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Generically you see the ~[DOF]^3 for dense matrix factorizations. For sparse, depending on the problem and space dimension 1, 2, or 3 you do much better than ~[DOF]^3 dof. Iterative solvers when working well offer the possibility of ~[DOF]
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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> Generically you see the <span style="font-size: 11pt; font-family: Aptos, sans-serif;">~[DOF]^3 for dense matrix factorizations. For sparse, depending on the problem and space dimension 1, 2, or 3 you do much better than </span><span style="font-family: Aptos, sans-serif; font-size: 14.666667px;">~[DOF]^3 dof. Iterative solvers when working well offer the possibility of </span><span style="font-family: Aptos, sans-serif; font-size: 14.666667px;">~[DOF] which is why they are needed for very large problems.</span><div><br><blockquote type="cite"><div>On Mar 29, 2024, at 3:29 PM, 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;">Note that [Wall Time] ~ [DOF]^1.333, instead of being ~[DOF]^3.<o:p></o:p></span></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">The [DOF]^3 rule was the scary part that I wanted to avoid LU.<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 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;">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>Date:<span class="Apple-converted-space"> </span></b>Friday, March 29, 2024 at 2:06 PM<br><b>To:<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>>, Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov" style="color: blue; text-decoration: underline;">hzhang@mcs.anl.gov</a>><br><b>Cc:<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>><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: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Hong, are these results somewhat expected? I don’t see any speed up for using 2 processors (maybe I don’t have 2 processors?).</span><o:p></o:p></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div><table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" style="border-collapse: collapse;"><tbody><tr><td width="312" valign="top" style="width: 233.75pt; border: 1pt solid windowtext; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Option</span><o:p></o:p></div></td><td width="312" valign="top" style="width: 233.75pt; border-width: 1pt 1pt 1pt medium; border-style: solid solid solid none; border-color: windowtext windowtext windowtext currentcolor; border-image: none; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Wall Time (sec)</span><o:p></o:p></div></td></tr><tr><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt; border-style: none solid solid; border-color: currentcolor windowtext windowtext; border-image: none; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-pc_type lu</span><o:p></o:p></div></td><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt medium; border-style: none solid solid none; border-color: currentcolor windowtext windowtext currentcolor; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">7.442</span><o:p></o:p></div></td></tr><tr><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt; border-style: none solid solid; border-color: currentcolor windowtext windowtext; border-image: none; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">mpiexec -n 2 -pc_type lu</span><o:p></o:p></div></td><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt medium; border-style: none solid solid none; border-color: currentcolor windowtext windowtext currentcolor; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">9.112</span><o:p></o:p></div></td></tr><tr><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt; border-style: none solid solid; border-color: currentcolor windowtext windowtext; border-image: none; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-pc_type lu -pc_factor_mat_solver_type mumps</span><o:p></o:p></div></td><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt medium; border-style: none solid solid none; border-color: currentcolor windowtext windowtext currentcolor; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">8.748</span><o:p></o:p></div></td></tr><tr><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt; border-style: none solid solid; border-color: currentcolor windowtext windowtext; border-image: none; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">mpiexec -n 2 -pc_type lu -pc_factor_mat_solver_type mumps</span><o:p></o:p></div></td><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt medium; border-style: none solid solid none; border-color: currentcolor windowtext windowtext currentcolor; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">9.013</span><o:p></o:p></div></td></tr></tbody></table><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">For different size problems</span><o:p></o:p></div><table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" style="border-collapse: collapse;"><tbody><tr><td width="312" valign="top" style="width: 233.75pt; border: 1pt solid windowtext; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-pc_type lu -m 1000 -n 1000</span><o:p></o:p></div></td><td width="312" valign="top" style="width: 233.75pt; border-width: 1pt 1pt 1pt medium; border-style: solid solid solid none; border-color: windowtext windowtext windowtext currentcolor; border-image: none; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">7.442</span><o:p></o:p></div></td></tr><tr><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt; border-style: none solid solid; border-color: currentcolor windowtext windowtext; border-image: none; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-pc_type lu -m 750 -n 