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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
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<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> 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).<div><br></div><div><br><div><br id="lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Mar 28, 2024, at 2:20 PM, Zou, Ling <lzou@anl.gov> wrote:</div><br class="Apple-interchange-newline"><div><meta charset="UTF-8"><div class="WordSection1" style="page: WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Thank you, Barry.<o:p></o:p></span></div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Yes, I have tried different preconditioners, but in a naïve way, i.e., looping through possible options using `-pc_type <option>` command line.<o:p></o:p></span></div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">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).<o:p></o:p></span></div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-Ling<o:p></o:p></span></div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div id="mail-editor-reference-message-container"><div><div style="border-width: 1pt medium medium; border-style: solid none none; border-color: rgb(181, 196, 223) currentcolor currentcolor; border-image: none; padding: 3pt 0in 0in;"><p class="MsoNormal" style="margin: 0in 0in 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b><span style="">From:<span class="Apple-converted-space"> </span></span></b><span style="">Barry Smith <<a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;">bsmith@petsc.dev</a>><br><b>Date:<span class="Apple-converted-space"> </span></b>Thursday, March 28, 2024 at 1:09 PM<br><b>To:<span class="Apple-converted-space"> </span></b>Zou, Ling <<a href="mailto:lzou@anl.gov" style="color: blue; text-decoration: underline;">lzou@anl.gov</a>><br><b>Cc:<span class="Apple-converted-space"> </span></b>Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov" style="color: blue; text-decoration: underline;">hzhang@mcs.anl.gov</a>>,<span class="Apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a><span class="Apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject:<span class="Apple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?<o:p></o:p></span></p></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; 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="Apple-converted-space"> </span><o:p></o:p></span></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerStart<o:p></o:p></span></div></div><div id="pfptBannerc5qmvvr" style="border-right-width: medium; border-bottom-width: medium; border-left-width: medium; border-right-style: none; border-bottom-style: none; border-left-style: none; border-right-color: currentcolor; border-bottom-color: currentcolor; border-left-color: currentcolor; border-image: none; display: block !important; text-align: left !important; margin: 0px !important; padding: 16px !important; border-radius: 4px !important; min-width: 200px !important; background-color: rgb(208, 216, 220) !important; border-top-width: medium !important; border-top-style: none !important; border-top-color: rgb(144, 164, 174) !important;"><div id="pfptBannerc5qmvvr"><div id="pfptBannerc5qmvvr"><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><b><span style="font-family: Arial, sans-serif;">This Message Is From an External Sender<o:p></o:p></span></b></div></div><div id="pfptBannerc5qmvvr"><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><span style="font-family: Arial, sans-serif;">This message came from outside your organization.<o:p></o:p></span></div></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: rgb(208, 216, 220);"><span style=""> </span><o:p></o:p></div></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerEnd<o:p></o:p></span></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><o:p> </o:p></div></div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> 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.<o:p></o:p></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><o:p> </o:p></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> 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.<o:p></o:p></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><o:p> </o:p></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><br><br><o:p></o:p></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;">On Mar 28, 2024, at 1:14<span style="font-family: Arial, sans-serif;"> </span>PM, Zou, Ling <<a href="mailto:lzou@anl.gov" style="color: blue; text-decoration: underline;">lzou@anl.gov</a>> wrote:<o:p></o:p></div></div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><o:p> </o:p></div><div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Thank you, Barry.</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Yeah, this is unfortunate given that the problem we are handling is quite heterogeneous (in both mesh and physics).</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">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><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">PS1:<span class="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.<o:p></o:p></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">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><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-Ling</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div id="mail-editor-reference-message-container"><div><div style="border-width: 1pt medium medium; border-style: solid none none; border-image: none; padding: 3pt 0in 0in; border-color: currentcolor;"><p class="MsoNormal" style="margin: 0in 0in 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b>From:<span class="apple-converted-space"> </span></b>Barry Smith <<a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;">bsmith@petsc.dev</a>><br><b>Date:<span class="apple-converted-space"> </span></b>Thursday, March 28, 2024 at 11:14 AM<br><b>To:<span class="apple-converted-space"> </span></b>Zou, Ling <<a href="mailto:lzou@anl.gov" style="color: blue; text-decoration: underline;">lzou@anl.gov</a>><br><b>Cc:<span class="apple-converted-space"> </span></b>Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov" style="color: blue; text-decoration: underline;">hzhang@mcs.anl.gov</a>>,<span class="apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a><span class="apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?<o:p></o:p></p></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; 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="apple-converted-space"> </span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerStart</span><o:p></o:p></div></div></div><div id="pfptBannerwwham91" style="border-right-width: medium; border-bottom-width: medium; border-left-width: medium; border-right-style: none; border-bottom-style: none; border-left-style: none; border-image: none; border-color: rgb(144, 164, 174) currentcolor currentcolor; display: block !important; text-align: left !important; margin: 0px !important; padding: 16px !important; border-radius: 4px !important; min-width: 200px !important; border-top-width: medium !important; border-top-style: none !important;"><div id="pfptBannerwwham91"><div id="pfptBannerwwham91"><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><b><span style="font-family: Arial, sans-serif;">This Message Is From an External Sender</span></b><o:p></o:p></div></div></div><div id="pfptBannerwwham91"><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><span style="font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: rgb(208, 216, 220);"><span style=""> </span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerEnd</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> 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.