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

[Mark Adams]

I observed poor scaling with mat/tests/ex13 on Fugaku recently.
I was running this test as is (eg, no threads and 4 MPI processes per
node/chip, which seems recomended). I did not dig into this.
A test with about 10% of the machine took about 45 minutes to run.
Mark

On Sat, Mar 6, 2021 at 9:49 PM Junchao Zhang <junchao.zhang at gmail.com>
wrote:

>
>
>
> 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
>>>
>>
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