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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
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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> 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.<div><br></div><div> 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.</div><div><br></div><div> Barry</div><div><br id="lineBreakAtBeginningOfMessage"><div><br><blockquote type="cite"><div>On Mar 28, 2024, at 11:43 AM, Zou, Ling via petsc-users <petsc-users@mcs.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: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Hong, thanks! That makes perfect sense.<o:p></o:p></span></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">A follow up question about ILU.<o:p></o:p></span></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0in; font-size: 10pt; 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?<o:p></o:p></span></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Background: the preconditioning matrix is finite difference generated, and should be exact.<o:p></o:p></span></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-Ling<o:p></o:p></span></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="s1">Time Step 21, time = -491.75, dt = 1</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">NL Step =</span><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">0, fnorm =</span><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">6.98749E+01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">0 KSP preconditioned resid norm 1.684131526824e+04 true resid norm 6.987489798042e+01 ||r(i)||/||b|| 1.000000000000e+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">1 KSP preconditioned resid norm 5.970568556551e+02 true resid norm 6.459553545222e+01 ||r(i)||/||b|| 9.244455064582e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">2 KSP preconditioned resid norm 3.349113985192e+02 true resid norm 7.250836872274e+01 ||r(i)||/||b|| 1.037688366186e+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">3 KSP preconditioned resid norm 3.290585904777e+01 true resid norm 1.186282435163e+02 ||r(i)||/||b|| 1.697723316169e+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">4 KSP preconditioned resid norm 8.530606201233e+00 true resid norm 4.088729421459e+01 ||r(i)||/||b|| 5.851499665310e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">Linear solve converged due to CONVERGED_RTOL iterations 4</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">NL Step =</span><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">1, fnorm =</span><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">4.08788E+01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">0 KSP preconditioned resid norm 1.851047973094e+03 true resid norm 4.087882723223e+01 ||r(i)||/||b|| 1.000000000000e+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">1 KSP preconditioned resid norm 3.696809614513e+01 true resid norm 2.720016413105e+01 ||r(i)||/||b|| 6.653851387793e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">2 KSP preconditioned resid norm 5.751891392534e+00 true resid norm 3.326338240872e+01 ||r(i)||/||b|| 8.137068663873e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">3 KSP preconditioned resid norm 8.540729397958e-01 true resid norm 8.672410748720e+00 ||r(i)||/||b|| 2.121492062249e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">Linear solve converged due to CONVERGED_RTOL iterations 3</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">NL Step =</span><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">2, fnorm =</span><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">8.67124E+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">0 KSP preconditioned resid norm 5.511333966852e+00 true resid norm 8.671237519593e+00 ||r(i)||/||b|| 1.000000000000e+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">1 KSP preconditioned resid norm 1.174962622023e+00 true resid norm 8.731034658309e+00 ||r(i)||/||b|| 1.006896032842e+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">2 KSP preconditioned resid norm 1.104604471016e+00 true resid norm 1.018397505468e+01 ||r(i)||/||b|| 1.174454630227e+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">3 KSP preconditioned resid norm 4.257063674222e-01 true resid norm 4.023093124996e+00 ||r(i)||/||b|| 4.639583584126e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">4 KSP preconditioned resid norm 1.023038868263e-01 true resid norm 2.365298462869e+00 ||r(i)||/||b|| 2.727751901068e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">5 KSP preconditioned resid norm 4.073772638935e-02 true resid norm 2.302623112025e+00 ||r(i)||/||b|| 2.655472309255e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">6 KSP preconditioned resid norm 1.510323179379e-02 true resid norm 2.300216593521e+00 ||r(i)||/||b|| 2.652697020839e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">7 KSP preconditioned resid norm 1.337324816903e-02 true resid norm 2.300057733345e+00 ||r(i)||/||b|| 2.652513817259e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">8 KSP preconditioned resid norm 1.247384902656e-02 true resid norm 2.300456226062e+00 ||r(i)||/||b|| 2.652973374174e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">9 KSP preconditioned resid norm 1.247038855375e-02 true resid norm 2.300532560993e+00 ||r(i)||/||b|| 2.653061406512e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">10 