TC_PI< NEWT > Class Template Reference

Proportional-integral step-size control from the solver's error measure. More...

#include <pi.hh>

Inheritance diagram for TC_PI< NEWT >:

Public Types
using	Base = TC_Default<NEWT>

Public Member Functions
	TC_PI (NEWT &newton_, unsigned int alg_order_, double t_, double max_t_, double dt_, double min_dt_, double max_dt_)
Public Member Functions inherited from TC_Default< NEWT >
	TC_Default (NEWT &newton_, unsigned int alg_order_, double t_, double max_t_, double dt_, double min_dt_, double max_dt_)
double	get_dt () const
	The step to take next.
double	get_t () const
	The current time.
unsigned int	get_stuck () const
	How many steps in a row did not advance the time.
bool	finished () const
	Whether max_t has been reached.
template<typename F >
void	advance (F &f)
	Attempt one step and plan the next.

Protected Member Functions
void	get_q ()
	Update q from the current error.
virtual void	step_success () override
	Advance the time and suggest the next step from the current and previous error.
virtual void	step_fail (const std::exception &) override
	On a fail, decrease the timestep by at least a factor of 2 relative to the failed step.
Protected Member Functions inherited from TC_Default< NEWT >

Protected Attributes
double	beta1
double	beta2
double	qsteady_min
double	qsteady_max
double	qmin
double	qmax
double	qoldinit
double	qold
double	q11
double	q
double	gamma
double	t
NEWT &	newton
double	cur_dt
double	sug_dt
unsigned int	alg_order
Protected Attributes inherited from TC_Default< NEWT >
NEWT &	newton
unsigned int	alg_order
double	t
double	max_t
double	sug_dt
double	min_dt
double	max_dt
double	cur_dt
double	last_t
unsigned int	stuck
bool	fin

Detailed Description

template<typename NEWT>
class DiFfRG::TC_PI< NEWT >

Proportional-integral step-size control from the solver's error measure.

With the error \(E_n\) = newton.get_error() of the accepted step and the one before, \(E_{n-1}\), the next step is \(\Delta t_{n+1} = \Delta t_n / q\) with

\[ q = \frac{1}{0.9}\, \frac{E_n^{\beta_1}}{E_{n-1}^{\beta_2}}\,, \qquad \beta_1 = \frac{0.7}{p}\,, \quad \beta_2 = \frac{0.4}{p}\,, \]

where \(p\) is the order of the method, \(q\) is clipped to [0.1, 5] and set to 1 within [0.99, 1.2]. \(E_{n-1}\) is floored at \(10^{-4}\). A failed step is retried with at most half the step size. The coefficients are close to the PI defaults of OrdinaryDiffEq.jl. For ImplicitEuler and TRBDF2 \(E\) is the weighted norm of their local error estimate; a step that throws (e.g. rejected with \(E > 1\)) is retried with a smaller step.

Template Parameters

NEWT	the solver; must provide set_ignore_nonconv(bool) and get_error().

Member Typedef Documentation

Base

template<typename NEWT >

using Base = TC_Default<NEWT>

Constructor & Destructor Documentation

TC_PI()

template<typename NEWT >

TC_PI ( NEWT & newton_, unsigned int alg_order_, double t_, double max_t_, double dt_, double min_dt_, double max_dt_ )

inline

Member Function Documentation

get_q()

template<typename NEWT >

void get_q ( )

inlineprotected

Update q from the current error.

step_fail()

template<typename NEWT >

virtual void step_fail ( const std::exception & )

inlineoverrideprotectedvirtual

On a fail, decrease the timestep by at least a factor of 2 relative to the failed step.

The error estimate alone cannot guarantee that: a failure need not come with EEst > 1, and the failed step may have been clipped below sug_dt (to hit max_t), so scaling sug_dt could retry the same step.

Reimplemented from TC_Default< NEWT >.

step_success()

template<typename NEWT >

virtual void step_success ( )

inlineoverrideprotectedvirtual

Advance the time and suggest the next step from the current and previous error.

Reimplemented from TC_Default< NEWT >.

Member Data Documentation

alg_order

template<typename NEWT >

unsigned int alg_order

protected

beta1

template<typename NEWT >

double beta1

protected

beta2

template<typename NEWT >

double beta2

protected

cur_dt

template<typename NEWT >

double cur_dt

protected

gamma

template<typename NEWT >

double gamma

protected

newton

template<typename NEWT >

NEWT& newton

protected

q

template<typename NEWT >

double q

protected

q11

template<typename NEWT >

double q11

protected

qmax

template<typename NEWT >

double qmax

protected

qmin

template<typename NEWT >

double qmin

protected

qold

template<typename NEWT >

double qold

protected

qoldinit

template<typename NEWT >

double qoldinit

protected

qsteady_max

template<typename NEWT >

double qsteady_max

protected

qsteady_min

template<typename NEWT >

double qsteady_min

protected

sug_dt

template<typename NEWT >

double sug_dt

protected

t

template<typename NEWT >

double t

protected

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

• /home/runner/work/DiFfRG/DiFfRG/DiFfRG/include/DiFfRG/timestepping/timestep_control/pi.hh