On Tue, Nov 4, 2025 at 1:25 PM Angus, Justin Ray via petsc-dev < [email protected]> 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 <[email protected]> *Date: *Monday, April 14, 2025 at 7:35 PM *To: *Angus, Justin Ray <[email protected]> *Cc: *[email protected] <[email protected]>, Ghosh, Debojyoti < [email protected]> *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 < [email protected]> 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!d... <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

-- 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 https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCf... <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfs... >