[petsc-users] DMPlex in Firedrake: scaling of mesh distribution

[Junchao Zhang]

On Sat, Mar 6, 2021 at 12:27 PM Matthew Knepley <knepley at buffalo.edu> wrote:

> On Fri, Mar 5, 2021 at 4:06 PM Alexei Colin <acolin at isi.edu> 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
>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20210306/bbee07e5/attachment.html>