750</span><o:p></o:p></div></td><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt medium; border-style: none solid solid none; border-color: currentcolor windowtext windowtext currentcolor; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">3.142</span><o:p></o:p></div></td></tr><tr><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt; border-style: none solid solid; border-color: currentcolor windowtext windowtext; border-image: none; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-pc_type lu -m 500 -n 500</span><o:p></o:p></div></td><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt medium; border-style: none solid solid none; border-color: currentcolor windowtext windowtext currentcolor; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">1.007</span><o:p></o:p></div></td></tr><tr><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt; border-style: none solid solid; border-color: currentcolor windowtext windowtext; border-image: none; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-pc_type lu -m 250 -n 250</span><o:p></o:p></div></td><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt medium; border-style: none solid solid none; border-color: currentcolor windowtext windowtext currentcolor; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">0.150</span><o:p></o:p></div></td></tr><tr><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt; border-style: none solid solid; border-color: currentcolor windowtext windowtext; border-image: none; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-pc_type lu -m 100 -n 100</span><o:p></o:p></div></td><td width="312" valign="top" style="width: 233.75pt; border-width: medium 1pt 1pt medium; border-style: none solid solid none; border-color: currentcolor windowtext windowtext currentcolor; padding: 0in 5.4pt;"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">0.016</span><o:p></o:p></div></td></tr></tbody></table><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><span id="cid:image001.png@01DA81E2.16A009F0"><image001.png></span></span><o:p></o:p></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></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;">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>Date:<span class="Apple-converted-space"> </span></b>Friday, March 29, 2024 at 12:50 PM<br><b>To:<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>Cc:<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>><br><b>Subject:<span class="Apple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?</span><o:p></o:p></p></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">I cannot believe that I typed: make ex<span style="background: yellow;">0</span>2</span><o:p></o:p></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Thanks, it works.</span><o:p></o:p></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-Ling</span><o:p></o:p></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></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;">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>Friday, March 29, 2024 at 12:43 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?</span><o:p></o:p></p></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">cd src/ksp/ksp/tutorials make ex2 On Mar 29, 2024, at 1:</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><span style="font-size: 1pt; color: white;">10 PM, Zou, Ling <lzou@</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><span style="font-size: 1pt; color: white;">anl.</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><span style="font-size: 1pt; color: white;">gov> wrote: Hong, thanks! That’s great to know. I’d like to try the ex2 tutorial case locally to see how it performs. I have already installed PETSc 3.</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><span style="font-size: 1pt; color: white;">20.</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><span style="font-size: 1pt; color: white;">5</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerStart</span><o:p></o:p></div></div><div id="pfptBannerpktqbaj" 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="pfptBannerpktqbaj"><div id="pfptBannerpktqbaj"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><b><span style="font-size: 12pt; font-family: Arial, sans-serif;">This Message Is From an External Sender</span></b><o:p></o:p></div></div><div id="pfptBannerpktqbaj"><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><span style="font-size: 12pt; font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: rgb(208, 216, 220);"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerEnd</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> cd </span><span style="font-size: 11pt;">src/ksp/ksp/tutorials</span><o:p></o:p></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> make ex2 </span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div><div><p class="MsoNormal" style="margin: 0in 0in 12pt; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></p><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">On Mar 29, 2024, at 1:10</span><span style="font-size: 12pt; font-family: Arial, sans-serif;"> </span><span style="font-size: 12pt;">PM, Zou, Ling <<a href="mailto:lzou@anl.gov" style="color: blue; text-decoration: underline;">lzou@anl.gov</a>> wrote:</span><o:p></o:p></div></div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Hong, thanks! That’s great to know.</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">I’d like to try the ex2 tutorial case locally to see how it performs. I have already installed PETSc 3.20.5 on my Mac.</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Here shows the very last step of installation.