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Ling,</div>
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MUMPS <a href="https://urldefense.us/v3/__https://mumps-solver.org/index.php__;!!G_uCfscf7eWS!ZsKnKahMkux3fTqW0NYBAAuRPfa8VNlYxJ2Hgzncb5usvfOcxUprP3hpnguiSsgrGL0pTveINquoqSfUnAu_MXFg$" id="LPlnk">https://mumps-solver.org/index.php</a> , superlu and superlu_dist
<a href="https://urldefense.us/v3/__https://portal.nersc.gov/project/sparse/superlu/__;!!G_uCfscf7eWS!ZsKnKahMkux3fTqW0NYBAAuRPfa8VNlYxJ2Hgzncb5usvfOcxUprP3hpnguiSsgrGL0pTveINquoqSfUnLQvhQfR$" id="LPlnk611032">https://portal.nersc.gov/project/sparse/superlu/</a></div>
<div class="elementToProof"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">are sparse LU solvers, i.e., they produce SPARSE LU matrix factors. For many applications,
they can solve </span><span style="font-family: Aptos, sans-serif; font-size: 14.6667px; color: rgb(36, 36, 36); background-color: rgb(255, 255, 255);">1 million DOF</span><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> easily
even in sequential mode. For example </span></div>
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petsc/src/ksp/ksp/tutorials </div>
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./ex2 -pc_type lu -pc_factor_mat_solver_type mumps -m 1000 -n 1000 -ksp_monitor_true_residual</div>
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0 KSP preconditioned resid norm 1.000000000000e+03 true resid norm 6.330876716538e+01 ||r(i)||/||b|| 1.000000000000e+00</div>
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1 KSP preconditioned resid norm 9.976801056860e-09 true resid norm 3.908107755078e-10 ||r(i)||/||b|| 6.173090916254e-12</div>
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Norm of error 9.98582e-09 iterations 1</div>
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MUMPS LU solves this matrix of size 1.e6 in one iteration (takes few sec on my laptop).</div>
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As Barry suggests, try mumps first. If it fails or it is too slow, then explore other solvers available in PETSc
<a href="https://urldefense.us/v3/__https://petsc.org/release/overview/linear_solve_table/__;!!G_uCfscf7eWS!ZsKnKahMkux3fTqW0NYBAAuRPfa8VNlYxJ2Hgzncb5usvfOcxUprP3hpnguiSsgrGL0pTveINquoqSfUnHZhPEJL$" id="LPlnk130338">
https://petsc.org/release/overview/linear_solve_table/</a></div>
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>From my experiments, MUMPS is faster and more robust than superlu/superlu_dist, yet it consumes slightly more memory.</div>
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See <a href="https://urldefense.us/v3/__https://petsc.org/release/manual/ksp/*using-external-linear-solvers__;Iw!!G_uCfscf7eWS!ZsKnKahMkux3fTqW0NYBAAuRPfa8VNlYxJ2Hgzncb5usvfOcxUprP3hpnguiSsgrGL0pTveINquoqSfUnNSk5BgM$" id="LPlnk453634">
https://petsc.org/release/manual/ksp/#using-external-linear-solvers</a> on how to install mumps with petsc.</div>
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Hong</div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Zou, Ling <lzou@anl.gov><br>
<b>Sent:</b> Thursday, March 28, 2024 2:34 PM<br>
<b>To:</b> Barry Smith <bsmith@petsc.dev><br>
<b>Cc:</b> Zhang, Hong <hzhang@mcs.anl.gov>; petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject:</b> Re: [petsc-users] Does ILU(15) still make sense or should just use LU?</font>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">Thank you. Those are great suggestions. Although I mentioned 1 million DOF, but we rarely go there, so maybe stick with what is working now, and meanwhile seeking helps from literatures.</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">-Ling</span></p>
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<p class="x_MsoNormal" style="margin-bottom:12.0pt"><b><span style="color:black">From:
</span></b><span style="color:black">Barry Smith <bsmith@petsc.dev><br>
<b>Date: </b>Thursday, March 28, 2024 at 2:26 PM<br>
<b>To: </b>Zou, Ling <lzou@anl.gov><br>
<b>Cc: </b>Zhang, Hong <hzhang@mcs.anl.gov>, petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?</span></p>
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<p class="x_MsoNormal" style=""><span style="font-size:1.0pt; color:white">You may benefit from a literature search on your model AND preconditioners to see what others have used. But I would try PETSc/MUMPS on the biggest size you want and see how it goes
(better it runs for a little longer and you don't waste months </span></p>
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<p class="x_MsoNormal"> You may benefit from a literature search on your model AND preconditioners to see what others have used. But I would try PETSc/MUMPS on the biggest size you want and see how it goes (better it runs for a little longer and you don't
