[Users] Timelike and null geodesic integrator

[Ian Hinder]

On 6 Aug 2015, at 16:48, Yosef Zlochower <yosef at astro.rit.edu> wrote:

> Hi,
> 
> I was looking for advice on implementing an integrator for timelike
> and null geodesics during an ET simulation. The confusion I have is
> how to deal with AMR. Ideally, I'd like to use RK4 and MoL, but I
> foresee several issues with geodesics crossing from coarser to finer
> and finer to coarser zones. I do have a horrible hack that may possibly
> be used, but it seems overly convoluted to me. Basically, I update the
> grid arrays in MoL in local mode, and unless the local grid happens to
> be the finest grid that owns the geodesic, I set RHS to zero (there are
> additional hacks because MoL copies the past time level onto the
> current one automatically). But
> still there is the issue of geodesics crossing AMR boundaries. In
> particular, when moving from fine to coarse, the geodesic may end up
> being behind because the finer grid may be at an earlier time than the
> coarser one.
> 
>  One possible workaround would be to update
> the geodesics during every iteration on the finest level. This would
> imply that I would need to interpolate the metric, shift, and lapse
> (and their derivatives) during each ministep of the finest level even
> if the point being interpolated doesn't exist on the finest level.

> This, in turn, means that the carpet would need to interpolate those
> points in time during the ministep where the local time will at some
> intermediate time between cctk_time(old) and cctk_time(new). I don't
> think this works correctly in the current version of carpet.

Correct.  The time used by the interpolator for time interpolation is not consistently cctk_time, so when MoL modified this variable during MoL_CalcRHS, this is ignored by CarpetInterp.  See the discussion in https://trac.einsteintoolkit.org/ticket/1656, and a patch with a parameter which makes it use cctk_time.

> An alternative method I was considering was a second-order in time
> integration. For this, I would need to be able to interpolate the
> metric and its derivatives during the current (finest level) time and
> the previous (finest level) time. For the moment, I'd be happy to
> assume that the finest refinement level will not change during the
> evolution.

"It's complicated".

I describe an approach in http://lists.einsteintoolkit.org/pipermail/users/2013-November/003280.html (the archive page seems to not know about line wrapping).  

-- 
Ian Hinder
http://members.aei.mpg.de/ianhin

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