#include <ImexTimeStepper.hpp>
Public Types | |
| using | provided_time_stepper_interfaces = tmpl::list< ImexTimeStepper, TimeStepper > |
 Public Types inherited from TimeStepper | |
| using | provided_time_stepper_interfaces = tmpl::list< TimeStepper > |
Public Member Functions | |
| 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... | |
| 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. Step sizes can never be changed on a substep. More... | |
Static Public Attributes | |
| static constexpr bool | imex = true |
| Static Public Attributes inherited from TimeStepper | |
| static constexpr bool | local_time_stepping = false |
| static constexpr bool | imex = false |
Detailed Description
Base class for TimeSteppers with IMEX support, derived from TimeStepper.
All supported time-stepping algorithms (both implicit and explicit) consist of substeps that add linear combinations of derivative values. For implicit substeps, it is convenient to split out the contribution of the final implicit term from contributions from the history. We therefore write an implicit substep as
\begin{equation} Y_{n+1} = Y_{n,\text{explicit}} + Y_{n,\text{inhomogeneous}} + w_n S(Y_{n+1}) \end{equation}
Here \(Y_{n,\text{explicit}}\) is the value of the evolved variables before the implicit substep is applied, \(Y_{n,\text{inhomogeneous}}\) is the contribution of the past values from the implicit derivative history, and \(S(\cdot)\) is the implicit portion of the right-hand-side (generally source terms for PDEs). We call \(w_n\) the implicit weight. This split form is convenient for most consumers of this class, so we present methods for calculating \(Y_{n,\text{inhomogeneous}}\) and \(w_n\) individually instead of a method to perform a full step update.
Dense output formulae are the same for the explicit and implicit parts of any conservative IMEX stepper. To evaluate dense output, call dense_update_u with the implicit history after a successful call to dense_update_u with the explicit history.
Several of the member functions of this class are templated and perform type erasure before forwarding their arguments to the derived classes. This is implemented using the macros IMEX_TIME_STEPPER_DECLARE_OVERLOADS, which must be placed in a private section of the class body, and IMEX_TIME_STEPPER_DEFINE_OVERLOADS(derived_class), which must be placed in the cpp file.
Member Function Documentation
◆ add_inhomogeneous_implicit_terms()
|
inline |
Add the change for the current implicit substep, \(Y_{n,\text{inhomogeneous}}\), to u, given a past history of the implicit derivatives.
Derived classes must implement this as a function with signature
- Note
- Unlike the
update_umethods, which overwrite their result arguments, this function adds the result to the existing value.
◆ imex_order()
|
pure virtual |
Convergence order of the integrator when used in IMEX mode.
Implemented in TimeSteppers::Heun2, TimeSteppers::Rk3Kennedy, TimeSteppers::Rk3Pareschi, and TimeSteppers::Rk4Kennedy.
◆ implicit_weight()
|
inline |
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.
Derived classes must implement this as a function with signature
The documentation for this class was generated from the following file:
- src/Time/TimeSteppers/ImexTimeStepper.hpp