</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">make PETSC_DIR=/Users/lingzou/Downloads/petsc-3.20.5 PETSC_ARCH=arch-opt check</span></span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">Running PETSc check examples to verify correct installation</span></span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">Using PETSC_DIR=/Users/lingzou/Downloads/petsc-3.20.5 and PETSC_ARCH=arch-opt</span></span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">C/C++ example src/snes/tutorials/ex19 run successfully with 1 MPI process</span></span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">C/C++ example src/snes/tutorials/ex19 run successfully with 2 MPI processes</span></span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="s1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">Completed PETSc check examples</span></span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">I found myself not knowing how to compile petsc/src/ksp/ksp/tutorials/ex2.c</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Do we have a page for how to do that?</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Best,</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; 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: 10pt; 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: 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" style="color: blue; text-decoration: underline;">hzhang@mcs.anl.gov</a>><br><b>Date:<span class="apple-converted-space"> </span></b>Thursday, March 28, 2024 at 4:59 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>>, Barry Smith <<a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;">bsmith@petsc.dev</a>><br><b>Cc:<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>><br><b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?</span><o:p></o:p></p></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">Ling,</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">MUMPS<span class="apple-converted-space"> </span></span><a href="https://urldefense.us/v3/__https:/mumps-solver.org/index.php__;!!G_uCfscf7eWS!b4SLVXTUaKyR1_NPGNEtGinrk2pTkW9odwoiYKcTjslyDUQxuhihIs1ZLqrh2z33R3C5VLIwl86Bvw$" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">https://mumps-solver.org/index.php</span></a><span style="font-size: 12pt;"> , superlu and superlu_dist<span class="apple-converted-space"> </span></span><a href="https://urldefense.us/v3/__https:/portal.nersc.gov/project/sparse/superlu/__;!!G_uCfscf7eWS!b4SLVXTUaKyR1_NPGNEtGinrk2pTkW9odwoiYKcTjslyDUQxuhihIs1ZLqrh2z33R3C5VLIHcCP4HQ$" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">https://portal.nersc.gov/project/sparse/superlu/</span></a><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">are sparse LU solvers, i.e., they produce SPARSE LU matrix factors. For many applications, they can solve<span class="apple-converted-space"> </span></span><span style="font-size: 11pt; color: rgb(36, 36, 36); background: white;">1 million DOF</span><span style="font-size: 12pt;"> easily even in sequential mode. For example </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">petsc/src/ksp/ksp/tutorials </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">./ex2 -pc_type lu -pc_factor_mat_solver_type mumps -m 1000 -n 1000 -ksp_monitor_true_residual</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> 0 KSP preconditioned resid norm 1.000000000000e+03 true resid norm 6.330876716538e+01 ||r(i)||/||b|| 1.000000000000e+00</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> 1 KSP preconditioned resid norm 9.976801056860e-09 true resid norm 3.908107755078e-10 ||r(i)||/||b|| 6.173090916254e-12</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">Norm of error 9.98582e-09 iterations 1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">MUMPS LU solves this matrix of size 1.e6 in one iteration (takes few sec on my laptop).</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">As Barry suggests, try mumps first. If it fails or it is too slow, then explore other solvers available in PETSc<span class="apple-converted-space"> </span></span><a href="https://urldefense.us/v3/__https:/petsc.org/release/overview/linear_solve_table/__;!!G_uCfscf7eWS!b4SLVXTUaKyR1_NPGNEtGinrk2pTkW9odwoiYKcTjslyDUQxuhihIs1ZLqrh2z33R3C5VLKPDawFmw$" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">https://petsc.org/release/overview/linear_solve_table/</span></a><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">From my experiments, MUMPS is faster and more robust than superlu/superlu_dist, yet it consumes slightly more memory.</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">See<span class="apple-converted-space"> </span></span><a href="https://urldefense.us/v3/__https:/petsc.org/release/manual/ksp/*using-external-linear-solvers__;Iw!!G_uCfscf7eWS!b4SLVXTUaKyR1_NPGNEtGinrk2pTkW9odwoiYKcTjslyDUQxuhihIs1ZLqrh2z33R3C5VLJJEKMXKA$" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">https://petsc.org/release/manual/ksp/#using-external-linear-solvers</span></a><span style="font-size: 12pt;"> on how to install mumps with petsc.</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">Hong</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></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><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 class="apple-converted-space"><span style="font-size: 11pt; font-family: Calibri, sans-serif;"> </span></span><span style="font-size: 11pt; font-family: Calibri, sans-serif;">Zou, Ling <<a href="mailto:lzou@anl.gov" style="color: blue; text-decoration: underline;">lzou@anl.gov</a>><br><b>Sent:</b><span class="apple-converted-space"> </span>Thursday, March 28, 2024 2:34 PM<br><b>To:</b><span class="apple-converted-space"> </span>Barry Smith <<a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;">bsmith@petsc.dev</a>><br><b>Cc:</b><span class="apple-converted-space"> </span>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:</b><span class="apple-converted-space"> </span>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?