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

Public Member Functions
	Heun2 (const Heun2 &)=default
Heun2 &	operator= (const Heun2 &)=default
	Heun2 (Heun2 &&)=default
Heun2 &	operator= (Heun2 &&)=default
variants::TaggedVariant< Tags::FixedOrder, Tags::VariableOrder >	order () const override
	The convergence order of the stepper.
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.
size_t	imex_order () const override
	Convergence order of the integrator when used in IMEX mode.
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
Public Member Functions inherited from TimeSteppers::RungeKutta
uint64_t	number_of_substeps () const override
	Number of substeps in this TimeStepper.
uint64_t	number_of_substeps_for_error () const override
	Number of substeps in this TimeStepper when providing an error measure for adaptive time-stepping.
size_t	number_of_past_steps () const override
	Number of past time steps needed for multi-step method.
bool	monotonic () const override
	Whether computational and temporal orderings of operations match.
TimeStepId	next_time_id (const TimeStepId &current_id, const TimeDelta &time_step) const override
	The TimeStepId after the current substep.
TimeStepId	next_time_id_for_error (const TimeStepId &current_id, const TimeDelta &time_step) const override
	The TimeStepId after the current substep when providing an error measure for adaptive time-stepping.
Public Member Functions inherited from TimeStepper
	WRAPPED_PUPable_abstract (TimeStepper)
template<typename Vars>
void	update_u (const gsl::not_null< Vars * > u, const TimeSteppers::History< Vars > &history, const TimeDelta &time_step) const
	Set `u` to the value at the end of the current substep.
template<typename Vars>
std::optional< StepperErrorEstimate >	update_u (const gsl::not_null< Vars * > u, const TimeSteppers::History< Vars > &history, const TimeDelta &time_step, const StepperErrorTolerances &tolerances) const
	Set `u` to the value at the end of the current substep; report the error measure when available.
template<typename Vars>
void	clean_history (const gsl::not_null< TimeSteppers::History< Vars > * > history) const
	Remove old entries from the history.
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.
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.
Public Member Functions inherited from ImexTimeStepper
	WRAPPED_PUPable_abstract (ImexTimeStepper)
template<typename Vars>
void	add_inhomogeneous_implicit_terms (const gsl::not_null< Vars * > u, const 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.
template<typename Vars>
double	implicit_weight (const 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.

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 [87]. 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()

const ButcherTableau & TimeSteppers::Heun2::butcher_tableau ( ) const

overridevirtual

Implements TimeSteppers::RungeKutta.

◆ imex_order()

size_t TimeSteppers::Heun2::imex_order ( ) const

overridevirtual

Convergence order of the integrator when used in IMEX mode.

Implements ImexTimeStepper.

◆ implicit_butcher_tableau()

const ImplicitButcherTableau & TimeSteppers::Heun2::implicit_butcher_tableau ( ) const

overridevirtual

Implements TimeSteppers::ImexRungeKutta.

◆ implicit_stage_order()

size_t TimeSteppers::Heun2::implicit_stage_order ( ) const

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()

variants::TaggedVariant< Tags::FixedOrder, Tags::VariableOrder > TimeSteppers::Heun2::order ( ) const

overridevirtual

The convergence order of the stepper.

Implements TimeStepper.

◆ stable_step()

double TimeSteppers::Heun2::stable_step ( ) const

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

Options::String TimeSteppers::Heun2::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

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ butcher_tableau()

◆ imex_order()

◆ implicit_butcher_tableau()

◆ implicit_stage_order()

◆ order()

◆ stable_step()

Member Data Documentation

◆ help