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

[Barry Smith]

  Alexei,

     Sorry to hear about your difficulties with the mesh distribution step. Based on the figures you included, the extreme difficulties  occur on the Oak Ridge Summit system? But on the Argonne Theta system though the distribution time goes up it does not dominate the computation? 

   There is a very short discussion of mesh distribution in https://arxiv.org/abs/2102.13018 <https://arxiv.org/abs/2102.13018> section 6.3 Figure 11 that was run on the Summit system.

    Certainly there is no intention that mesh distribution dominates the entire computation, your particular case and the behavior of DMPLEX would need to understood on Summit to determine the problems.

    DMPLEX and all its related components are rapidly evolving and hence performance can change quickly with new updates. I urge you to use the main branch of PETSc for HPC and timing studies of DMPLEX performance on large systems, do not just use PETSc releases. You can communicate directly with those working on scaling DMPLEX at gitlab.com/petsc/petsc <http://gitlab.com/petsc/petsc> who can help understand the cause of the performance issues on Summit.

  Barry






> On Mar 5, 2021, at 3:06 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
> (B) take an amount of time that increases with the number of ranks, and
> (C) take an amount of memory on rank 0 that does not decrease with the
> number of ranks
> ?
> 
> 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
> <ch-mesh-dist.pdf><ch-mem.pdf>

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