[Users] Timelike and null geodesic integrator

Yosef Zlochower yosef at astro.rit.edu
Wed Aug 19 11:08:55 CDT 2015 

Thanks Erik. This should work quite well for most cases.
The only possible issue I see is when one is using a weight
that is zero outside some given sphere.


On 08/19/2015 11:22 AM, Erik Schnetter wrote:
> Yosef
>
> One easy way is to look at CarpetReduce: It will ignore points that are
> invalid. There is a grid function CarpetReduce::weight that specifies
> how much a point should contribute towards reductions; if the weight is
> zero, then the points is either an outer boundary, a buffer zone, or
> will be overwritten by restriction. The sum of all weights (modulo the
> level's grid spacing) is the volume of the simulation domain. The weight
> is 1 for "regular points", 0 for points that should be ignored, and a
> fraction of 1 for points near refinement and near outer boundaries.
>
> I don't recall whether the weight is zero in inter-process boundaries
> and symmetry boundaries; it may not be, but you can use cctk_bbox and
> cctk_nghostzones in the usual way to exclude these.
>
> -erik
>
>
> On Wed, Aug 19, 2015 at 10:51 AM, Yosef Zlochower <yosef at astro.rit.edu
> <mailto:yosef at astro.rit.edu>> wrote:
>
>     I'm working on a thorn that uses local interpolations to
>     get the RHS for the geodesic evolution. I have an issue when points
>     get too close (or inside of) buffer zones (because then the RHS won't
>     contain correct data during the MoL ministeps). How can I determine
>     if the interpolation stencil around a given point contains any buffer
>     zone points?
>
>
>
>     On 08/11/2015 03:06 PM, Yosef Zlochower wrote:
>      > Thanks for the help. I guess if I used interpolation in time the
>      > geodesics would only be accurate to 2nd order.
>      >
>      > On 08/11/2015 09:15 AM, Ian Hinder wrote:
>      >>
>      >> On 6 Aug 2015, at 16:48, Yosef Zlochower <yosef at astro.rit.edu
>     <mailto:yosef at astro.rit.edu>
>      >> <mailto:yosef at astro.rit.edu <mailto: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
>      >>
>      >
>      >
>
>
>     --
>     Dr. Yosef Zlochower
>     Center for Computational Relativity and Gravitation
>     Associate Professor
>     School of Mathematical Sciences
>     Rochester Institute of Technology
>     85 Lomb Memorial Drive
>     Rochester, NY 14623
>
>     Office:74-2067
>     Phone: +1 585-475-6103 <tel:%2B1%20585-475-6103>
>
>     yosef at astro.rit.edu <mailto:yosef at astro.rit.edu>
>
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>
>
> --
> Erik Schnetter <schnetter at cct.lsu.edu <mailto:schnetter at cct.lsu.edu>>
> http://www.perimeterinstitute.ca/personal/eschnetter/


-- 
Dr. Yosef Zlochower
Center for Computational Relativity and Gravitation
Associate Professor
School of Mathematical Sciences
Rochester Institute of Technology
85 Lomb Memorial Drive
Rochester, NY 14623

Office:74-2067
Phone: +1 585-475-6103

yosef at astro.rit.edu

CONFIDENTIALITY NOTE: The information transmitted, including
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