Structure representing the subsidiary function for the standard arc-length method. More...

#include <ikarus/controlroutines/pathfollowingfunctions.hh>

Public Member Functions
void	operator() (SubsidiaryArgs &args) const
	Evaluates the subsidiary function for the standard arc-length method. More...

template<typename NLO >
void	initialPrediction (NLO &nonLinearOperator, SubsidiaryArgs &args)
	Performs the initial prediction for the standard arc-length method. More...

template<typename NLO >
void	intermediatePrediction (NLO &nonLinearOperator, SubsidiaryArgs &args)
	Performs intermediate prediction for the standard arc-length method. More...

constexpr auto	name () const
	The name of the PathFollowing method. More...

Detailed Description

This structure provides methods to evaluate the subsidiary function, perform initial prediction, and perform intermediate prediction for the standard arc-length control method.

The equation for the arc length method reads

\[ f(\mathrm{D}\mathbf{D}, \mathrm{D} \lambda)= \sqrt{||\mathrm{D}\mathbf{D}||^2+ \psi^2 (\mathrm{D} \lambda)^2 }- \hat{s}, \]

where \(\mathrm{D}\mathbf{D}\) is the increment of the solution vector and \(\mathrm{D} \lambda\) is the load factor increment. \(\psi\) is the to-be-determined correction factor for the different dimensionalities between \(\mathrm{D}\mathbf{D}\) and \(\mathrm{D} \lambda\). The scalar \(\hat{s} \) defines the requested size of the step.

Member Function Documentation

◆ intermediatePrediction()

template<typename NLO >

void Ikarus::ArcLength::intermediatePrediction	(	NLO &	nonLinearOperator,
		SubsidiaryArgs &	args
	)

inline

This method updates the prediction step for the standard arc-length method.

Template Parameters

NLO	Type of the nonlinear operator.

Parameters

nonLinearOperator	The nonlinear operator.
args	The subsidiary function arguments.

◆ name()

constexpr auto Ikarus::ArcLength::name ( ) const

inlineconstexpr

◆ operator()()

void Ikarus::ArcLength::operator() ( SubsidiaryArgs & args ) const