[Carpet] Tracking the puncture with Carpet

[Ian Hawke]

Yosef Zlochower wrote:

>    I want to evolve d Y^a / dt =  - beta^a (Y) to track the location
> of the punctures. With a unigrid code I simply added this as an
> evolved array to MoL. However, it seems that this is not simply
> done with mesh refinement.

Unfortunately not; Bela had a similar problem and it was just going to 
be too difficult (if not impossible) to fit in with MoL.

> Is there some way of knowing if the current
> level and component is the finest available resolution for the point 
> Y^a. If there is, then I suppose that I could set d Y^a = 0 for all
> levels and all components but the right one. 

The only way that I can see to do this is to use Christian's trick to 
get the refinement level and then check the coordinate boundaries of the 
patch (taking into account ghost/boundary zones) against the location of 
the puncture. This will of course only work if you can guarantee that 
the puncture is always located on a grid at the finest refinement level.

> I can think of another 
> method where I interpolate beta at y^a after the timestep is complete.
> Will the interpolator give me beta at the highest refinement level
> at point y^a, and if so, how do I get the appropriate dt for this 
> refinement level?

Yes, you will get beta as accurately as possible given the position of 
the puncture in the refinement hierarchy. The simplest approach would be 
a two step method where first a routine is scheduled in the appropriate 
mode to get the shift, and then a follow-up routine is scheduled in 
local/level mode to evolve the puncture, where you would use Christian's 
hack to only do this on the finest level.

In many ways I believe that this is the better approach as you would 
then have the correct puncture location on every processor, as the 
interpolator would return the puncture location globally.

Ian