[petsc-dev] Additive Schwarz Method + ILU on GPU platforms

[Angus, Justin Ray]

Thanks for the reply.

The work per block should be the same for the weak scaling. I know LU is not scalable with respect to the block size.

Perhaps our setup is not doing what we think it is doing. I’ll look into it further.

-Justin

From: Mark Adams <mfadams at lbl.gov>
Date: Wednesday, November 5, 2025 at 6:14 AM
To: Matthew Knepley <knepley at gmail.com>
Cc: Angus, Justin Ray <angus1 at llnl.gov>, petsc-dev at mcs.anl.gov <petsc-dev at mcs.anl.gov>
Subject: Re: [petsc-dev] Additive Schwarz Method + ILU on GPU platforms

And we do not have sparse LU on GPUs so that is done on the CPU.

And I don't know why it would not weak scale well.
Your results are consistent with just using one process with one domain, (re Matt) while you double the problem size.

On Tue, Nov 4, 2025 at 2:27 PM Matthew Knepley <knepley at gmail.com<mailto:knepley at gmail.com>> wrote:
On Tue, Nov 4, 2025 at 1:25 PM Angus, Justin Ray via petsc-dev <petsc-dev at mcs.anl.gov<mailto:petsc-dev at mcs.anl.gov>> wrote:
Hi Junchao,

We have recently been using ASM + LU for 2D problems on both CPU and GPU. However, I found that this method has very bad weak scaling. I find that the cost of PCApply increases by about a factor of 4 each time I increase the problem size in 1 dimension by a factor of 2 while keeping the load per core/gpu the same. The total number of GMRES iterations does not increase, just the cost of PCApply (and PCSetup). Is this scaling behavior expected? Any ideas of how to optimize the preconditioner?

The cost of PCApply for ASM is dominated by the cost of process-local block solves. You are using LU for the block solve. (Sparse) LU has cost roughly O(N^2) for the apply (depending on the structure of the matrix). So, if you double the size of a local block, your runtime should increase by about 4x. Thus LU is not a scalable method.

  Thanks,

     Matt

Thank you.

-Justin

From: Junchao Zhang <junchao.zhang at gmail.com<mailto:junchao.zhang at gmail.com>>
Date: Monday, April 14, 2025 at 7:35 PM
To: Angus, Justin Ray <angus1 at llnl.gov<mailto:angus1 at llnl.gov>>
Cc: petsc-dev at mcs.anl.gov<mailto:petsc-dev at mcs.anl.gov> <petsc-dev at mcs.anl.gov<mailto:petsc-dev at mcs.anl.gov>>, Ghosh, Debojyoti <ghosh5 at llnl.gov<mailto:ghosh5 at llnl.gov>>
Subject: Re: [petsc-dev] Additive Schwarz Method + ILU on GPU platforms

Petsc supports ILU0/ICC0 numeric factorization (without reordering) and then triangular solve on GPUs. It is done by calling vendor libraries (ex. cusparse).
We have options -pc_factor_mat_factor_on_host <bool>  -pc_factor_mat_solve_on_host <bool> to force doing the factorization and MatSolve on the host for device matrix types.

You can try to see if it works for your case.

--Junchao Zhang


On Mon, Apr 14, 2025 at 4:39 PM Angus, Justin Ray via petsc-dev <petsc-dev at mcs.anl.gov<mailto:petsc-dev at mcs.anl.gov>> wrote:
Hello,

A project I work on uses GMRES via PETSc. In particular, we have had good successes using the Additive Schwarz Method + ILU preconditioner setup using a CPU-based code. I found online where it is stated that “Parts of most preconditioners run directly on the GPU” (https://urldefense.us/v3/__https://petsc.org/release/faq/__;!!G_uCfscf7eWS!eY5NwHL1F-2SQmDwOKuiNCUIHimFnDzVPm2I6ohCj3Pmro8KSfumU2BjOySFOx5vRZOU_pKzzShuN4a_VKnooQ$ <https://urldefense.us/v3/__https://petsc.org/release/faq/__;!!G_uCfscf7eWS!bw6qeKcY7MKSvlEgcogdKR7fpjZSOFvka6zfDprUZ_sJHdE-YZmRD6UTqWQW3_uGVBII4P-AG0zaGTLbI67_fQ$>). Is ASM + ILU also available for GPU platforms?

-Justin


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