[petsc-users] Auto sparsity detection?

[Zou, Ling]

Thank you, Matt.
Seems that at least the matrix coloring part I am following the ‘best practice’.

-Ling

From: Matthew Knepley <knepley at gmail.com>
Date: Thursday, January 16, 2025 at 9:01 PM
To: Zou, Ling <lzou at anl.gov>
Cc: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Auto sparsity detection?
On Thu, Jan 16, 2025 at 9: 50 PM Zou, Ling via petsc-users <petsc-users@ mcs. anl. gov> wrote: Hi all, Does PETSc has some automatic matrix sparsity detection algorithm available? Something like: https: //docs. sciml. ai/NonlinearSolve/stable/basics/sparsity_detection/
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On Thu, Jan 16, 2025 at 9:50 PM Zou, Ling via petsc-users <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>> wrote:
Hi all,

Does PETSc has some automatic matrix sparsity detection algorithm available?
Something like: https://urldefense.us/v3/__https://docs.sciml.ai/NonlinearSolve/stable/basics/sparsity_detection/__;!!G_uCfscf7eWS!e2UJSeesJYrQcCcqAr_ecKtOzfunVxto3kBxGHMZUSLdwstXEZhtFmKA8_fBeRE19FoFChtexPD3ya-IFZs$ <https://urldefense.us/v3/__https:/docs.sciml.ai/NonlinearSolve/stable/basics/sparsity_detection/__;!!G_uCfscf7eWS!ccEx6zmuNrVADqtN50hO2N0k4Qs-A70nztAjMLu-JElnjhK5w84BpYC8CAINd6KihSxaS2rx_LgpqUVM49U$>

Sparsity detection would rely on introspection of the user code for ComputeFunction(), which is not
possible in C (unless you were to code up your evaluation in some symbolic framework).

The background is that I use finite differencing plus matrix coloring to (efficiently) get the Jacobian.
For the matrix coloring part, I color the matrix based on mesh connectivity and variable dependencies, which is not bad, but just try to be lazy to even eliminating this part.

This is how the automatic frameworks also work. This is how we compute the sparsity pattern for PetscFE and PetscFV.

A related but different question, how much does PETSc support automatic differentiation?
I see some old paper:
https://ftp.mcs.anl.gov/pub/tech_reports/reports/P922.pdf
and discussion in the roadmap:
https://urldefense.us/v3/__https://petsc.org/release/community/roadmap/__;!!G_uCfscf7eWS!e2UJSeesJYrQcCcqAr_ecKtOzfunVxto3kBxGHMZUSLdwstXEZhtFmKA8_fBeRE19FoFChtexPD37cms1Jc$ <https://urldefense.us/v3/__https:/petsc.org/release/community/roadmap/__;!!G_uCfscf7eWS!ccEx6zmuNrVADqtN50hO2N0k4Qs-A70nztAjMLu-JElnjhK5w84BpYC8CAINd6KihSxaS2rx_Lgpw6v6hKE$>
I am thinking that if AD works so I don’t even need to do finite differencing Jacobian, or have it as another option.

Other people understand that better than I do.

  Thanks,

     Matt

Best,

-Ling


--
What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
-- Norbert Wiener

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