SpECTRE
v2024.05.11
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#include <DormandPrince5.hpp>
Public Types | |
using | options = tmpl::list<> |
Public Types inherited from TimeStepper | |
using | provided_time_stepper_interfaces = tmpl::list< TimeStepper > |
Public Member Functions | |
DormandPrince5 (const DormandPrince5 &)=default | |
DormandPrince5 & | operator= (const DormandPrince5 &)=default |
DormandPrince5 (DormandPrince5 &&)=default | |
DormandPrince5 & | operator= (DormandPrince5 &&)=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... | |
WRAPPED_PUPable_decl_template (DormandPrince5) | |
DormandPrince5 (CkMigrateMessage *) | |
const ButcherTableau & | butcher_tableau () const override |
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. Step sizes can never be changed on a substep. 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 |
The standard 5th-order Dormand-Prince time stepping method, given e.g. in Sec. 7.2 of [154].
\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^{(1)} & = dt \mathcal{L}(t^n, u^n),\\ k^{(i)} & = dt \mathcal{L}(t^n + c_i dt, u^n + \sum_{j=1}^{i-1} a_{ij} k^{(j)}), \mbox{ } 2 \leq i \leq 6,\\ u^{n+1} & = u^n + \sum_{i=1}^{6} b_i k^{(i)}. \end{align}
Here the coefficients \(a_{ij}\), \(b_i\), and \(c_i\) are given in e.g. Sec. 7.2 of [154]. Note that \(c_1 = 0\).
The CFL factor/stable step size is 1.6532839463174733.
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overridevirtual |
Implements TimeSteppers::RungeKutta.
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overridevirtual |
The convergence order of the stepper error measure.
Implements TimeStepper.
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overridevirtual |
The convergence order of the stepper.
Implements TimeStepper.
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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.
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staticconstexpr |