waste months trying to find a good preconditioner).</p>
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<p class="x_MsoNormal">On Mar 28, 2024, at 2:20<span style="font-family:"Arial",sans-serif"> </span>PM, Zou, Ling <lzou@anl.gov> wrote:</p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">Thank you, Barry.</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">Yes, I have tried different preconditioners, but in a naïve way, i.e., looping through possible options using `-pc_type <option>` command line.</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">But no, not in a meaningful way because the lack of understanding of the connection between physics (the problem we are dealing with) to math (the correct combination of those preconditioners).</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">-Ling</span></p>
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<p class="x_MsoNormal" style="margin-bottom:12.0pt"><b>From:<span class="x_apple-converted-space"> </span></b>Barry Smith <<a href="mailto:bsmith@petsc.dev">bsmith@petsc.dev</a>><br>
<b>Date:<span class="x_apple-converted-space"> </span></b>Thursday, March 28, 2024 at 1:09 PM<br>
<b>To:<span class="x_apple-converted-space"> </span></b>Zou, Ling <<a href="mailto:lzou@anl.gov">lzou@anl.gov</a>><br>
<b>Cc:<span class="x_apple-converted-space"> </span></b>Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov">hzhang@mcs.anl.gov</a>>,<span class="x_apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><span class="x_apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:<span class="x_apple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?</p>
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<p class="x_MsoNormal"><span style="font-size:1.0pt; color:white">1 million is possible for direct solvers using PETSc with the MUMPS direct solver when you cannot get a preconditioner to work well for your problems. ILU are not very robust preconditioners
and I would not rely on them. Have you investigated<span class="x_apple-converted-space"> </span></span></p>
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<p class="x_MsoNormal"> 1 million is possible for direct solvers using PETSc with the MUMPS direct solver when you cannot get a preconditioner to work well for your problems.</p>
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<p class="x_MsoNormal"> ILU are not very robust preconditioners and I would not rely on them. Have you investigated other preconditioners in PETSc, PCGAMG, PCASM, PCFIELDSPLIT or some combination of these preconditioners work for many problems, though certainly
not all.</p>
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<p class="x_MsoNormal">On Mar 28, 2024, at 1:14<span style="font-family:"Arial",sans-serif"> </span>PM, Zou, Ling <<a href="mailto:lzou@anl.gov">lzou@anl.gov</a>> wrote:</p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">Thank you, Barry.</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">Yeah, this is unfortunate given that the problem we are handling is quite heterogeneous (in both mesh and physics).</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">I expect that our problem sizes will be mostly smaller than 1 million DOF, should LU still be a practical solution? Can it scale well if we choose to run the problem in a parallel way?</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">PS1:<span class="x_apple-converted-space"> </span></span>-ksp_norm_type unpreconditioned did not work as the true residual did not go down, even with 300 linear iterations.</p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">PS2: what do you think if it will be beneficial to have more detailed discussions (e.g., a presentation?) on the problem we are solving to seek more advice?</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">-Ling</span></p>
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<p class="x_MsoNormal" style="margin-bottom:12.0pt"><b>From:<span class="x_apple-converted-space"> </span></b>Barry Smith <<a href="mailto:bsmith@petsc.dev">bsmith@petsc.dev</a>><br>
<b>Date:<span class="x_apple-converted-space"> </span></b>Thursday, March 28, 2024 at 11:14 AM<br>
<b>To:<span class="x_apple-converted-space"> </span></b>Zou, Ling <<a href="mailto:lzou@anl.gov">lzou@anl.gov</a>><br>
<b>Cc:<span class="x_apple-converted-space"> </span></b>Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov">hzhang@mcs.anl.gov</a>>,<span class="x_apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><span class="x_apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:<span class="x_apple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?</p>
