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<p class="MsoNormal"><span style="font-size:11.0pt">Hong, thanks! That makes perfect sense.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">A follow up question about ILU.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">The following is the performance of ILU(5). Note that each KPS solving reports converged but as the output shows, the preconditioned residual does while true residual does not. Is there any way this performance
could be improved?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Background: the preconditioning matrix is finite difference generated, and should be exact.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">-Ling<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="p1"><span class="s1">Time Step 21, time = -491.75, dt = 1</span><o:p></o:p></p>
<p class="p1"><span class="apple-converted-space"> </span><span class="s1">NL Step =</span><span class="apple-converted-space">
</span><span class="s1">0, fnorm =</span><span class="apple-converted-space"> </span>
<span class="s1">6.98749E+01</span><o:p></o:p></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </span><span class="s1">Linear solve converged due to CONVERGED_RTOL iterations 4</span><o:p></o:p></p>
<p class="p1"><span class="apple-converted-space"> </span><span class="s1">NL Step =</span><span class="apple-converted-space">
</span><span class="s1">1, fnorm =</span><span class="apple-converted-space"> </span>
<span class="s1">4.08788E+01</span><o:p></o:p></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </span><span class="s1">Linear solve converged due to CONVERGED_RTOL iterations 3</span><o:p></o:p></p>
<p class="p1"><span class="apple-converted-space"> </span><span class="s1">NL Step =</span><span class="apple-converted-space">
</span><span class="s1">2, fnorm =</span><span class="apple-converted-space"> </span>
<span class="s1">8.67124E+00</span><o:p></o:p></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </span><span class="s1">Linear solve converged due to CONVERGED_RTOL iterations 13</span><o:p></o:p></p>
<p class="p1"><span class="apple-converted-space"> </span><span class="s1">NL Step =</span><span class="apple-converted-space">
</span><span class="s1">3, fnorm =</span><span class="apple-converted-space"> </span>
<span class="s1">1.59729E-01</span><o:p></o:p></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </span><span class="s1">Linear solve converged due to CONVERGED_RTOL iterations 3</span><o:p></o:p></p>
<p class="p1"><span class="apple-converted-space"> </span><span class="s1">NL Step =</span><span class="apple-converted-space">
</span><span class="s1">4, fnorm =</span><span class="apple-converted-space"> </span>
<span class="s1">1.59564E-01</span><o:p></o:p></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </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></p>
<p class="p1"><span class="apple-converted-space"> </span><span class="s1">Linear solve converged due to CONVERGED_RTOL iterations 3</span><o:p></o:p></p>
<p class="p1"><span class="s1">Nonlinear solve did not converge due to DIVERGED_LINE_SEARCH iterations 4</span><o:p></o:p></p>
<p class="p2"><span class="apple-converted-space"> </span><span class="s1">Solve Did NOT Converge!</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">Zhang, Hong <hzhang@mcs.anl.gov><br>
<b>Date: </b>Wednesday, March 27, 2024 at 4:59 PM<br>
<b>To: </b>petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov>, Zou, Ling <lzou@anl.gov><br>
<b>Subject: </b>Re: Does ILU(15) still make sense or should just use LU?<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black">Ling,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black">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></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black">Hong<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black">From:</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black"> petsc-users <petsc-users-bounces@mcs.anl.gov> on behalf of Zou,
Ling via petsc-users <petsc-users@mcs.anl.gov><br>
<b>Sent:</b> Wednesday, March 27, 2024 4:24 PM<br>
<b>To:</b> petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject:</b> [petsc-users] Does ILU(15) still make sense or should just use LU?</span><span style="font-size:12.0pt">
<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"> <o:p></o:p></span></p>
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<p><span style="font-size:11.0pt">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:12.0pt"><o:p></o:p></span></p>
<p><span style="font-size:11.0pt"> </span><span style="font-size:12.0pt"><o:p></o:p></span></p>
<p><span style="font-size:11.0pt">For this particular case, ~2k DoF, and both ILU(15) and LU perform similarly in terms of wall time.</span><span style="font-size:12.0pt"><o:p></o:p></span></p>
<p><span style="font-size:11.0pt"> </span><span style="font-size:12.0pt"><o:p></o:p></span></p>
<p><span style="font-size:11.0pt">-Ling</span><span style="font-size:12.0pt"><o:p></o:p></span></p>
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