#include <deal.II/base/time_stepping.h>

Inheritance diagram for TimeStepping::RungeKutta< VectorType >:

Public Member Functions
virtual	~RungeKutta () override=default

virtual void	initialize (const runge_kutta_method method)=0

double	evolve_one_time_step (std::vector< std::function< VectorType(const double, const VectorType &)>> &F, std::vector< std::function< VectorType(const double, const double, const VectorType &)>> &J_inverse, double t, double delta_t, VectorType &y) override

virtual double	evolve_one_time_step (const std::function< VectorType(const double, const VectorType &)> &f, const std::function< VectorType(const double, const double, const VectorType &)> &id_minus_tau_J_inverse, double t, double delta_t, VectorType &y)=0

Public Member Functions inherited from TimeStepping::TimeStepping< VectorType >
virtual	~TimeStepping ()=default

virtual const Status &	get_status () const =0

Protected Attributes
unsigned int	n_stages

std::vector< double >	b

std::vector< double >	c

std::vector< std::vector< double > >	a

Detailed Description

template<typename VectorType>
class TimeStepping::RungeKutta< VectorType >

Base class for the Runge-Kutta method

Author: Damien Lebrun-Grandie, Bruno Turcksin

Date: 2014

Definition at line 146 of file time_stepping.h.

Constructor & Destructor Documentation

◆ ~RungeKutta()

template<typename VectorType >

virtual TimeStepping::RungeKutta< VectorType >::~RungeKutta ( )

overridevirtualdefault

Virtual destructor.

Member Function Documentation

◆ initialize()

template<typename VectorType >

virtual void TimeStepping::RungeKutta< VectorType >::initialize ( const runge_kutta_method method )

pure virtual

Purely virtual method used to initialize the Runge-Kutta method.

Implemented in TimeStepping::EmbeddedExplicitRungeKutta< VectorType >, TimeStepping::ImplicitRungeKutta< VectorType >, and TimeStepping::ExplicitRungeKutta< VectorType >.

◆ evolve_one_time_step() [1/2]

template<typename VectorType >

double TimeStepping::RungeKutta< VectorType >::evolve_one_time_step	(	std::vector< std::function< VectorType(const double, const VectorType &)>> &	F,
		std::vector< std::function< VectorType(const double, const double, const VectorType &)>> &	J_inverse,
		double	t,
		double	delta_t,
		VectorType &	y
	)

overridevirtual

This function is used to advance from time t to t+ delta_t. F is a vector of functions \( f(t,y) \) that should be integrated, the input parameters are the time t and the vector y and the output is value of f at this point. J_inverse is a vector functions that compute the inverse of the Jacobians associated to the implicit problems. The input parameters are the time, \( \tau \), and a vector. The output is the value of function at this point. This function returns the time at the end of the time step. When using Runge-Kutta methods, F and @ J_inverse can only contain one element.

Implements TimeStepping::TimeStepping< VectorType >.

◆ evolve_one_time_step() [2/2]

template<typename VectorType >

virtual double TimeStepping::RungeKutta< VectorType >::evolve_one_time_step	(	const std::function< VectorType(const double, const VectorType &)> &	f,
		const std::function< VectorType(const double, const double, const VectorType &)> &	id_minus_tau_J_inverse,
		double	t,
		double	delta_t,
		VectorType &	y
	)

pure virtual

Purely virtual function. This function is used to advance from time t to t+ delta_t. f is the function \( f(t,y) \) that should be integrated, the input parameters are the time t and the vector y and the output is value of f at this point. id_minus_tau_J_inverse is a function that computes \( inv(I-\tau J)\) where \( I \) is the identity matrix, \( \tau \) is given, and \( J \) is the Jacobian \( \frac{\partial J}{\partial y} \). The input parameters are the time, \( \tau \), and a vector. The output is the value of function at this point. evolve_one_time_step returns the time at the end of the time step.

Implemented in TimeStepping::EmbeddedExplicitRungeKutta< VectorType >, TimeStepping::ImplicitRungeKutta< VectorType >, and TimeStepping::ExplicitRungeKutta< VectorType >.