#include <AdamsMoultonPc.hpp>

Classes
struct	Order

Public Types
using	options = tmpl::list< Order >

Public Types inherited from TimeStepper
using	provided_time_stepper_interfaces = tmpl::list< TimeStepper >

Public Member Functions
	AdamsMoultonPc (size_t order)

	AdamsMoultonPc (const AdamsMoultonPc &)=default

AdamsMoultonPc &	operator= (const AdamsMoultonPc &)=default

	AdamsMoultonPc (AdamsMoultonPc &&)=default

AdamsMoultonPc &	operator= (AdamsMoultonPc &&)=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...

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...

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...

bool	monotonic () const override
	Whether computational and temporal orderings of operations match. More...

TimeStepId	next_time_id (const TimeStepId &current_id, const TimeDelta &time_step) const override
	The TimeStepId after the current substep. More...

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. More...

	WRAPPED_PUPable_decl_template (AdamsMoultonPc)

	AdamsMoultonPc (CkMigrateMessage *)

void	pup (PUP::er &p) override

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 &current_id, const TimeDelta &time_step) const =0
	The TimeStepId after the current substep. More...

virtual TimeStepId	next_time_id_for_error (const TimeStepId &current_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...

Static Public Member Functions
static std::string	name ()

Static Public Attributes
static constexpr size_t	minimum_order = 2

static constexpr size_t	maximum_order = 8

static constexpr Options::String	help

Static Public Attributes inherited from TimeStepper
static constexpr bool	local_time_stepping = false

static constexpr bool	imex = false

Detailed Description

template<bool Monotonic>
class TimeSteppers::AdamsMoultonPc< Monotonic >

An $N\$th order Adams-Moulton predictor-corrector method using an \f$(N - 1)$th order Adams-Bashforth predictor.

If Monotonic is true, dense output is performed using the predictor stage, otherwise the corrector is used. The corrector results are more accurate (but still formally the same order), but require a RHS evaluation at the end of the step before dense output can be performed.

The stable step size factors for different orders are (to approximately 4-5 digits):

Order	CFL Factor
2	1
3	0.981297
4	0.794227
5	0.612340
6	0.464542
7	0.350596
8	0.264373

Member Function Documentation

◆ error_estimate_order()

template<bool Monotonic>

size_t TimeSteppers::AdamsMoultonPc< Monotonic >::error_estimate_order ( ) const

overridevirtual

The convergence order of the stepper error measure.

Implements TimeStepper.

◆ monotonic()

template<bool Monotonic>

bool TimeSteppers::AdamsMoultonPc< Monotonic >::monotonic ( ) const

overridevirtual

Whether computational and temporal orderings of operations match.

If this method returns true, then, for two time-stepper operations occurring at different simulation times, the temporally earlier operation will be performed first. These operations include RHS evaluation, dense output, and neighbor communication. In particular, dense output never requires performing a RHS evaluation later than the output time, so control systems measurements cannot cause deadlocks.

Warning: This guarantee only holds if the time steps themselves are monotonic, which can be violated during initialization.

Implements TimeStepper.

◆ next_time_id()

template<bool Monotonic>

TimeStepId TimeSteppers::AdamsMoultonPc< Monotonic >::next_time_id	(	const TimeStepId &	current_id,
		const TimeDelta &	time_step
	)		const

overridevirtual

The TimeStepId after the current substep.

Implements TimeStepper.

◆ next_time_id_for_error()

template<bool Monotonic>

TimeStepId TimeSteppers::AdamsMoultonPc< Monotonic >::next_time_id_for_error	(	const TimeStepId &	current_id,
		const TimeDelta &	time_step
	)		const

overridevirtual

The TimeStepId after the current substep when providing an error measure for adaptive time-stepping.

Certain substep methods (e.g. embedded RK4(3)) require additional steps when providing an error measure of the integration.

Implements TimeStepper.

◆ number_of_past_steps()

template<bool Monotonic>

size_t TimeSteppers::AdamsMoultonPc< Monotonic >::number_of_past_steps ( ) const

overridevirtual

Number of past time steps needed for multi-step method.

Implements TimeStepper.

◆ number_of_substeps()

template<bool Monotonic>

uint64_t TimeSteppers::AdamsMoultonPc< Monotonic >::number_of_substeps ( ) const

overridevirtual

Number of substeps in this TimeStepper.

Implements TimeStepper.

◆ number_of_substeps_for_error()

template<bool Monotonic>

uint64_t TimeSteppers::AdamsMoultonPc< Monotonic >::number_of_substeps_for_error ( ) const

overridevirtual

Number of substeps in this TimeStepper when providing an error measure for adaptive time-stepping.

Details

Certain substep methods (e.g. embedded RK4(3)) require additional steps when providing an error measure of the integration.

Implements TimeStepper.

◆ order()

template<bool Monotonic>

size_t TimeSteppers::AdamsMoultonPc< Monotonic >::order ( ) const

overridevirtual

The convergence order of the stepper.

Implements TimeStepper.

◆ stable_step()

template<bool Monotonic>

double TimeSteppers::AdamsMoultonPc< Monotonic >::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

template<bool Monotonic>

constexpr Options::String TimeSteppers::AdamsMoultonPc< Monotonic >::help

staticconstexpr

Initial value:

=
      Monotonic
          ? "An Adams-Moulton predictor-corrector time-stepper with monotonic "
            "dense output."
          : "An Adams-Moulton predictor-corrector time-stepper."

The documentation for this class was generated from the following file:

src/Time/TimeSteppers/AdamsMoultonPc.hpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ error_estimate_order()

◆ monotonic()

◆ next_time_id()

◆ next_time_id_for_error()

◆ number_of_past_steps()

◆ number_of_substeps()

◆ number_of_substeps_for_error()

Details

◆ order()

◆ stable_step()

Member Data Documentation

◆ help