<html aria-label="message body"><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div><br></div> An overlap of 16 is huge and would rarely if ever, be done in practice. It is not surprising that the subproblems become as large as they do with such a large overlap. <div><br></div><div> How the overlap is used. </div><div><br></div><div> while (overlap--) {</div><div> add to the subproblem all degrees of freedom that are coupled by nonzeros in the matrix to all the current degrees of freedom in the subproblem.</div><div> }</div><div><br></div><div> So it is grabbing all the neighbors for 16 rounds of grabbing.</div><div><br></div><div><br id="lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Nov 5, 2025, at 3:05 PM, Angus, Justin Ray via petsc-dev <petsc-dev@mcs.anl.gov> wrote:</div><br class="Apple-interchange-newline"><div>
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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.</div>
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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:</div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;">PC Object: (sub_) 1 MPI process</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> type: lu</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> out-of-place factorization</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> Reusing fill from past factorization</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> Reusing reordering from past factorization</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> tolerance for zero pivot 2.22045e-14</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> matrix ordering: nd</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> factor fill ratio given 5., needed 4.02544</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> Factored matrix follows:</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> Mat Object: (sub_) 1 MPI process</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> type: seqaij</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;">
</span><span style="font-family: Menlo; font-size: 18px; background-color: rgb(255, 255, 0);">rows=402, cols=402</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> package used to perform factorization: petsc</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> total: nonzeros=16295, allocated nonzeros=16295</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> not using I-node routines</span></div>
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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.</div>
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However, if I set the overlap to 16 (which is larger than by box size on a given rank), I get the following</div>
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<b>224x16 gid on 112 ranks: </b></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;">PC Object: (sub_) 1 MPI process</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> type: lu</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> out-of-place factorization</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> Reusing fill from past factorization</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> Reusing reordering from past factorization</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> tolerance for zero pivot 2.22045e-14</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> matrix ordering: nd</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> factor fill ratio given 5., needed 6.52557</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> Factored matrix follows:</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> Mat Object: (sub_) 1 MPI process</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> type: seqaij</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;">
</span><span style="font-family: Menlo; font-size: 18px; background-color: rgb(255, 255, 0);">rows=1316, cols=1316</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> package used to perform factorization: petsc</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> total: nonzeros=95195, allocated nonzeros=95195</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Menlo; font-size: 18px;"> not using I-node routines</span></div>
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<b>224x16 gid on 112 ranks: </b></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;">PC Object: (sub_) 1 MPI process</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> type: lu</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> out-of-place factorization</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> Reusing fill from past factorization</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> Reusing reordering from past factorization</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> tolerance for zero pivot 2.22045e-14</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> matrix ordering: nd</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> factor fill ratio given 5., needed 8.59182</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> Factored matrix follows:</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> Mat Object: (sub_) 1 MPI process</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> type: seqaij</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;">
</span><span style="font-family: Monaco; font-size: 18px; background-color: rgb(255, 255, 0);">rows=2632, cols=2632</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> package used to perform factorization: petsc</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> total: nonzeros=250675, allocated nonzeros=250675</span></div><div style="line-height: normal; margin: 0px;"><span style="font-family: Monaco; font-size: 18px;"> not using I-node routines</span></div>
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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. </div>
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Why is this?</div>
