Reference documentation for deal.II version 8.4.1
Classes | Public Member Functions | Private Member Functions | Private Attributes | List of all members
TimeStepping::EmbeddedExplicitRungeKutta< VectorType > Class Template Reference

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

Inheritance diagram for TimeStepping::EmbeddedExplicitRungeKutta< VectorType >:
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Classes

struct  Status
 

Public Member Functions

 EmbeddedExplicitRungeKutta ()
 
 EmbeddedExplicitRungeKutta (runge_kutta_method method, double coarsen_param=1.2, double refine_param=0.8, double min_delta=1e-14, double max_delta=1e100, double refine_tol=1e-8, double coarsen_tol=1e-12)
 
 ~EmbeddedExplicitRungeKutta ()
 
void free_memory ()
 
void initialize (runge_kutta_method method)
 
double evolve_one_time_step (std_cxx11::function< VectorType(const double, const VectorType &)> f, std_cxx11::function< VectorType(const double, const double, const VectorType &)> id_minus_tau_J_inverse, double t, double delta_t, VectorType &y)
 
double evolve_one_time_step (std_cxx11::function< VectorType(const double, const VectorType &)> f, double t, double delta_t, VectorType &y)
 
void set_time_adaptation_parameters (double coarsen_param, double refine_param, double min_delta, double max_delta, double refine_tol, double coarsen_tol)
 
const Statusget_status () const
 
- Public Member Functions inherited from TimeStepping::RungeKutta< VectorType >
virtual ~RungeKutta ()
 
double evolve_one_time_step (std::vector< std_cxx11::function< VectorType(const double, const VectorType &)> > &F, std::vector< std_cxx11::function< VectorType(const double, const double, const VectorType &)> > &J_inverse, double t, double delta_t, VectorType &y)
 
- Public Member Functions inherited from TimeStepping::TimeStepping< VectorType >
virtual ~TimeStepping ()
 

Private Member Functions

void compute_stages (std_cxx11::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
 

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::EmbeddedExplicitRungeKutta< VectorType >

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

Definition at line 413 of file time_stepping.h.

Constructor & Destructor Documentation

template<typename VectorType>
TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::EmbeddedExplicitRungeKutta ( )
inline

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.

Definition at line 423 of file time_stepping.h.

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

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

template<typename VectorType>
TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::~EmbeddedExplicitRungeKutta ( )
inline

Destructor.

Definition at line 440 of file time_stepping.h.

Member Function Documentation

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

If necessary, deallocate memory allocated by the object.

template<typename VectorType>
void TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::initialize ( runge_kutta_method  method)
virtual

Initialize the embedded explicit Runge-Kutta method.

Implements TimeStepping::RungeKutta< VectorType >.

template<typename VectorType>
double TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::evolve_one_time_step ( std_cxx11::function< VectorType(const double, const VectorType &)>  f,
std_cxx11::function< VectorType(const double, const double, const VectorType &)>  id_minus_tau_J_inverse,
double  t,
double  delta_t,
VectorType &  y 
)
virtual

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 >.

template<typename VectorType>
double TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::evolve_one_time_step ( std_cxx11::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.

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

Set the parameters necessary for the time adaptation.

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

Return the status of the current object.

Implements TimeStepping::TimeStepping< VectorType >.

template<typename VectorType>
void TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::compute_stages ( std_cxx11::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.

Member Data Documentation

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 530 of file time_stepping.h.

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 536 of file time_stepping.h.

template<typename VectorType>
double TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::min_delta_t
private

Smallest time step allowed.

Definition at line 541 of file time_stepping.h.

template<typename VectorType>
double TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::max_delta_t
private

Largest time step allowed.

Definition at line 546 of file time_stepping.h.

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 552 of file time_stepping.h.

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 558 of file time_stepping.h.

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 564 of file time_stepping.h.

template<typename VectorType>
std::vector<double> TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::b1
private

Butcher tableau coefficients.

Definition at line 569 of file time_stepping.h.

template<typename VectorType>
std::vector<double> TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::b2
private

Butcher tableau coefficients.

Definition at line 574 of file time_stepping.h.

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 580 of file time_stepping.h.

template<typename VectorType>
Status TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::status
private

Status structure of the object.

Definition at line 585 of file time_stepping.h.


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