TimeSteppers::Heun2 Class Reference
A second order continuous-extension RK method that provides 2nd-order dense output. More...
#include <Heun2.hpp>
Public Types | |
| using | options = tmpl::list<> |
 Public Types inherited from TimeStepper | |
| using | provided_time_stepper_interfaces = tmpl::list< TimeStepper > |
| Public Types inherited from ImexTimeStepper | |
| using | provided_time_stepper_interfaces = tmpl::list< ImexTimeStepper, TimeStepper > |
Public Member Functions | |
| Heun2 (const Heun2 &)=default | |
| Heun2 & | operator= (const Heun2 &)=default |
| Heun2 (Heun2 &&)=default | |
| Heun2 & | operator= (Heun2 &&)=default |
| size_t | order () const override |
| The convergence order of the stepper. More... | |
| size_t | error_estimate_order () const override |
| The convergence order of the stepper error measure. More... | |
| double | stable_step () const override |
| Rough estimate of the maximum step size this method can take stably as a multiple of the step for Euler's method. More... | |
| size_t | imex_order () const override |
| Convergence order of the integrator when used in IMEX mode. More... | |
| size_t | implicit_stage_order () const override |
| WRAPPED_PUPable_decl_template (Heun2) | |
| Heun2 (CkMigrateMessage *) | |
| const ButcherTableau & | butcher_tableau () const override |
| const ImplicitButcherTableau & | implicit_butcher_tableau () const override |
| virtual size_t | implicit_stage_order () const =0 |
| virtual const ImplicitButcherTableau & | implicit_butcher_tableau () const =0 |
| Public Member Functions inherited from TimeSteppers::RungeKutta | |
| uint64_t | number_of_substeps () const override |
| Number of substeps in this TimeStepper. More... | |
| uint64_t | number_of_substeps_for_error () const override |
| Number of substeps in this TimeStepper when providing an error measure for adaptive time-stepping. More... | |
| size_t | number_of_past_steps () const override |
| Number of past time steps needed for multi-step method. More... | |
| bool | monotonic () const override |
| Whether computational and temporal orderings of operations match. More... | |
| TimeStepId | next_time_id (const TimeStepId ¤t_id, const TimeDelta &time_step) const override |
| The TimeStepId after the current substep. More... | |
| TimeStepId | next_time_id_for_error (const TimeStepId ¤t_id, const TimeDelta &time_step) const override |
| The TimeStepId after the current substep when providing an error measure for adaptive time-stepping. More... | |
| virtual const ButcherTableau & | butcher_tableau () const =0 |
| Public Member Functions inherited from TimeStepper | |
| WRAPPED_PUPable_abstract (TimeStepper) | |
| template<typename Vars > | |
| void | update_u (const gsl::not_null< Vars * > u, const gsl::not_null< TimeSteppers::History< Vars > * > history, const TimeDelta &time_step) const |
Set u to the value at the end of the current substep. More... | |
| template<typename Vars , typename ErrVars > | |
| bool | update_u (const gsl::not_null< Vars * > u, const gsl::not_null< ErrVars * > u_error, const gsl::not_null< TimeSteppers::History< Vars > * > history, const TimeDelta &time_step) const |
Set u to the value at the end of the current substep; report the error measure when available. More... | |
| template<typename Vars > | |
| bool | dense_update_u (const gsl::not_null< Vars * > u, const TimeSteppers::History< Vars > &history, const double time) const |
| Compute the solution value at a time between steps. To evaluate at a time within a given step, call this method at the start of the step containing the time. The function returns true on success, otherwise the call should be retried after the next substep. More... | |
| virtual size_t | order () const =0 |
| The convergence order of the stepper. More... | |
| virtual size_t | error_estimate_order () const =0 |
| The convergence order of the stepper error measure. More... | |
| virtual uint64_t | number_of_substeps () const =0 |
| Number of substeps in this TimeStepper. More... | |
| virtual uint64_t | number_of_substeps_for_error () const =0 |
| Number of substeps in this TimeStepper when providing an error measure for adaptive time-stepping. More... | |
| virtual size_t | number_of_past_steps () const =0 |