<o:p></o:p></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> 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.<o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> Barry<o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div><div><div><p class="MsoNormal" style="margin: 0in 0in 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><o:p> </o:p></p></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;">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" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a>> wrote:<o:p></o:p></div></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div><div><div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Hong, thanks! That makes perfect sense.</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">A follow up question about ILU.</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Background: the preconditioning matrix is finite difference generated, and should be exact.</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-Ling</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">Time Step 21, time = -491.75, dt = 1</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">NL Step =</span></span><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">0, fnorm =</span></span><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">6.98749E+01</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">Linear solve converged due to CONVERGED_RTOL iterations 4</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">NL Step =</span></span><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">1, fnorm =</span></span><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">4.08788E+01</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">Linear solve converged due to CONVERGED_RTOL iterations 3</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">NL Step =</span></span><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">2, fnorm =</span></span><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">8.67124E+00</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">Linear solve converged due to CONVERGED_RTOL iterations 13</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">NL Step =</span></span><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">3, fnorm =</span></span><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">1.59729E-01</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; 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><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">Linear solve converged due to CONVERGED_RTOL iterations 3</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">NL Step =</span></span><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">4, fnorm =</span></span><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">1.59564E-01</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">0 KSP preconditioned resid norm 1.509663716414e+03 true resid norm 1.595641817504e-01 ||r(i)||/||b|| 1.000000000000e+00</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">1 KSP preconditioned resid norm 1.995956587709e+00 true resid norm 1.712323298361e+00 ||r(i)||/||b|| 1.073125108390e+01</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">2 KSP preconditioned resid norm 1.994336275847e+00 true resid norm 1.741263472491e+00 ||r(i)||/||b|| 1.091262119975e+01</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">3 KSP preconditioned resid norm 1.268035008497e-01 true resid norm 8.197057317360e-01 ||r(i)||/||b|| 5.137153731769e+00</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">Linear solve converged due to CONVERGED_RTOL iterations 3</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">Nonlinear solve did not converge due to DIVERGED_LINE_SEARCH iterations 4</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; background: black;"><span class="apple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: rgb(180, 36, 25);"> </span></span><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: rgb(180, 36, 25);">Solve Did NOT Converge!</span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div id="mail-editor-reference-message-container"><div><div style="border-width: 1pt medium medium; border-style: solid none none; border-image: none; padding: 3pt 0in 0in; border-color: currentcolor;"><p class="MsoNormal" style="margin: 0in 0in 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b>From:<span class="apple-converted-space"> </span></b>Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov" style="color: blue; text-decoration: underline;">hzhang@mcs.anl.gov</a>><br><b>Date:<span class="apple-converted-space"> </span></b>Wednesday, March 27, 2024 at 4:59 PM<br><b>To:<span class="apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a><span class="apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a>>, Zou, Ling <<a href="mailto:lzou@anl.gov" style="color: blue; text-decoration: underline;">lzou@anl.gov</a>><br><b>Subject:<span class="apple-converted-space"> </span></b>Re: Does ILU(15) still make sense or should just use LU?<o:p></o:p></p></div><div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;">Ling,<o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;">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.<o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;">Hong<o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div></div><div class="MsoNormal" align="center" style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif; text-align: center;"><hr size="0" width="100%" align="center"></div><div id="divRplyFwdMsg"><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><b><span style="font-size: 11pt; font-family: Calibri, sans-serif;">From:</span></b><span style="font-size: 11pt; font-family: Calibri, sans-serif;"> petsc-users <<a href="mailto:petsc-users-bounces@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users-bounces@mcs.anl.gov</a>> on behalf of Zou, Ling via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">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" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a><span class="apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject:</b> [petsc-users] Does ILU(15) still make sense or should just use LU?</span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div></div></div><p><span style="font-size: 11pt; 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;"><o:p></o:p></span></p><p><span style="font-size: 11pt; font-family: Helvetica;"> </span><span style="font-size: 13.5pt; font-family: Helvetica;"><o:p></o:p></span></p><p><span style="font-size: 11pt; 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;"><o:p></o:p></span></p><p><span style="font-size: 11pt; font-family: Helvetica;"> </span><span style="font-size: 13.5pt; font-family: Helvetica;"><o:p></o:p></span></p><p><span style="font-size: 11pt; font-family: Helvetica;">-Ling</span></p></div></div></div></div></blockquote></div></div></div></div></div></div></blockquote></div></div></div></div></div></div></blockquote></div><br></div></div></body></html>