[Carpet] getting dt for the finest grid

[Yosef Zlochower]

Hi,

  So if I want to evolve a geodesic or a curve normal to the timeslice
 (or something else which depends on the ADMBase vars),  then I'll
have to schedule the evolution of the curve in the PostEvol bin?

Yosef

Erik Schnetter wrote:
> On Aug 28, 2007, at 11:55:09, Yosef Zlochower wrote:
>
>> Hi,
>>
>>  Can you clarify one point for me? Suppose I schedule a local routine
>> in a schedule group "mygroup" and a global routine after "mygroup"
>> but in the same schedule bin (and perhaps even within the same group),
>> can I force the global routine to be called after carpet finishes 
>> calling
>> the local routine on all the appropriate levels using the AFTER keyword?
>
> No, that is very unfortunately not possible.  The schedule is executed 
> by the flesh, not by Carpet, and this happens in level mode.  Global 
> mode means only to skip some calls that would otherwise happen, i.e., 
> to ensure that this routine is only called once per time step.  It 
> will be called together with the first or the last level mode routine 
> in a particular bin, depending on the bin.  If there is interest, I 
> can implement new options such as GLOBAL_FIRST and GLOBAL_LAST, or 
> GLOBAL_COARSEST and GLOBAL_FINEST, which would do what you intend.  
> Ultimately the Cactus scheduler needs to be made more flexible and 
> taught about the recursive evolution.
>
>
>
> Consider the case where one wants to evolve some additional equation 
> together with the main evolution system, e.g. some geodesic or some 
> global quantity, and which is coupled with the main evolution system.  
> Let's call this quantity Q.  That means that e.g. the BSSN gauge RHS 
> depends on Q, and the RHS for Q depends on the metric via an 
> interpolation or reduction.
>
> With mesh refinement, it is not trivial to make this happen 
> correctly.  If you schedule the evolution for Q after the metric 
> evolution, then the metric evolution doesn't have access to Q.  And 
> vice versa.  Similar to the spacetime/hydro coupling, you want to 
> evolve Q at the same time as the BSSN equations.  If you look at how 
> the BSSN evolution proceeds -- it is quite non-monotonic in time -- 
> then you'll find that you have to evolve first Q a large step into the 
> future, then undo that for the next finer level and evolve it by 
> several smaller steps.
>
> If you just evolve Q in many fine steps, then you cannot access a good 
> value for Q for the first coarse grid BSSN step, since that BSSN step 
> is the first thing that happens in the Berger-Oliger scheme.
>
>
>
> Unless you come up with a clean scheme, you can only achieve 
> independent time evolution, which means a first order coupling between 
> Q and the BSSN quantities.  The error will be first order in the 
> coarse grid time step, which can be significant.
>
> If you can guarantee that Q depends only on the finest grid, and that 
> only the fine grid evolution depends on Q (e.g. if it has something to 
> do with excision), then you can evolve Q together with the finest 
> grid, achieving easily first order accuracy in the fine grid dt, or 
> (if you use MoL for Q) also e.g. 4th order coupling with BSSN.
>
>
>
> If Q is a pure analysis quantity (which does not influence the RHS of 
> the BSSN system), then you are lucky.
>
> -erik
>