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<p class="x_MsoNormal"><span style="font-size:1.0pt; color:white">This is a bad situation, the solver is not really converging. This can happen with ILU() sometimes, it so badly scales things that the preconditioned residual decreases a lot but the true residual
is not really getting smaller. Since your matrices<span class="x_apple-converted-space"> </span></span></p>
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<p class="x_MsoNormal"> This is a bad situation, the solver is not really converging. This can happen with ILU() sometimes, it so badly scales things that the preconditioned residual decreases a lot but the true residual is not really getting smaller. Since
your matrices are small best to stick to LU.</p>
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<p class="x_MsoNormal"> </p>
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<p class="x_MsoNormal"> You can use -ksp_norm_type unpreconditioned to force the convergence test to use the true residual for a convergence test and the solver will discover that it is not converging.</p>
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<p class="x_MsoNormal"> </p>
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<p class="x_MsoNormal"> Barry</p>
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<p class="x_MsoNormal"> </p>
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<p class="x_MsoNormal" style="margin-bottom:12.0pt"> </p>
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<blockquote style="margin-top:5.0pt; margin-bottom:5.0pt">
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<p class="x_MsoNormal">On Mar 28, 2024, at 11:43<span style="font-family:"Arial",sans-serif"> </span>AM, Zou, Ling via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>> wrote:</p>
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<p class="x_MsoNormal"> </p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">Hong, thanks! That makes perfect sense.</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">A follow up question about ILU.</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">The following is the performance of ILU(5). Note that each KPS solving reports converged but as the output shows, the preconditioned residual does while true residual does not. Is there any way this performance
could be improved?</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">Background: the preconditioning matrix is finite difference generated, and should be exact.</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">-Ling</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">Time Step 21, time = -491.75, dt = 1</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">NL
Step =</span></span><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">0, fnorm =</span></span><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">6.98749E+01</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">0
KSP preconditioned resid norm 1.684131526824e+04 true resid norm 6.987489798042e+01 ||r(i)||/||b|| 1.000000000000e+00</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">1
KSP preconditioned resid norm 5.970568556551e+02 true resid norm 6.459553545222e+01 ||r(i)||/||b|| 9.244455064582e-01</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">2
KSP preconditioned resid norm 3.349113985192e+02 true resid norm 7.250836872274e+01 ||r(i)||/||b|| 1.037688366186e+00</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">3
KSP preconditioned resid norm 3.290585904777e+01 true resid norm 1.186282435163e+02 ||r(i)||/||b|| 1.697723316169e+00</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">4
KSP preconditioned resid norm 8.530606201233e+00 true resid norm 4.088729421459e+01 ||r(i)||/||b|| 5.851499665310e-01</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">Linear
solve converged due to CONVERGED_RTOL iterations 4</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">NL
Step =</span></span><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">1, fnorm =</span></span><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">4.08788E+01</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">0
KSP preconditioned resid norm 1.851047973094e+03 true resid norm 4.087882723223e+01 ||r(i)||/||b|| 1.000000000000e+00</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">1
KSP preconditioned resid norm 3.696809614513e+01 true resid norm 2.720016413105e+01 ||r(i)||/||b|| 6.653851387793e-01</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">2
KSP preconditioned resid norm 5.751891392534e+00 true resid norm 3.326338240872e+01 ||r(i)||/||b|| 8.137068663873e-01</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">3
