<!-- BaNnErBlUrFlE-BoDy-start -->
<!-- Preheader Text : BEGIN -->
<div style="display:none !important;display:none;visibility:hidden;mso-hide:all;font-size:1px;color:#ffffff;line-height:1px;height:0px;max-height:0px;opacity:0;overflow:hidden;">
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
</div>
<!-- Preheader Text : END -->
<!-- Email Banner : BEGIN -->
<div style="display:none !important;display:none;visibility:hidden;mso-hide:all;font-size:1px;color:#ffffff;line-height:1px;height:0px;max-height:0px;opacity:0;overflow:hidden;">ZjQcmQRYFpfptBannerStart</div>
<!--[if ((ie)|(mso))]>
<table border="0" cellspacing="0" cellpadding="0" width="100%" style="padding: 16px 0px 16px 0px; direction: ltr" ><tr><td>
<table border="0" cellspacing="0" cellpadding="0" style="padding: 0px 10px 5px 6px; width: 100%; border-radius:4px; border-top:4px solid #90a4ae;background-color:#D0D8DC;"><tr><td valign="top">
<table align="left" border="0" cellspacing="0" cellpadding="0" style="padding: 4px 8px 4px 8px">
<tr><td style="color:#000000; font-family: 'Arial', sans-serif; font-weight:bold; font-size:14px; direction: ltr">
This Message Is From an External Sender
</td></tr>
<tr><td style="color:#000000; font-weight:normal; font-family: 'Arial', sans-serif; font-size:12px; direction: ltr">
This message came from outside your organization.
</td></tr>
</table>
</td></tr></table>
</td></tr></table>
<![endif]-->
<![if !((ie)|(mso))]>
<div dir="ltr" id="pfptBannerct63bmx" style="all: revert !important; display:block !important; text-align: left !important; margin:16px 0px 16px 0px !important; padding:8px 16px 8px 16px !important; border-radius: 4px !important; min-width: 200px !important; background-color: #D0D8DC !important; background-color: #D0D8DC; border-top: 4px solid #90a4ae !important; border-top: 4px solid #90a4ae;">
<div id="pfptBannerct63bmx" style="all: unset !important; float:left !important; display:block !important; margin: 0px 0px 1px 0px !important; max-width: 600px !important;">
<div id="pfptBannerct63bmx" style="all: unset !important; display:block !important; visibility: visible !important; background-color: #D0D8DC !important; color:#000000 !important; color:#000000; font-family: 'Arial', sans-serif !important; font-family: 'Arial', sans-serif; font-weight:bold !important; font-weight:bold; font-size:14px !important; line-height:18px !important; line-height:18px">
This Message Is From an External Sender
</div>
<div id="pfptBannerct63bmx" style="all: unset !important; display:block !important; visibility: visible !important; background-color: #D0D8DC !important; color:#000000 !important; color:#000000; font-weight:normal; font-family: 'Arial', sans-serif !important; font-family: 'Arial', sans-serif; font-size:12px !important; line-height:18px !important; line-height:18px; margin-top:2px !important;">
This message came from outside your organization.
</div>
</div>
<div style="clear: both !important; display: block !important; visibility: hidden !important; line-height: 0 !important; font-size: 0.01px !important; height: 0px"> </div>
</div>
<![endif]>
<div style="display:none !important;display:none;visibility:hidden;mso-hide:all;font-size:1px;color:#ffffff;line-height:1px;height:0px;max-height:0px;opacity:0;overflow:hidden;">ZjQcmQRYFpfptBannerEnd</div>
<!-- Email Banner : END -->
<!-- BaNnErBlUrFlE-BoDy-end -->
<html><head><!-- BaNnErBlUrFlE-HeAdEr-start -->
<style>
#pfptBannerct63bmx { all: revert !important; display: block !important;
visibility: visible !important; opacity: 1 !important;
background-color: #D0D8DC !important;
max-width: none !important; max-height: none !important }
.pfptPrimaryButtonct63bmx:hover, .pfptPrimaryButtonct63bmx:focus {
background-color: #b4c1c7 !important; }
.pfptPrimaryButtonct63bmx:active {
background-color: #90a4ae !important; }
</style>
<!-- BaNnErBlUrFlE-HeAdEr-end -->
<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> 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.<div><br></div><div> 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.</div><div><br id="lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Mar 28, 2024, at 1:14 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;">Yeah, this is unfortunate given that the problem we are handling is quite heterogeneous (in both mesh and physics).<o:p></o:p></span></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?<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;">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.<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;">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?<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 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></span></p></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><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="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-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="pfptBannerwwham91"><div id="pfptBannerwwham91"><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="pfptBannerwwham91"><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;"> 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 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;"> 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 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;"> Barry<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 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 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;">Hong, thanks! That makes perfect sense.</span><span style="font-size: 10pt;"><o:p></o:p></span></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><span style="font-size: 10pt;"><o:p></o:p></span></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><span style="font-size: 10pt;"><o:p></o:p></span></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><span style="font-size: 10pt;"><o:p></o:p></span></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><span style="font-size: 10pt;"><o:p></o:p></span></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><span style="font-size: 10pt;"><o:p></o:p></span></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-Ling</span><span style="font-size: 10pt;"><o:p></o:p></span></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><span style="font-size: 10pt;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"><o:p></o:p></span></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><span style="font-size: 9pt; font-family: "Andale Mono"; color: rgb(180, 36, 25);"><o:p></o:p></span></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><span style="font-size: 10pt;"><o:p></o:p></span></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><span style="font-size: 10pt;"><o:p></o:p></span></div></div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><span style="font-size: 10pt;"><o:p></o:p></span></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?<span style="font-size: 10pt;"><o:p></o:p></span></p></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;">Ling,<span style="font-size: 10pt;"><o:p></o:p></span></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.<span style="font-size: 10pt;"><o:p></o:p></span></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;">Hong<span style="font-size: 10pt;"><o:p></o:p></span></div></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> <span style="font-size: 10pt;"><o:p></o:p></span></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 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><span style="font-size: 10pt;"><o:p></o:p></span></div></div><div><div><div style="margin: 0in; font-size: 12pt; font-family: Aptos, sans-serif;"> <span style="font-size: 10pt;"><o:p></o:p></span></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><br></div></body></html>