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

Inheritance diagram for TimeStepping::ImplicitRungeKutta< VectorType >:

Classes
struct	Status

Public Member Functions
	ImplicitRungeKutta ()=default

	ImplicitRungeKutta (const runge_kutta_method method, const unsigned int max_it=100, const double tolerance=1e-6)

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

void	set_newton_solver_parameters (const unsigned int max_it, const double tolerance)

const Status &	get_status () const override

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

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

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

Private Member Functions
void	compute_stages (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, std::vector< VectorType > &f_stages)

void	newton_solve (const std::function< void(const VectorType &, VectorType &)> &get_residual, const std::function< VectorType(const VectorType &)> &id_minus_tau_J_inverse, VectorType &y)

void	compute_residual (const std::function< VectorType(const double, const VectorType &)> &f, double t, double delta_t, const VectorType &new_y, const VectorType &y, VectorType &tendency, VectorType &residual) const

Private Attributes
bool	skip_linear_combi

unsigned int	max_it

double	tolerance

Status	status

Additional Inherited Members
Protected Attributes inherited from TimeStepping::RungeKutta< VectorType >
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::ImplicitRungeKutta< VectorType >

This class is derived from RungeKutta and implement the implicit methods. This class works only for Diagonal Implicit Runge-Kutta (DIRK) methods.

Definition at line 332 of file time_stepping.h.

Constructor & Destructor Documentation

template<typename VectorType>

TimeStepping::ImplicitRungeKutta< VectorType >::ImplicitRungeKutta ( )

default

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

template<typename VectorType>

TimeStepping::ImplicitRungeKutta< VectorType >::ImplicitRungeKutta	(	const runge_kutta_method	method,
		const unsigned int	max_it = `100`,
		const double	tolerance = `1e-6`
	)

Constructor. This function calls initialize(runge_kutta_method) and initialize the maximum number of iterations and the tolerance of the Newton solver.

Member Function Documentation

template<typename VectorType>

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

overridevirtual

Initialize the implicit Runge-Kutta method.

Implements TimeStepping::RungeKutta< VectorType >.

template<typename VectorType>

double TimeStepping::ImplicitRungeKutta< 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 \( (I-\tau J)^{-1}\) where \( I \) is the identity matrix, \( \tau \) is given, and \( J \) is the Jacobian \( \frac{\partial J}{\partial y} \). The input parameters this function receives 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 >.

template<typename VectorType>

void TimeStepping::ImplicitRungeKutta< VectorType >::set_newton_solver_parameters	(	const unsigned int	max_it,
		const double	tolerance
	)

Set the maximum number of iterations and the tolerance used by the Newton solver.

template<typename VectorType>

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

overridevirtual

Return the status of the current object.

Implements TimeStepping::TimeStepping< VectorType >.

template<typename VectorType>

void TimeStepping::ImplicitRungeKutta< VectorType >::compute_stages	(	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,
		std::vector< VectorType > &	f_stages
	)

private

Compute the different stages needed.

template<typename VectorType>

void TimeStepping::ImplicitRungeKutta< VectorType >::newton_solve	(	const std::function< void(const VectorType &, VectorType &)> &	get_residual,
		const std::function< VectorType(const VectorType &)> &	id_minus_tau_J_inverse,
		VectorType &	y
	)

private

Newton solver used for the implicit stages.

template<typename VectorType>

void TimeStepping::ImplicitRungeKutta< VectorType >::compute_residual	(	const std::function< VectorType(const double, const VectorType &)> &	f,
		double	t,
		double	delta_t,
		const VectorType &	new_y,
		const VectorType &	y,
		VectorType &	tendency,
		VectorType &	residual
	)		const

private

Compute the residual needed by the Newton solver.

Member Data Documentation

template<typename VectorType>

bool TimeStepping::ImplicitRungeKutta< VectorType >::skip_linear_combi

private

When using SDIRK, there is no need to compute the linear combination of the stages. Thus, when this flag is true, the linear combination is skipped.

Definition at line 454 of file time_stepping.h.

template<typename VectorType>

unsigned int TimeStepping::ImplicitRungeKutta< VectorType >::max_it

private

Maximum number of iterations of the Newton solver.

Definition at line 459 of file time_stepping.h.

template<typename VectorType>

double TimeStepping::ImplicitRungeKutta< VectorType >::tolerance

private

Tolerance of the Newton solver.

Definition at line 464 of file time_stepping.h.

template<typename VectorType>

Status TimeStepping::ImplicitRungeKutta< VectorType >::status

private

Status structure of the object.

Definition at line 469 of file time_stepping.h.

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

deal.II/base/time_stepping.h

Classes

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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