KSP preconditioned resid norm 8.540729397958e-01 true resid norm 8.672410748720e+00 ||r(i)||/||b|| 2.121492062249e-01</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">Linear
solve converged due to CONVERGED_RTOL iterations 3</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">NL
Step =</span></span><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">2, fnorm =</span></span><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">8.67124E+00</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">0
KSP preconditioned resid norm 5.511333966852e+00 true resid norm 8.671237519593e+00 ||r(i)||/||b|| 1.000000000000e+00</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">1
KSP preconditioned resid norm 1.174962622023e+00 true resid norm 8.731034658309e+00 ||r(i)||/||b|| 1.006896032842e+00</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">2
KSP preconditioned resid norm 1.104604471016e+00 true resid norm 1.018397505468e+01 ||r(i)||/||b|| 1.174454630227e+00</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">3
KSP preconditioned resid norm 4.257063674222e-01 true resid norm 4.023093124996e+00 ||r(i)||/||b|| 4.639583584126e-01</span></span></p>
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<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">4
KSP preconditioned resid norm 1.023038868263e-01 true resid norm 2.365298462869e+00 ||r(i)||/||b|| 2.727751901068e-01</span></span></p>
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<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">5
KSP preconditioned resid norm 4.073772638935e-02 true resid norm 2.302623112025e+00 ||r(i)||/||b|| 2.655472309255e-01</span></span></p>
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<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">6
KSP preconditioned resid norm 1.510323179379e-02 true resid norm 2.300216593521e+00 ||r(i)||/||b|| 2.652697020839e-01</span></span></p>
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<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">7
KSP preconditioned resid norm 1.337324816903e-02 true resid norm 2.300057733345e+00 ||r(i)||/||b|| 2.652513817259e-01</span></span></p>
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<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">8
KSP preconditioned resid norm 1.247384902656e-02 true resid norm 2.300456226062e+00 ||r(i)||/||b|| 2.652973374174e-01</span></span></p>
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<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">9
KSP preconditioned resid norm 1.247038855375e-02 true resid norm 2.300532560993e+00 ||r(i)||/||b|| 2.653061406512e-01</span></span></p>
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<div>
<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">10
KSP preconditioned resid norm 1.244611343317e-02 true resid norm 2.299441241514e+00 ||r(i)||/||b|| 2.651802855496e-01</span></span></p>
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<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">11
KSP preconditioned resid norm 1.227243209527e-02 true resid norm 2.273668115236e+00 ||r(i)||/||b|| 2.622080308720e-01</span></span></p>
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<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">12
KSP preconditioned resid norm 1.172621459354e-02 true resid norm 2.113927895437e+00 ||r(i)||/||b|| 2.437861828442e-01</span></span></p>
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<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">13
KSP preconditioned resid norm 2.880752338189e-03 true resid norm 1.076190247720e-01 ||r(i)||/||b|| 1.241103412620e-02</span></span></p>
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<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">Linear
solve converged due to CONVERGED_RTOL iterations 13</span></span></p>
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<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">NL
Step =</span></span><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">3, fnorm =</span></span><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">1.59729E-01</span></span></p>
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<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">0
KSP preconditioned resid norm 1.676948440854e+03 true resid norm 1.597288981238e-01 ||r(i)||/||b|| 1.000000000000e+00</span></span></p>
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<div>
<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">1
KSP preconditioned resid norm 2.266131510513e+00 true resid norm 1.819663943811e+00 ||r(i)||/||b|| 1.139220244542e+01</span></span></p>
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<div>
<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">2
