<div dir="ltr"><div dir="ltr">On Fri, Mar 5, 2021 at 4:06 PM Alexei Colin <<a href="mailto:acolin@isi.edu">acolin@isi.edu</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">To PETSc DMPlex users, Firedrake users, Dr. Knepley and Dr. Karpeev:<br>
<br>
Is it expected for mesh distribution step to<br>
(A) take a share of 50-99% of total time-to-solution of an FEM problem, and<br></blockquote><div><br></div><div>No</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
(B) take an amount of time that increases with the number of ranks, and<br></blockquote><div><br></div><div>See below.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
(C) take an amount of memory on rank 0 that does not decrease with the<br>
number of ranks<br></blockquote><div><br></div><div>The problem here is that a serial mesh is being partitioned and sent to all processes. This is fundamentally</div><div>non-scalable, but it is easy and works well for modest clusters < 100 nodes or so. Above this, it will take</div><div>increasing amounts of time. There are a few techniques for mitigating this.</div><div><br></div><div>a) For simple domains, you can distribute a coarse grid, then regularly refine that in parallel with DMRefine() or -dm_refine <k>.</div><div> These steps can be repeated easily, and redistribution in parallel is fast, as shown for example in [1].</div><div><br></div><div>b) For complex meshes, you can read them in parallel, and then repeat a). This is done in [1]. It is a little more involved,</div><div> but not much.</div><div><br></div><div>c) You can do a multilevel partitioning, as they do in [2]. I cannot find the paper in which they describe this right now. It is feasible,</div><div> but definitely the most expert approach.</div><div><br></div><div>Does this make sense?</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div><br></div><div>[1] Fully Parallel Mesh I/O using PETSc DMPlex with an Application to Waveform Modeling, Hapla <a href="http://et.al">et.al</a>.</div><div> <a href="https://arxiv.org/abs/2004.08729">https://arxiv.org/abs/2004.08729</a></div><div>[2] On the robustness and performance of entropy stable discontinuous collocation methods for the compressible Navier-Stokes equations, ROjas .<a href="http://et.al">et.al</a>.</div><div> <a href="https://arxiv.org/abs/1911.10966">https://arxiv.org/abs/1911.10966</a></div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
?<br>
<br>
The attached plots suggest (A), (B), and (C) is happening for<br>
Cahn-Hilliard problem (from firedrake-bench repo) on a 2D 8Kx8K<br>
unit-square mesh. The implementation is here [1]. Versions are<br>
Firedrake, PyOp2: 20200204.0; PETSc 3.13.1; ParMETIS 4.0.3.<br>
<br>
Two questions, one on (A) and the other on (B)+(C):<br>
<br>
1. Is (A) result expected? Given (A), any effort to improve the quality<br>
of the compiled assembly kernels (or anything else other than mesh<br>
distribution) appears futile since it takes 1% of end-to-end execution<br>
time, or am I missing something?<br>
<br>
1a. Is mesh distribution fundamentally necessary for any FEM framework,<br>
or is it only needed by Firedrake? If latter, then how do other<br>
frameworks partition the mesh and execute in parallel with MPI but avoid<br>
the non-scalable mesh destribution step?<br>
<br>
2. Results (B) and (C) suggest that the mesh distribution step does<br>
not scale. Is it a fundamental property of the mesh distribution problem<br>
that it has a central bottleneck in the master process, or is it<br>
a limitation of the current implementation in PETSc-DMPlex?<br>
<br>
2a. Our (B) result seems to agree with Figure 4(left) of [2]. Fig 6 of [2]<br>
suggests a way to reduce the time spent on sequential bottleneck by<br>
"parallel mesh refinment" that creates high-resolution meshes from an<br>
initial coarse mesh. Is this approach implemented in DMPLex? If so, any<br>
pointers on how to try it out with Firedrake? If not, any other<br>
directions for reducing this bottleneck?<br>
<br>
2b. Fig 6 in [3] shows plots for Assembly and Solve steps that scale well up<br>
to 96 cores -- is mesh distribution included in those times? Is anyone<br>
reading this aware of any other publications with evaluations of<br>
Firedrake that measure mesh distribution (or explain how to avoid or<br>
exclude it)?<br>
<br>
Thank you for your time and any info or tips.<br>
<br>
<br>
[1] <a href="https://github.com/ISI-apex/firedrake-bench/blob/master/cahn_hilliard/firedrake_cahn_hilliard_problem.py" rel="noreferrer" target="_blank">https://github.com/ISI-apex/firedrake-bench/blob/master/cahn_hilliard/firedrake_cahn_hilliard_problem.py</a><br>
<br>
[2] Unstructured Overlapping Mesh Distribution in Parallel, Matthew G.<br>
Knepley, Michael Lange, Gerard J. Gorman, 2015.<br>
<a href="https://arxiv.org/pdf/1506.06194.pdf" rel="noreferrer" target="_blank">https://arxiv.org/pdf/1506.06194.pdf</a><br>
<br>
[3] Efficient mesh management in Firedrake using PETSc-DMPlex, Michael<br>
Lange, Lawrence Mitchell, Matthew G. Knepley and Gerard J. Gorman, SISC,<br>
38(5), S143-S155, 2016. <a href="http://arxiv.org/abs/1506.07749" rel="noreferrer" target="_blank">http://arxiv.org/abs/1506.07749</a><br>
</blockquote></div></div>