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Reference documentation for deal.II version 9.6.0
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#include <deal.II/base/time_stepping.h>
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 = false |
std::vector< double > | b1 |
std::vector< double > | b2 |
VectorType * | last_stage = nullptr |
Status | status |
This class is derived from RungeKutta and implements embedded explicit methods.
Definition at line 669 of file time_stepping.h.
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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.
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.
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inlineoverride |
Destructor.
Definition at line 696 of file time_stepping.h.
void TimeStepping::EmbeddedExplicitRungeKutta< VectorType >::free_memory | ( | ) |
If necessary, deallocate memory allocated by the object.
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overridevirtual |
Initialize the embedded explicit Runge-Kutta method.
Implements TimeStepping::RungeKutta< VectorType >.
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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.
id_minus_tau_J_inverse
is ignored since the method is explicit. Implements TimeStepping::RungeKutta< 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.
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.
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overridevirtual |
Return the status of the current object.
Implements TimeStepping::TimeStepping< VectorType >.
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private |
Compute the different stages needed.
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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 >.
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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.
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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.
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private |
Smallest time step allowed.
Definition at line 813 of file time_stepping.h.
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private |
Largest time step allowed.
Definition at line 818 of file time_stepping.h.
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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.
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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.
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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.
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private |
Butcher tableau coefficients.
Definition at line 841 of file time_stepping.h.
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private |
Butcher tableau coefficients.
Definition at line 846 of file time_stepping.h.
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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.
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private |
Status structure of the object.
Definition at line 857 of file time_stepping.h.
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protectedinherited |
Number of stages of the Runge-Kutta method.
Definition at line 281 of file time_stepping.h.
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protectedinherited |
Butcher tableau coefficients.
Definition at line 286 of file time_stepping.h.
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protectedinherited |
Butcher tableau coefficients.
Definition at line 291 of file time_stepping.h.
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protectedinherited |
Butcher tableau coefficients.
Definition at line 296 of file time_stepping.h.