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

[Mark Adams]

Is phase 1 the old method and 2 the new?
Is this 128^3 mesh per process?

On Sun, Mar 7, 2021 at 7:27 AM Stefano Zampini <stefano.zampini at gmail.com>
wrote:

>
>
> [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
>>
>
> This is not the proper reference, here is the correct one
> https://www.sciencedirect.com/science/article/pii/S0021999120306185?dgcid=rss_sd_all
> However, there the algorithm is only outlined, and performances related to
> the mesh distribution are not really reported.
> We observed a large gain for large core counts and one to all
> distributions (from minutes to seconds) by splitting the several
> communication rounds needed by DMPlex into stages: from rank 0 to 1 rank
> per node, and then decomposing independently within the node.
> Attached the total time for one-to-all DMPlexDistrbute for a 128^3 mesh
>
>
>>
>>
>>> ?
>>>
>>> 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
>>>
>>
>
> --
> Stefano
>
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