[Carpet] getting dt for the finest grid

[Erik Schnetter]

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

> E.G.
>
> schedule.ccl:
>
> schedule MyGlobal in SomeEvolGroup AFTER MyGroup
> {
>   options: global
>   LANG: C
> } "do some interpolation of gfs"
>
> schedule group mygroup in SomeEvolGroup
> {
> } "schedule group"
>
> schedule MyEvolutionCode in mygroup
> {
>   options: local
>   LANG: C
> } "update the gfs"

-- 
Erik Schnetter <schnetter at cct.lsu.edu>

My email is as private as my paper mail.  I therefore support encrypting
and signing email messages.  Get my PGP key from www.keyserver.net.



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