<div dir="ltr"><div><div>Dear Cosima,<br><br></div>Regarding solving for thousands of geodesics, a faster alternative would be to solve them as a PDE, i.e. as a dust fluid. This is analogous to solving the Burgers equation (the pressureless Euler equation) for nonrelativistic flows. The Einstein Toolkit is naturally designed to handle such scenarios. But the details depend on what you are trying to simulate.<br><br>For example, for timelike geodesics, this could be done by evolving eq. (10) in<br><a href="https://arxiv.org/abs/1410.7777">https://arxiv.org/abs/1410.7777</a><br></div><div>with p_a given by eq. (8) and H given by eq. (16), setting the specific enthalpy to h=1.<br><br></div><div>Some caveats:<br></div><div>1) For null geodesics, you can do something similar, but need a different foliation.<br></div><div>2) If you try to use the Valencia formulation to evolve dust, you must evolve the continuity equation for the density \rho, along with the Euler equation for the velocity. This system is ill-posed and unstable for dust (pressure = 0), because you are evolving an equation that is no-longer needed: One needs to drop the continuity equation, eliminate \rho completely from the equations, and evolve only 3 equations for the spatial components of the 4-velocity. Then the system is well-posed (strongly hyperbolic), just like the Burgers equation (whose relativistic generalization you are solving). Eq. (10) in the above paper does this.<br></div><div>3) As Roland Haas pointed out, because you are evolving dust as a pressureless fluid, even though the flow is geodesic, caustics or shocks may form. If that happens, the way to handle it depends on what you are trying to simulate with geodesics. If you need to simulate the actual geodesics, and not dust, you can use the method of characteristics and disregard shock solutions. (For null geodesics you won't have this problem.)<br></div><div>4) If you need to know where each geodesic particle is at a given time, along with eq. (10) above, you can solve the other Hamilton equation for the position x^a conjugate to p_a,<br>$ dx^a/dt=\partial H / \partial p_a $,<br>written in Eulerian PDE form. This evolves a 'label' of the initial position of each particle.<br><br></div><div>For any clarification, please feel free to contact me or Roland Haas.<br><br></div><div>Best regards,<br><br></div><div>Haris Markakis<br><br>
________________________________________________<br>
<br>
Charalampos Markakis<br>
Postdoctoral Research Associate<br>
<br>
National Center for Supercomputing Applications<br>
University of Illinois at Urbana-Champaign<br>
1205 West Clark St, Room 4022, MC-257, Urbana, IL 61801<br>
<a href="mailto:markakis@illinois.edu">markakis@illinois.edu</a><br>
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<br></div><div><br><div><div><div class="gmail_extra"><br><div class="gmail_quote">On 21 November 2016 at 10:56, Frank Loeffler <span dir="ltr"><<a href="mailto:knarf@cct.lsu.edu" target="_blank">knarf@cct.lsu.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><span class="gmail-">On Mon, Nov 21, 2016 at 12:26:59AM -0600, Frank Loeffler wrote:<br>
</span><span class="gmail-"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
Please consider joining the weekly Einstein Toolkit phone call at<br>
</blockquote>
<br></span>
The following group called in:<br>
<br>
Cosima (and a few others from the Frankfurt group;<br>
I don't remember your names, sorry)<br>
Erik<br>
Frank<br>
Harry<br>
Ian<br>
Peter<br>
Roberto<br>
Vassili<br>
Yosef<br>
Zach<br>
<br>
One topic was how to optimized a geodesics iteration thorn written by Ian Hinder <a href="http://et.al" rel="noreferrer" target="_blank">et.al</a>., and now used by the Frankfurt group. The main problem is that it was written with a few geodesics in mind, but should now be used for millions. Erik strongly suggests to profile what exactly is slow before starting to heavily optimized what you might think is slow. Assuming it is communication, he gave a few hints which functions might help (locatePosition?).<br>
<br>
Connected to this it was mentioned that integrating GAs is currently broken if you have more than one component per process, as they are currently integrated (by MoL) fore each component. Current workaround: use more processes (to get 1 component per process).<br>
<br>
Release related issues:<br>
<br>
- Llama was added to the thornlist, including testsuites<br>
- initial test results look quite good<br>
(a few failures from usual suspects)<br>
- Intel 17 compiler crashes on bbox.cc in Carpet.<br>
- current workaround: lower optimization of that file to -O1<br>
- maybe better: use bbox1-class instead of newer bbox2 class.<br>
however: you will have worse scaling for large runs<br>
- current machines showing this problem: marconi, stampede-knl<br>
- Only a few machines saw testing so far. We need more!<br>
<br>
A first shot at a new design of the ET pages is online:<br>
<br>
<a href="http://einsteintoolkit.org/new/" rel="noreferrer" target="_blank">http://einsteintoolkit.org/ne<wbr>w/</a><br>
<br>
These aren't polished yet, but should give a first impression. They are responsive, i.e., they should look presentable also on small screens (phones). When you test them, please use different browsers, different font sizes (zoom levels), different window sized, and different devices.<br>
<br>
Please send feedback either to the list, or directly to Frank <<a href="mailto:knarf@cct.lsu.edu" target="_blank">knarf@cct.lsu.edu</a>>.<span class="gmail-HOEnZb"><font color="#888888"><br>
<br>
Frank<br>
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<br></blockquote></div><br></div></div></div></div></div>