<html><head><meta http-equiv="Content-Type" content="text/html charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><br><div><div>On 6 Aug 2015, at 16:48, Yosef Zlochower <<a href="mailto:yosef@astro.rit.edu">yosef@astro.rit.edu</a>> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite">Hi,<br><br>I was looking for advice on implementing an integrator for timelike<br>and null geodesics during an ET simulation. The confusion I have is<br>how to deal with AMR. Ideally, I'd like to use RK4 and MoL, but I<br>foresee several issues with geodesics crossing from coarser to finer<br>and finer to coarser zones. I do have a horrible hack that may possibly<br>be used, but it seems overly convoluted to me. Basically, I update the<br>grid arrays in MoL in local mode, and unless the local grid happens to<br>be the finest grid that owns the geodesic, I set RHS to zero (there are<br>additional hacks because MoL copies the past time level onto the<br>current one automatically). But<br>still there is the issue of geodesics crossing AMR boundaries. In<br>particular, when moving from fine to coarse, the geodesic may end up<br>being behind because the finer grid may be at an earlier time than the<br>coarser one.<br><br> One possible workaround would be to update<br>the geodesics during every iteration on the finest level. This would<br>imply that I would need to interpolate the metric, shift, and lapse<br>(and their derivatives) during each ministep of the finest level even<br>if the point being interpolated doesn't exist on the finest level.<br></blockquote><br><blockquote type="cite">This, in turn, means that the carpet would need to interpolate those<br>points in time during the ministep where the local time will at some<br>intermediate time between cctk_time(old) and cctk_time(new). I don't<br>think this works correctly in the current version of carpet.<br></blockquote><div><br></div><div>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 <a href="https://trac.einsteintoolkit.org/ticket/1656">https://trac.einsteintoolkit.org/ticket/1656</a>, and a patch with a parameter which makes it use cctk_time.</div><br><blockquote type="cite">An alternative method I was considering was a second-order in time<br>integration. For this, I would need to be able to interpolate the<br>metric and its derivatives during the current (finest level) time and<br>the previous (finest level) time. For the moment, I'd be happy to<br>assume that the finest refinement level will not change during the<br>evolution.<br></blockquote><div><br></div></div>"It's complicated".<div><br></div><div>I describe an approach in <a href="http://lists.einsteintoolkit.org/pipermail/users/2013-November/003280.html">http://lists.einsteintoolkit.org/pipermail/users/2013-November/003280.html</a> (the archive page seems to not know about line wrapping). </div><div><br><div apple-content-edited="true">
<div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div>-- </div><div>Ian Hinder</div><div><a href="http://members.aei.mpg.de/ianhin">http://members.aei.mpg.de/ianhin</a></div></div></div></div></div>
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