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

Inheritance diagram for TimeStepping::EmbeddedExplicitRungeKutta< VectorType >:

Classes
struct	Status

Public Member Functions
	EmbeddedExplicitRungeKutta ()=default

	EmbeddedExplicitRungeKutta (const runge_kutta_method method, const double coarsen_param=1.2, const double refine_param=0.8, const double min_delta=1e-14, const double max_delta=1e100, const double refine_tol=1e-8, const double coarsen_tol=1e-12)

	~EmbeddedExplicitRungeKutta () override

void	free_memory ()

void	initialize (const runge_kutta_method method) override

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) override

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

void	set_time_adaptation_parameters (const double coarsen_param, const double refine_param, const double min_delta, const double max_delta, const double refine_tol, const double coarsen_tol)

const Status &	get_status () const override

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

Protected Attributes
unsigned int	n_stages

std::vector< double >	b

std::vector< double >	c

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

Private Member Functions
void	compute_stages (const std::function< VectorType(const double, const VectorType &)> &f, const double t, const double delta_t, const VectorType &y, std::vector< VectorType > &f_stages)

Private Attributes
double	coarsen_param

double	refine_param

double	min_delta_t

double	max_delta_t

double	refine_tol

double	coarsen_tol

bool	last_same_as_first

std::vector< double >	b1

std::vector< double >	b2

VectorType *	last_stage

Status	status

Detailed Description

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

This class is derived from RungeKutta and implements embedded explicit methods.

Definition at line 675 of file time_stepping.h.

Constructor & Destructor Documentation

◆ EmbeddedExplicitRungeKutta() [1/2]

template<typename VectorType >

TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::EmbeddedExplicitRungeKutta ( )

default

Default constructor. initialize(runge_kutta_method) and set_time_adaptation_parameters(double, double, double, double, double, double) need to be called before the object can be used.

◆ EmbeddedExplicitRungeKutta() [2/2]

template<typename VectorType >

TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::EmbeddedExplicitRungeKutta	(	const runge_kutta_method	method,
		const double	coarsen_param = `1.2`,
		const double	refine_param = `0.8`,
		const double	min_delta = `1e-14`,
		const double	max_delta = `1e100`,
		const double	refine_tol = `1e-8`,
		const double	coarsen_tol = `1e-12`
	)

Constructor. This function calls initialize(runge_kutta_method) and initialize the parameters needed for time adaptation.

◆ ~EmbeddedExplicitRungeKutta()

template<typename VectorType >

TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::~EmbeddedExplicitRungeKutta ( )

inlineoverride

Destructor.

Definition at line 702 of file time_stepping.h.

Member Function Documentation

◆ free_memory()

template<typename VectorType >

void TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::free_memory ( )

If necessary, deallocate memory allocated by the object.

◆ initialize()

template<typename VectorType >

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

overridevirtual

Initialize the embedded explicit Runge-Kutta method.

Implements TimeStepping::RungeKutta< VectorType >.

◆ evolve_one_time_step() [1/3]

template<typename VectorType >

double TimeStepping::EmbeddedExplicitRungeKutta< 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
	)

overridevirtual

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.

Implements TimeStepping::RungeKutta< VectorType >.

◆ evolve_one_time_step() [2/3]

template<typename VectorType >

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

This function is used to advance from time t to t+ delta_t. This function is similar to the one derived from TimeStepping, but does not required id_minus_tau_J_inverse because it is not used for explicit methods. evolve_one_time_step returns the time at the end of the time step.

◆ set_time_adaptation_parameters()

template<typename VectorType >

void TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::set_time_adaptation_parameters	(	const double	coarsen_param,
		const double	refine_param,
		const double	min_delta,
		const double	max_delta,
		const double	refine_tol,
		const double	coarsen_tol
	)

Set the parameters necessary for the time adaptation.

◆ get_status()

template<typename VectorType >

const Status & TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::get_status ( ) const

overridevirtual

Return the status of the current object.

Implements TimeStepping::TimeStepping< VectorType >.