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How exactly is the overlap parameter used?</div>
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Thank you.</div>
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-Justin</div>
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<b>From: </b>Angus, Justin Ray <angus1@llnl.gov><br>
<b>Date: </b>Wednesday, November 5, 2025 at 8:17 AM<br>
<b>To: </b>MFAdams@LBL.GOV <MFAdams@LBL.GOV>, Matthew Knepley <knepley@gmail.com><br>
<b>Cc: </b>petsc-dev@mcs.anl.gov <petsc-dev@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-dev] Additive Schwarz Method + ILU on GPU platforms<br>
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Thanks for the reply.</div>
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The work per block should be the same for the weak scaling. I know LU is not scalable with respect to the block size.</div>
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Perhaps our setup is not doing what we think it is doing. I’ll look into it further.</div>
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-Justin</div>
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<b>From: </b>Mark Adams <mfadams@lbl.gov><br>
<b>Date: </b>Wednesday, November 5, 2025 at 6:14 AM<br>
<b>To: </b>Matthew Knepley <knepley@gmail.com><br>
<b>Cc: </b>Angus, Justin Ray <angus1@llnl.gov>, petsc-dev@mcs.anl.gov <petsc-dev@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-dev] Additive Schwarz Method + ILU on GPU platforms<br>
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<div dir="ltr" class="ms-outlook-mobile-reference-message skipProofing">And we do not have sparse LU on GPUs so that is done on the CPU.</div>
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<div dir="ltr" class="ms-outlook-mobile-reference-message skipProofing">And I don't know why it would not weak scale well. </div>
<div dir="ltr" class="ms-outlook-mobile-reference-message skipProofing">Your results are consistent with just using one process with one domain, (re Matt) while you double the problem size.</div>
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<div dir="ltr" class="gmail_attr">On Tue, Nov 4, 2025 at 2:27 PM Matthew Knepley <<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>> wrote:</div>
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<div dir="ltr" class="gmail_quote">On Tue, Nov 4, 2025 at 1:25 PM Angus, Justin Ray via petsc-dev <<a href="mailto:petsc-dev@mcs.anl.gov" target="_blank">petsc-dev@mcs.anl.gov</a>> wrote:</div>
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Hi Junchao,</div>
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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?</div>
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<div dir="ltr" class="gmail_quote">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.</div>
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<div dir="ltr" class="gmail_quote"> Thanks,</div>
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<div dir="ltr" class="gmail_quote"> Matt</div>
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Thank you.</div>
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-Justin</div>
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<b>From: </b>Junchao Zhang <<a href="mailto:junchao.zhang@gmail.com" target="_blank">junchao.zhang@gmail.com</a>><br>
<b>Date: </b>Monday, April 14, 2025 at 7:35 PM<br>
<b>To: </b>Angus, Justin Ray <<a href="mailto:angus1@llnl.gov" target="_blank">angus1@llnl.gov</a>><br>
<b>Cc: </b><a href="mailto:petsc-dev@mcs.anl.gov" target="_blank">petsc-dev@mcs.anl.gov</a> <<a href="mailto:petsc-dev@mcs.anl.gov" target="_blank">petsc-dev@mcs.anl.gov</a>>, Ghosh, Debojyoti <<a href="mailto:ghosh5@llnl.gov" target="_blank">ghosh5@llnl.gov</a>><br>
<b>Subject: </b>Re: [petsc-dev] Additive Schwarz Method + ILU on GPU platforms<br>
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<div dir="ltr">Petsc supports ILU0/ICC0 numeric factorization (without reordering) and then triangular solve on GPUs. It is done by calling vendor libraries (ex. cusparse).</div>
<div dir="ltr">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.</div>
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<div dir="ltr">You can try to see if it works for your case.</div>
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<div dir="ltr" class="gmail_signature">--Junchao Zhang</div>
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<div dir="ltr" class="gmail_attr">On Mon, Apr 14, 2025 at 4:39 PM Angus, Justin Ray via petsc-dev <<a href="mailto:petsc-dev@mcs.anl.gov" target="_blank">petsc-dev@mcs.anl.gov</a>> wrote:</div>
<blockquote style="margin: 0px 0px 0px 0.8ex; padding-left: 1ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204);"><p class="MsoNormal"><span style="font-size: 11pt;">Hello,</span></p><div><span style="font-size: 11pt;"> </span><br class="webkit-block-placeholder"></div><p class="MsoNormal"><span style="font-size: 11pt;">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” (<a href="https://urldefense.us/v3/__https://petsc.org/release/faq/__;!!G_uCfscf7eWS!bw6qeKcY7MKSvlEgcogdKR7fpjZSOFvka6zfDprUZ_sJHdE-YZmRD6UTqWQW3_uGVBII4P-AG0zaGTLbI67_fQ$" target="_blank" style="margin-top: 0px; margin-bottom: 0px;">https://petsc.org/release/faq/</a>).
Is ASM + ILU also available for GPU platforms?</span></p><div><span style="font-size: 11pt;"> </span><br class="webkit-block-placeholder"></div><p class="MsoNormal"><span style="font-size: 11pt;">-Justin</span></p>
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<div dir="ltr" class="gmail_quote">--</div>
<div dir="ltr" class="gmail_signature">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener</div>
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<div dir="ltr" class="gmail_signature"><a href="https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!dXQeQOf4ckc4MRP64tltlc6e1FJgPXuEuzX8tHsTreO_vIP2Lbge1es994i-WdQTd1zpmNP2R9dbEHfLa0v_$" target="_blank">https://www.cse.buffalo.edu/~knepley/</a></div>
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