[Users] global reductions in specified domains

[Roland Haas]

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Hello Vassilios,

> Is there a way to use the global Cactus reduction functions on
> fractions of the entire grid?
> 
> I am interested in summing grid scalars (say rho) in spherical
> shells in the grid. Is there a way to perform the "sum" reduction
> on those shells specified by a global radius variable? Or do I need
> to write my own MPI function that sums the contributions from all
> processors that have grid point that fall within the shell I am
> interested in?
There is no such facility build into Cactus unfortunately. The easiest
way to achieve a reduction using only points satisfying some criterion
(having coordinates inside the shells in your case) is to set up a
helper grid function which is set to:

          / rho : if condition is true
helper = {
          \ 0   : otherwise

For multiple shells you will have to set up multiple helper grid
functions (or re-use the same one several times). One way of doing
this is:

schedule.ccl:
STORAGE: helper[1]
schedule setup_integrand in CCTK_ANALYSIS
{
  OPTIONS: global loop-local
  LANG: C
} "compute 'helper' grid function for integrand"
schedule integrate in CCTK_ANALYSIS AFTER setup_integrand
{
  OPTIONS: global
  LANG: C
} "reduce 'helper' grid function on all processes"

You can have a look at the thorn ADMMass (in AEIThorns) and its
ADMMass_Volume routines to see how this is done in practise.

Doing the reduction by hand can be tricky since you will have to
properly handle mesh refinement boundaries. Roughly speaking you have
to multiply your integrand by the CarpetReduce::weight grid function
and only include the non-ghost zones points (ie start cctk_nghostzones
points from the edge of each component). Outer boundaries require
special treatment (detectable via cctk_bbox) and you have to include
all points there. I am right now not sure how symmetry boundaries need
to be handled (ie whether for vertex centering weight is set to 1/2
already or of you'll have to query the symmetry thorn whether an outer
boundary is a symmetry boundary).

Yours,
Roland

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