I think the issue is my overlap is too large. Perhaps I don’t fully understand how the overlap parameter is used. Let me explain my setup below. My vector of unknowns is the electric field on a Yee grid in a 2D geometry. I’m using 4x4 grid cells per rank. This gives 4*5 = 20 degrees of freedom for each of the two in-plane components of E, and 5*5 = 25 for the out-of-plane component. The total is 65 degrees of freedom per rank. My global problem size is 224x16 on 224 ranks for one case, and 224x32 on 448 ranks for another. Using ASM overlap 4, I get the following for PC sub blocks on a rank: PC Object: (sub_) 1 MPI process type: lu out-of-place factorization Reusing fill from past factorization Reusing reordering from past factorization tolerance for zero pivot 2.22045e-14 matrix ordering: nd factor fill ratio given 5., needed 4.02544 Factored matrix follows: Mat Object: (sub_) 1 MPI process type: seqaij rows=402, cols=402 package used to perform factorization: petsc total: nonzeros=16295, allocated nonzeros=16295 not using I-node routines The above is for a 224x16 size domain in 224 total ranks, but I get the same thing for a 224x32 size domain on 448 ranks, which is what I am expected to get. However, if I set the overlap to 16 (which is larger than by box size on a given rank), I get the following 224x16 gid on 112 ranks: PC Object: (sub_) 1 MPI process type: lu out-of-place factorization Reusing fill from past factorization Reusing reordering from past factorization tolerance for zero pivot 2.22045e-14 matrix ordering: nd factor fill ratio given 5., needed 6.52557 Factored matrix follows: Mat Object: (sub_) 1 MPI process type: seqaij rows=1316, cols=1316 package used to perform factorization: petsc total: nonzeros=95195, allocated nonzeros=95195 not using I-node routines 224x16 gid on 112 ranks: PC Object: (sub_) 1 MPI process type: lu out-of-place factorization Reusing fill from past factorization Reusing reordering from past factorization tolerance for zero pivot 2.22045e-14 matrix ordering: nd factor fill ratio given 5., needed 8.59182 Factored matrix follows: Mat Object: (sub_) 1 MPI process type: seqaij rows=2632, cols=2632 package used to perform factorization: petsc total: nonzeros=250675, allocated nonzeros=250675 not using I-node routines In this case, with an overlap much larger than the box size, the rows/cols per rank go up by a factor of 2 when doubling the problem size at fixed work per rank. Why is this? How exactly is the overlap parameter used? Thank you. -Justin From: Angus, Justin Ray <[email protected]> Date: Wednesday, November 5, 2025 at 8:17 AM To: [email protected] <[email protected]>, Matthew Knepley <[email protected]> Cc: [email protected] <[email protected]> Subject: Re: [petsc-dev] Additive Schwarz Method + ILU on GPU platforms 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 <[email protected]> Date: Wednesday, November 5, 2025 at 6:14 AM To: Matthew Knepley <[email protected]> Cc: Angus, Justin Ray <[email protected]>, [email protected] <[email protected]> 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 <[email protected]<mailto:[email protected]>> wrote: On Tue, Nov 4, 2025 at 1:25 PM Angus, Justin Ray via petsc-dev <[email protected]<mailto:[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]<mailto:[email protected]>> Date: Monday, April 14, 2025 at 7:35 PM To: Angus, Justin Ray <[email protected]<mailto:[email protected]>> Cc: [email protected]<mailto:[email protected]> <[email protected]<mailto:[email protected]>>, Ghosh, Debojyoti <[email protected]<mailto:[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]<mailto:[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!c... <https://urldefense.us/v3/__https://petsc.org/release/faq/__;!!G_uCfscf7eWS!bw6qeKcY7MKSvlEgcogdKR7fpjZSOFvka6zfDprUZ_sJHdE-YZmRD6UTqWQW3_uGVBII4P-AG0zaGTLbI67_fQ$>). Is ASM + ILU also available for GPU platforms? -Justin -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCf... <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!dXQeQOf4ckc4MRP64tltlc6e1FJgPXuEuzX8tHsTreO_vIP2Lbge1es994i-WdQTd1zpmNP2R9dbEHfLa0v_$>