TimeStepping::LowStorageRungeKutta< VectorType > Class Template Reference

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

Inheritance diagram for TimeStepping::LowStorageRungeKutta< VectorType >:

Classes
struct	Status

Public Member Functions
	LowStorageRungeKutta ()=default
	LowStorageRungeKutta (const runge_kutta_method method)
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 &solution, VectorType &vec_ri, VectorType &vec_ki)
void	get_coefficients (std::vector< double > &a, std::vector< double > &b, std::vector< double > &c) const
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_one_stage (const std::function< VectorType(const double, const VectorType &)> &f, const double t, const double factor_solution, const double factor_ai, const VectorType &corrent_ri, VectorType &vec_ki, VectorType &solution, VectorType &next_ri) const

Private Attributes
Status	status

Detailed Description

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

The LowStorageRungeKutta class is derived from RungeKutta and implements a specific class of explicit methods. The main advantages of low-storage methods are the reduced memory consumption and the reduced memory access.

Definition at line 411 of file time_stepping.h.

Constructor & Destructor Documentation

LowStorageRungeKutta() [1/2]

template<typename VectorType >

TimeStepping::LowStorageRungeKutta< VectorType >::LowStorageRungeKutta ( )

default

Default constructor. This constructor creates an object for which you will want to call initialize(runge_kutta_method) before it can be used.

LowStorageRungeKutta() [2/2]

template<typename VectorType >

TimeStepping::LowStorageRungeKutta< VectorType >::LowStorageRungeKutta

(

const runge_kutta_method

method

)

Constructor. This function calls initialize(runge_kutta_method).

Member Function Documentation

initialize()

template<typename VectorType >

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

overridevirtual

Initialize the explicit Runge-Kutta method.

Implements TimeStepping::RungeKutta< VectorType >.

evolve_one_time_step() [1/3]

template<typename VectorType >

double TimeStepping::LowStorageRungeKutta< 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 \( \frac{\partial f}{\partial y} \). 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::LowStorageRungeKutta< VectorType >::evolve_one_time_step	(	const std::function< VectorType(const double, const VectorType &)> &	f,
		double	t,
		double	delta_t,
		VectorType &	solution,
		VectorType &	vec_ri,
		VectorType &	vec_ki
	)

This function is used to advance from time t to t+ delta_t. This function is similar to the one derived from RungeKutta, 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. Note that vec_ki holds the evaluation of the differential operator, and vec_ri holds the right-hand side for the differential operator application.

get_coefficients()

template<typename VectorType >

void TimeStepping::LowStorageRungeKutta< VectorType >::get_coefficients	(	std::vector< double > &	a,
		std::vector< double > &	b,
		std::vector< double > &	c
	)		const

Get the coefficients of the scheme. Note that here vector a is not the conventional definition in terms of a Butcher tableau but merely one of the sub-diagonals. More details can be found in step-67 and the references therein.

get_status()

template<typename VectorType >

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

overridevirtual

Return the status of the current object.

Implements TimeStepping::TimeStepping< VectorType >.

compute_one_stage()

template<typename VectorType >

void TimeStepping::LowStorageRungeKutta< VectorType >::compute_one_stage ( const std::function< VectorType(const double, const VectorType &)> &  f, const double  t, const double  factor_solution, const double  factor_ai, const VectorType &  corrent_ri, VectorType &  vec_ki, VectorType &  solution, VectorType &  next_ri  ) const

private

Compute one stage of low storage rk.

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

status

template<typename VectorType >

Status TimeStepping::LowStorageRungeKutta< VectorType >::status

private

Status structure of the object.

Definition at line 520 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.

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

• include/deal.II/base/time_stepping.h