[Users] Reduction operations with weights; 3 refinement centres

[Erik Schnetter]

On Wed, Jul 13, 2022 at 9:50 AM Konrad Topolski
<topolski at itp.uni-frankfurt.de> wrote:
>
> Dear ETK community,
>
> I'm writing with questions about two unrelated topics.
>
> 1. I would like to ask if there is a simple way of obtaining an L1 or L2 norm that comes from the integral with the sqrt(det(g)) measure, or a self-defined and stored weighing function?
>
> I realize it could be done most simply by defining an auxiliary variable with storage, whose value is the relevant field times "sqrt(det(g))", but perhaps this is already incorporated in some Cactus routines?
>
> Otherwise, I suppose the most efficient alternative is to assign storage for (and perfom reductions on) a new, detg-weighted variable, at only certain iterations, in the relevant thorn's schedule.ccl and only set values for it at these iterations?.

There is no functionality for this. Setting up a new grid function
would be the way to go.

For example, GRHydro has an evolved variable "dens" that contains the
sqrt{det g} weighted physical density. This is the one that should be
integrated to obtain the total mass.

> 2. I would like to learn, if there's a general guide for choosing the radii of 3 refinement centres, meaning a third, central, stationary one, in addition to the two moving ones. I want to prevent the edges of the 3rd refinement centre's levels from cutting into the objects, or the levels being unoptimally placed.
>
> For example, if I would like to have max_ref_lvl = L for the two moving centres, and L-1 (or L-2) for the third one, should the finest level of the third refinement centre (call it level N) have the radius R=(initial_separation) + r where r is the radius chosen for the other two refinement centres at level N?

I am not aware of a guide. I assume most people use trial-and-error to
find good placements. It is possible to update the locations, sizes,
and depths of the refined regions at run time by modifying the
respective grid scalars. You would have to write a thorn that does
this.

-erik

> Best regards
> Konrad
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-- 
Erik Schnetter <schnetter at gmail.com>
http://www.perimeterinstitute.ca/personal/eschnetter/