| Number of past time steps needed for multi-step method. More... | |
| virtual double | stable_step () const =0 |
| Rough estimate of the maximum step size this method can take stably as a multiple of the step for Euler's method. More... | |
| virtual bool | monotonic () const =0 |
| Whether computational and temporal orderings of operations match. More... | |
| virtual TimeStepId | next_time_id (const TimeStepId ¤t_id, const TimeDelta &time_step) const =0 |
| The TimeStepId after the current substep. More... | |
| virtual TimeStepId | next_time_id_for_error (const TimeStepId ¤t_id, const TimeDelta &time_step) const =0 |
| The TimeStepId after the current substep when providing an error measure for adaptive time-stepping. More... | |
| template<typename Vars > | |
| bool | can_change_step_size (const TimeStepId &time_id, const TimeSteppers::History< Vars > &history) const |
| Whether a change in the step size is allowed before taking a step. More... | |
| Public Member Functions inherited from ImexTimeStepper | |
| WRAPPED_PUPable_abstract (ImexTimeStepper) | |
| virtual size_t | imex_order () const =0 |
| Convergence order of the integrator when used in IMEX mode. More... | |
| template<typename Vars > | |
| void | add_inhomogeneous_implicit_terms (const gsl::not_null< Vars * > u, const gsl::not_null< TimeSteppers::History< Vars > * > implicit_history, const TimeDelta &time_step) const |
| Add the change for the current implicit substep, \(Y_{n,\text{inhomogeneous}}\), to u, given a past history of the implicit derivatives. More... | |
| template<typename Vars > | |
| double | implicit_weight (const gsl::not_null< TimeSteppers::History< Vars > * > implicit_history, const TimeDelta &time_step) const |
| The coefficient \(w_n\) of the implicit derivative for the current substep. For a Runge-Kutta method, this is the coefficient on the diagonal of the Butcher tableau. More... | |
Static Public Attributes | |
| static constexpr Options::String | help |
| Static Public Attributes inherited from TimeStepper | |
| static constexpr bool | local_time_stepping = false |
| static constexpr bool | imex = false |
| Static Public Attributes inherited from ImexTimeStepper | |
| static constexpr bool | imex = true |
Detailed Description
A second order continuous-extension RK method that provides 2nd-order dense output.
\begin{eqnarray} \frac{du}{dt} & = & \mathcal{L}(t,u). \end{eqnarray}
Given a solution \(u(t^n)=u^n\), this stepper computes \(u(t^{n+1})=u^{n+1}\) using the following equations:
\begin{align} k^{(i)} & = \mathcal{L}(t^n + c_i \Delta t, u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k^{(j)}), \mbox{ } 1 \leq i \leq s,\\ u^{n+1}(t^n + \theta \Delta t) & = u^n + \Delta t \sum_{i=1}^{s} b_i(\theta) k^{(i)}. \end{align}
Here the coefficients \(a_{ij}\), \(b_i\), and \(c_i\) are given in [75]. Note that \(c_1 = 0\), \(s\) is the number of stages, and \(\theta\) is the fraction of the step.
When used as an IMEX method, the implicit portion uses the trapezoid rule, which is stiffly accurate and A-stable.
The CFL factor/stable step size is 1.0.
Member Function Documentation
◆ butcher_tableau()
|
overridevirtual |
Implements TimeSteppers::RungeKutta.
◆ error_estimate_order()
|
overridevirtual |
The convergence order of the stepper error measure.
Implements TimeStepper.
◆ imex_order()
|
overridevirtual |
Convergence order of the integrator when used in IMEX mode.
Implements ImexTimeStepper.
◆ implicit_butcher_tableau()
|
overridevirtual |
Implements TimeSteppers::ImexRungeKutta.
◆ implicit_stage_order()
|
overridevirtual |
Smallest order of the intermediate result at any substep. For the methods supported by this class, this cannot exceed 2.
Implements TimeSteppers::ImexRungeKutta.
◆ order()
|
overridevirtual |
The convergence order of the stepper.
Implements TimeStepper.
◆ stable_step()
|
overridevirtual |
Rough estimate of the maximum step size this method can take stably as a multiple of the step for Euler's method.
Implements TimeStepper.
Member Data Documentation
◆ help
|
staticconstexpr |
Initial value:
= {
"Heun's method, a 2nd order Runge-Kutta method."}
The documentation for this class was generated from the following file:
- src/Time/TimeSteppers/Heun2.hpp