[Developers] [Patches] ADMConstraints: Recompute constraints after regridding and restricting

Erik Schnetter schnetter at cct.lsu.edu
Wed Dec 9 13:57:29 CST 2009


On Dec 8, 2009, at 14:48 , Frank Loeffler wrote:

> Hi,
> 
> On Tue, Dec 08, 2009 at 02:11:58PM -0600, Erik Schnetter wrote:
>> These changes only modify the behaviour if constraints_persist is set to true.  In this case, the constraints are supposed to be treated like an evolved variable, and are supposed to be either evaluated after each substep (in MoL_PostStep) or in EVOL after MoL_Evolution.  In particular, the coarse-grid constraints are then supposed to be restricted from finer grids, same as an evolved variable.
> 
> I didn't think of this when I commited the patch. I was thinking this
> way: the ADMConstraints are an analysis quantity. They depend on
> derivatives, so the restricted value will often be different from the
> value which would be obtained by recomputing on the coarse timelevel.
> 
> Since the ADMConstraints are 'only' an analysis quantity, one might as
> well be interested in their values on coarse refinement levels but
> within a domain which is also covered by a finer grid (which would hold
> the values on that grid).
> 
> Now the question would be: what should we expect this quantity to be on
> coarser levels within a domain which is also covered by a finer level?
> Both options sound reasonable to me, and I don't really need one or the
> other myself.


My main argument is: It is numerically not a good idea to first interpolate the ADM quantities and then calculated the constraints.  Interpolated data are not smooth, and calculating derivatives leads to very large errors.  It is necessary to first evaluate the constraints from the ADM variables, and then interpolate the constraints.

I therefore suggest to evaluate the constraints from the ADM variables whenever the ADM variables change, either in MoL_Poststep or only in EVOL, depending on where the constraints are required.  Whenever the ADM variables are prolongated/restricted/have boundary conditions applied, then the constraints should also be prolongated or restricted or have their boundary conditions applied.

-erik

-- 
Erik Schnetter <schnetter at cct.lsu.edu>   http://www.cct.lsu.edu/~eschnett/






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