KSP preconditioned resid norm 2.239911493901e+00 true resid norm 1.923976907755e+00 ||r(i)||/||b|| 1.204526501062e+01</span></span></p>
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<div>
<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">3
KSP preconditioned resid norm 1.446859034276e-01 true resid norm 8.692945031946e-01 ||r(i)||/||b|| 5.442312026225e+00</span></span></p>
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<div>
<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">Linear
solve converged due to CONVERGED_RTOL iterations 3</span></span></p>
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<div>
<div>
<div>
<p class="x_MsoNormal" style="background:black"><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">NL
Step =</span></span><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">4, fnorm =</span></span><span class="x_apple-converted-space"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white"> </span></span><span class="x_s1"><span style="font-size:9.0pt; font-family:"Andale Mono"; color:white">1.59564E-01</span></span></p>
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KSP preconditioned resid norm 1.509663716414e+03 true resid norm 1.595641817504e-01 ||r(i)||/||b|| 1.000000000000e+00</span></span></p>
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KSP preconditioned resid norm 1.995956587709e+00 true resid norm 1.712323298361e+00 ||r(i)||/||b|| 1.073125108390e+01</span></span></p>
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KSP preconditioned resid norm 1.994336275847e+00 true resid norm 1.741263472491e+00 ||r(i)||/||b|| 1.091262119975e+01</span></span></p>
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KSP preconditioned resid norm 1.268035008497e-01 true resid norm 8.197057317360e-01 ||r(i)||/||b|| 5.137153731769e+00</span></span></p>
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Did NOT Converge!</span></span></p>
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<p class="x_MsoNormal" style="margin-bottom:12.0pt"><b>From:<span class="x_apple-converted-space"> </span></b>Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov">hzhang@mcs.anl.gov</a>><br>
<b>Date:<span class="x_apple-converted-space"> </span></b>Wednesday, March 27, 2024 at 4:59 PM<br>
<b>To:<span class="x_apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><span class="x_apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>>, Zou, Ling <<a href="mailto:lzou@anl.gov">lzou@anl.gov</a>><br>
<b>Subject:<span class="x_apple-converted-space"> </span></b>Re: Does ILU(15) still make sense or should just use LU?</p>
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<p class="x_MsoNormal">Ling,</p>
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<p class="x_MsoNormal">ILU(level) is used for saving storage space with more computations. Normally, we use level=1 or 2. It does not make sense to use level 15. If you have sufficient space, LU would be the best.</p>
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<p class="x_MsoNormal">Hong</p>
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<p class="x_MsoNormal"><b><span style="font-size:11.0pt; font-family:"Calibri",sans-serif">From:</span></b><span style="font-size:11.0pt; font-family:"Calibri",sans-serif"> petsc-users <<a href="mailto:petsc-users-bounces@mcs.anl.gov">petsc-users-bounces@mcs.anl.gov</a>>
on behalf of Zou, Ling via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Sent:</b> Wednesday, March 27, 2024 4:24 PM<br>
<b>To:</b> <a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><span class="x_apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:</b> [petsc-users] Does ILU(15) still make sense or should just use LU?</span></p>
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<p><span style="font-size:11.0pt; font-family:Helvetica">Hi, I’d like to avoid using LU, but in some cases to use ILU and still converge, I have to go to ILU(15), i.e., `-pc_factor_levels 15`. Does it still make sense, or should I give it up and switch to LU?</span><span style="font-size:13.5pt; font-family:Helvetica"></span></p>
<p><span style="font-size:11.0pt; font-family:Helvetica"> </span><span style="font-size:13.5pt; font-family:Helvetica"></span></p>
<p><span style="font-size:11.0pt; font-family:Helvetica">For this particular case, ~2k DoF, and both ILU(15) and LU perform similarly in terms of wall time.</span><span style="font-size:13.5pt; font-family:Helvetica"></span></p>
<p><span style="font-size:11.0pt; font-family:Helvetica"> </span><span style="font-size:13.5pt; font-family:Helvetica"></span></p>
<p><span style="font-size:11.0pt; font-family:Helvetica">-Ling</span><span style="font-size:13.5pt; font-family:Helvetica"></span></p>
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