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

[Stefano Zampini]

[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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