtonSolver< SystemMatrix >::updateForcingTerm	(	const double	ratio,
		const double	stopTolerance,
		const double	fnorm
	)

Update forcing term according to Eisenstat-Walker criteria.

See also: http://softlib.rice.edu/pub/CRPC-TRs/reports/CRPC-TR94463.pdf.

Parameters

ratio	Ratio of consecutive function norms
stopTolerance	Linear combinarion of relative and absolute tolerances
fnorm	Current function norm

Todo:: Log this

Definition at line 171 of file imstkNewtonSolver.cpp.

◆ updateJacobian()

template<typename SystemMatrix >

double imstk::NewtonSolver< SystemMatrix >::updateJacobian ( const Vectord & x )

Update jacobians.

Parameters

x	Current iterate

Definition at line 135 of file imstkNewtonSolver.cpp.

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

Source/Solvers/imstkNewtonSolver.h
Source/Solvers/imstkNewtonSolver.cpp

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

template<typename SystemMatrix> class imstk::NewtonSolver< SystemMatrix >

Member Function Documentation

◆ setAbsoluteTolerance()

◆ setEtaMax()

◆ setGamma()

◆ setLinearSolver()

◆ setRelativeTolerance()

◆ solveGivenState()

◆ updateForcingTerm()

◆ updateJacobian()

template<typename SystemMatrix>
class imstk::NewtonSolver< SystemMatrix >