Re: [Yanl-develop] Stepper Design

[Karsten A. <kar...@gm...>]

Hi everyone,

just one short notes:

maybe people are confused if the controlled step is a stepper. It does
not perform one step it tries one step. Maybe we should call the method
try_step(). We can also clarify the method names for the the Stepper and
ErrorStep by chaning next_step() to do_step().

Regards,

Karsten





Mario Mulansky wrote:
> Hi everyone,
> 
> I have just reorganized the code of the stepsize_controller and created 
> controlled_stepper on its behalf.  So I want to take the opportunity to give 
> a short review on current status of the stepper design:
> 
> There are three different types (you may say concepts) of stepper classes:
>  - Stepper: fixed step size, no error estimation, examples: stepper_euler, 
> stepper_rk4
> 
>  - ErrorStepper: fixed step size, with error estimation, examples: 
> stepper_half_step, stepper_rk5_ck
> 
>  - ControlledStepper: variable step size, uses error estimation for adjusting 
> the stepsize, example: controlled_stepper_standard
> 
> As you might imagine, they have the following purposes: Steppers are for 
> simple, fixed step size, straight forward integration without thinking about 
> errors at all. ErrorSteppers give you the opportunity to check the errors 
> while integrating. They are hardly used alone, but serves as a basis for 
> ControlledSteppers. The ControlledSteppers can control the error of a step 
> and adjust step size (and maybe also order) of the individual integration 
> steps. This enables you to ensure that the error of each step is below a  
> certain threshold, for example. ControlledSteppers require some underlying 
> ErrorStepper which actually does the step and estimates the error. 
> 
> The respective steppers provide the following methods:
> 
> Stepper:
> 
>   order_type order() Returns the order of the method. that is the error of hte 
> method scales as dt^(order+1). order_type is typically unsigned short
> 
>   void next_step( system, x, t, dt ) Applies one integration step of size dt 
> using x as starting point at time t. system represents the rhs of the 
> equation x' = f(x,t). The result of the step is stored in x (in-place step).
> 
>   void next_step( system, x, dxdt, t, dt ) Same as above, but additionally 
> x'(x,t) is provided in dxdt, which might reduce calls of the system function.
> 
> 
> ErrorStepper:
> 
>   order_type order() 
> Returns the order of the method. that is the error of hte method scales as 
> dt^(order+1). order_type is typically unsigned short
> 
>   order_type order_error() 
> Returns the order of the error estimation, that is the error of the error 
> estimation scales as dt^(order_error+1)
> 
>   next_step( system, x, t, dt, xerr ) 
> Applies one integration step of size dt using x as starting point at time t. 
> system represents the rhs of the equation x' = f(x,t). The result of the step 
> is stored in x (in-place step). An additional error estimation is performed 
> and the result is stored in xerr.
> 
>   next_step( system, x, dxdt, t, dt, xerr ) 
> Same as above, but with dxdt = x'(x,t) provided as an additional parameter.
> 
> 
> ControlledStepper:
> 
>   order_type order() 
> Returns the order of the last step(!) performed by this class.
> 
>   controlled_step_result next_step( system, x, t, dt ) 
> Performs a controlled step starting with x at t using system to define the rhs 
> of x' = f(x,t). This means to try a step with dt and check the error (usually 
> by using an ErrorStepper). If the error is too large, the result of the step 
> is discarded, an appropriate step size dt is set (dt is an In/Out parameter 
> here) and the value step_size_decreased is returned. If the error was too 
> small, the step is applied (result stored in x), t is increased t+=dt (t is 
> also In/Out), dt is set to a better stepsize and step_size_increased is 
> returned. If the error was ok, the result of the step is stored in x, t is 
> increased t += dt and success is returned.
> 
> Regards, Mario
> 
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