On Sat, Mar 6, 2021 at 12:27 PM Matthew Knepley <[email protected]> wrote:
> On Fri, Mar 5, 2021 at 4:06 PM Alexei Colin <[email protected]> wrote: > >> To PETSc DMPlex users, Firedrake users, Dr. Knepley and Dr. Karpeev: >> >> Is it expected for mesh distribution step to >> (A) take a share of 50-99% of total time-to-solution of an FEM problem, >> and >> > > No > > >> (B) take an amount of time that increases with the number of ranks, and >> > > See below. > > >> (C) take an amount of memory on rank 0 that does not decrease with the >> number of ranks >> > > The problem here is that a serial mesh is being partitioned and sent to > all processes. This is fundamentally > non-scalable, but it is easy and works well for modest clusters < 100 > nodes or so. Above this, it will take > increasing amounts of time. There are a few techniques for mitigating this. > Is this one-to-all communication only done once? If yes, one MPI_Scatterv() is enough and should not cost much. a) For simple domains, you can distribute a coarse grid, then regularly > refine that in parallel with DMRefine() or -dm_refine <k>. > These steps can be repeated easily, and redistribution in parallel is > fast, as shown for example in [1]. > > 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, > but not much. > > 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, > but definitely the most expert approach. > > Does this make sense? > > Thanks, > > Matt > > [1] Fully Parallel Mesh I/O using PETSc DMPlex with an Application to > Waveform Modeling, Hapla et.al. > https://arxiv.org/abs/2004.08729 > [2] On the robustness and performance of entropy stable discontinuous > collocation methods for the compressible Navier-Stokes equations, ROjas . > et.al. > https://arxiv.org/abs/1911.10966 > > >> ? >> >> The attached plots suggest (A), (B), and (C) is happening for >> Cahn-Hilliard problem (from firedrake-bench repo) on a 2D 8Kx8K >> unit-square mesh. The implementation is here [1]. Versions are >> Firedrake, PyOp2: 20200204.0; PETSc 3.13.1; ParMETIS 4.0.3. >> >> Two questions, one on (A) and the other on (B)+(C): >> >> 1. Is (A) result expected? Given (A), any effort to improve the quality >> of the compiled assembly kernels (or anything else other than mesh >> distribution) appears futile since it takes 1% of end-to-end execution >> time, or am I missing something? >> >> 1a. Is mesh distribution fundamentally necessary for any FEM framework, >> or is it only needed by Firedrake? If latter, then how do other >> frameworks partition the mesh and execute in parallel with MPI but avoid >> the non-scalable mesh destribution step? >> >> 2. Results (B) and (C) suggest that the mesh distribution step does >> not scale. Is it a fundamental property of the mesh distribution problem >> that it has a central bottleneck in the master process, or is it >> a limitation of the current implementation in PETSc-DMPlex? >> >> 2a. Our (B) result seems to agree with Figure 4(left) of [2]. Fig 6 of [2] >> suggests a way to reduce the time spent on sequential bottleneck by >> "parallel mesh refinment" that creates high-resolution meshes from an >> initial coarse mesh. Is this approach implemented in DMPLex? If so, any >> pointers on how to try it out with Firedrake? If not, any other >> directions for reducing this bottleneck? >> >> 2b. Fig 6 in [3] shows plots for Assembly and Solve steps that scale well >> up >> to 96 cores -- is mesh distribution included in those times? Is anyone >> reading this aware of any other publications with evaluations of >> Firedrake that measure mesh distribution (or explain how to avoid or >> exclude it)? >> >> Thank you for your time and any info or tips. >> >> >> [1] >> https://github.com/ISI-apex/firedrake-bench/blob/master/cahn_hilliard/firedrake_cahn_hilliard_problem.py >> >> [2] Unstructured Overlapping Mesh Distribution in Parallel, Matthew G. >> Knepley, Michael Lange, Gerard J. Gorman, 2015. >> https://arxiv.org/pdf/1506.06194.pdf >> >> [3] Efficient mesh management in Firedrake using PETSc-DMPlex, Michael >> Lange, Lawrence Mitchell, Matthew G. Knepley and Gerard J. Gorman, SISC, >> 38(5), S143-S155, 2016. http://arxiv.org/abs/1506.07749 >> >