KSP preconditioned resid norm 1.244611343317e-02 true resid norm 2.299441241514e+00 ||r(i)||/||b|| 2.651802855496e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">11 KSP preconditioned resid norm 1.227243209527e-02 true resid norm 2.273668115236e+00 ||r(i)||/||b|| 2.622080308720e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">12 KSP preconditioned resid norm 1.172621459354e-02 true resid norm 2.113927895437e+00 ||r(i)||/||b|| 2.437861828442e-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">13 KSP preconditioned resid norm 2.880752338189e-03 true resid norm 1.076190247720e-01 ||r(i)||/||b|| 1.241103412620e-02</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">Linear solve converged due to CONVERGED_RTOL iterations 13</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">NL Step =</span><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">3, fnorm =</span><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">1.59729E-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">0 KSP preconditioned resid norm 1.676948440854e+03 true resid norm 1.597288981238e-01 ||r(i)||/||b|| 1.000000000000e+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">1 KSP preconditioned resid norm 2.266131510513e+00 true resid norm 1.819663943811e+00 ||r(i)||/||b|| 1.139220244542e+01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">2 KSP preconditioned resid norm 2.239911493901e+00 true resid norm 1.923976907755e+00 ||r(i)||/||b|| 1.204526501062e+01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">3 KSP preconditioned resid norm 1.446859034276e-01 true resid norm 8.692945031946e-01 ||r(i)||/||b|| 5.442312026225e+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">Linear solve converged due to CONVERGED_RTOL iterations 3</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">NL Step =</span><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">4, fnorm =</span><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">1.59564E-01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">0 KSP preconditioned resid norm 1.509663716414e+03 true resid norm 1.595641817504e-01 ||r(i)||/||b|| 1.000000000000e+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">1 KSP preconditioned resid norm 1.995956587709e+00 true resid norm 1.712323298361e+00 ||r(i)||/||b|| 1.073125108390e+01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">2 KSP preconditioned resid norm 1.994336275847e+00 true resid norm 1.741263472491e+00 ||r(i)||/||b|| 1.091262119975e+01</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">3 KSP preconditioned resid norm 1.268035008497e-01 true resid norm 8.197057317360e-01 ||r(i)||/||b|| 5.137153731769e+00</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="apple-converted-space"> <span class="Apple-converted-space"> </span></span><span class="s1">Linear solve converged due to CONVERGED_RTOL iterations 3</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: white;"><span class="s1">Nonlinear solve did not converge due to DIVERGED_LINE_SEARCH iterations 4</span><o:p></o:p></div><div style="margin: 0in; background: black; font-size: 9pt; font-family: "Andale Mono"; color: rgb(180, 36, 25);"><span class="apple-converted-space"> </span><span class="s1">Solve Did NOT Converge!</span><o:p></o:p></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0in; font-size: 10pt; 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: 10pt; font-family: Aptos, sans-serif;"><b><span style="font-size: 12pt;">From:<span class="Apple-converted-space"> </span></span></b><span style="font-size: 12pt;">Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov">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">petsc-users@mcs.anl.gov</a><span class="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="Apple-converted-space"> </span></b>Re: 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: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">Ling,<o:p></o:p></span></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">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></span></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">Hong<o:p></o:p></span></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"><o:p> </o:p></span></div></div><div class="MsoNormal" align="center" style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; text-align: center;"><span style="font-size: 12pt;"><hr size="0" width="100%" align="center"></span></div><div id="divRplyFwdMsg"><div style="margin: 0in; font-size: 10pt; 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">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="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><span style="font-size: 12pt;"><o:p></o:p></span></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> <o:p></o:p></span></div></div></div><p><span style="font-size: 11pt;">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: 12pt;"><o:p></o:p></span></p><p><span style="font-size: 11pt;"> </span><span style="font-size: 12pt;"><o:p></o:p></span></p><p><span style="font-size: 11pt;">For this particular case, ~2k DoF, and both ILU(15) and LU perform similarly in terms of wall time.</span><span style="font-size: 12pt;"><o:p></o:p></span></p><p><span style="font-size: 11pt;"> </span><span style="font-size: 12pt;"><o:p></o:p></span></p><p><span style="font-size: 11pt;">-Ling</span></p></div></div></div></div></blockquote></div><br></div></body></html>