◆ compute_stages()

template<typename VectorType >

void TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::compute_stages	(	const std::function< VectorType(const double, const VectorType &)> &	f,
		const double	t,
		const double	delta_t,
		const VectorType &	y,
		std::vector< VectorType > &	f_stages
	)

private

Compute the different stages needed.

◆ evolve_one_time_step() [3/3]

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
	)

overridevirtualinherited

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 >.

Member Data Documentation

◆ coarsen_param

template<typename VectorType >

double TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::coarsen_param

private

This parameter is the factor (>1) by which the time step is multiplied when the time stepping can be coarsen.

Definition at line 802 of file time_stepping.h.

◆ refine_param

template<typename VectorType >

double TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::refine_param

private

This parameter is the factor (<1) by which the time step is multiplied when the time stepping must be refined.

Definition at line 808 of file time_stepping.h.

◆ min_delta_t

template<typename VectorType >

double TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::min_delta_t

private

Smallest time step allowed.

Definition at line 813 of file time_stepping.h.

◆ max_delta_t

template<typename VectorType >

double TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::max_delta_t

private

Largest time step allowed.

Definition at line 818 of file time_stepping.h.

◆ refine_tol

template<typename VectorType >

double TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::refine_tol

private

Refinement tolerance: if the error estimate is larger than refine_tol, the time step is refined.

Definition at line 824 of file time_stepping.h.

◆ coarsen_tol

template<typename VectorType >

double TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::coarsen_tol

private

Coarsening tolerance: if the error estimate is smaller than coarse_tol, the time step is coarsen.

Definition at line 830 of file time_stepping.h.

◆ last_same_as_first

template<typename VectorType >

bool TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::last_same_as_first

private

If the flag is true, the last stage is the same as the first stage and one evaluation of f can be saved.

Definition at line 836 of file time_stepping.h.

◆ b1

template<typename VectorType >

std::vector<double> TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::b1

private

Butcher tableau coefficients.

Definition at line 841 of file time_stepping.h.

◆ b2

template<typename VectorType >

std::vector<double> TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::b2

private

Butcher tableau coefficients.

Definition at line 846 of file time_stepping.h.

◆ last_stage

template<typename VectorType >

VectorType* TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::last_stage

private

If the last_same_as_first flag is set to true, the last stage is saved and reused as the first stage of the next time step.

Definition at line 852 of file time_stepping.h.

◆ status

template<typename VectorType >

Status TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::status

private

Status structure of the object.

Definition at line 857 of file time_stepping.h.

◆ n_stages

template<typename VectorType >

unsigned int TimeStepping::RungeKutta< VectorType >::n_stages

protectedinherited

Number of stages of the Runge-Kutta method.

Definition at line 282 of file time_stepping.h.

◆ b

template<typename VectorType >

std::vector<double> TimeStepping::RungeKutta< VectorType >::b

protectedinherited

Butcher tableau coefficients.

Definition at line 287 of file time_stepping.h.

◆ c

template<typename VectorType >

std::vector<double> TimeStepping::RungeKutta< VectorType >::c

protectedinherited

Butcher tableau coefficients.

Definition at line 292 of file time_stepping.h.

◆ a

template<typename VectorType >

std::vector<std::vector<double> > TimeStepping::RungeKutta< VectorType >::a

protectedinherited

Butcher tableau coefficients.

Definition at line 297 of file time_stepping.h.

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

include/deal.II/base/time_stepping.h

Classes

Public Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ EmbeddedExplicitRungeKutta() [1/2]

◆ EmbeddedExplicitRungeKutta() [2/2]

◆ ~EmbeddedExplicitRungeKutta()

Member Function Documentation

◆ free_memory()

◆ initialize()

◆ evolve_one_time_step() [1/3]

◆ evolve_one_time_step() [2/3]

◆ set_time_adaptation_parameters()

◆ get_status()

◆ compute_stages()

◆ evolve_one_time_step() [3/3]

Member Data Documentation

◆ coarsen_param

◆ refine_param

◆ min_delta_t

◆ max_delta_t

◆ refine_tol

◆ coarsen_tol

◆ last_same_as_first

◆ b1

◆ b2

◆ last_stage

◆ status

◆ n_stages

◆ b

◆ c

◆ a