</span><o:p></o:p></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Thank you. Those are great suggestions. Although I mentioned 1 million DOF, but we rarely go there, so maybe stick with what is working now, and meanwhile seeking helps from literatures.</span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0in; font-size: 10pt; 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: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div id="x_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="xmsonormal" style="margin-right: 0in; margin-left: 0in; font-size: 10pt; font-family: Aptos, sans-serif; margin-bottom: 12pt;"><b><span style="font-size: 12pt;">From:<span class="apple-converted-space"> </span></span></b><span style="font-size: 12pt;">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 2:26 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?</span><o:p></o:p></p></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">You may benefit from a literature search on your model AND preconditioners to see what others have used. But I would try PETSc/MUMPS on the biggest size you want and see how it goes (better it runs for a little longer and you don't waste months<span class="apple-converted-space"> </span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerStart</span><o:p></o:p></div></div></div><div id="x_pfptBannerq8v2m71"><div id="x_pfptBannerq8v2m71"><div id="x_pfptBannerq8v2m71"><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><b><span style="font-size: 12pt; font-family: Arial, sans-serif;">This Message Is From an External Sender</span></b><o:p></o:p></div></div></div><div id="x_pfptBannerq8v2m71"><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><span style="font-size: 12pt; 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: 10pt; font-family: Aptos, sans-serif; background: rgb(208, 216, 220);"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; 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: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> 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).</span><o:p></o:p></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div><div><p class="xmsonormal" style="margin-right: 0in; margin-left: 0in; font-size: 10pt; font-family: Aptos, sans-serif; margin-bottom: 12pt;"><span style="font-size: 12pt;"> </span><o:p></o:p></p><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">On Mar 28, 2024, at 2:20</span><span style="font-size: 12pt; font-family: Arial, sans-serif;"> </span><span style="font-size: 12pt;">PM, Zou, Ling <<a href="mailto:lzou@anl.gov" style="color: blue; text-decoration: underline;">lzou@anl.gov</a>> wrote:</span><o:p></o:p></div></div></div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Thank you, Barry.</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; 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.</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; 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).</span><o:p></o:p></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; 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: 10pt; 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: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div id="x_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="xmsonormal" style="margin-right: 0in; margin-left: 0in; font-size: 10pt; font-family: Aptos, sans-serif; margin-bottom: 12pt;"><b><span style="font-size: 12pt;">From:<span class="xapple-converted-space"> </span></span></b><span style="font-size: 12pt;">Barry Smith <</span><a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">bsmith@petsc.dev</span></a><span style="font-size: 12pt;">><br><b>Date:<span class="xapple-converted-space"> </span></b>Thursday, March 28, 2024 at 1:09 PM<br><b>To:<span class="xapple-converted-space"> </span></b>Zou, Ling <</span><a href="mailto:lzou@anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">lzou@anl.gov</span></a><span style="font-size: 12pt;">><br><b>Cc:<span class="xapple-converted-space"> </span></b>Zhang, Hong <</span><a href="mailto:hzhang@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">hzhang@mcs.anl.gov</span></a><span style="font-size: 12pt;">>,<span class="xapple-converted-space"> </span></span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">petsc-users@mcs.anl.gov</span></a><span class="xapple-converted-space"><span style="font-size: 12pt;"> </span></span><span style="font-size: 12pt;"><</span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 12pt;">><br><b>Subject:<span class="xapple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?</span><o:p></o:p></p></div><div><div><div><div style="margin: 0in; font-size: 10pt; 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="xapple-converted-space"> </span></span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerStart</span><o:p></o:p></div></div></div></div><div id="x_pfptBannerc5qmvvr"><div id="x_pfptBannerc5qmvvr"><div id="x_pfptBannerc5qmvvr"><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><b><span style="font-size: 12pt; font-family: Arial, sans-serif;">This Message Is From an External Sender</span></b><o:p></o:p></div></div></div></div><div id="x_pfptBannerc5qmvvr"><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><span style="font-size: 12pt; font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: rgb(208, 216, 220);"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerEnd</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> 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.</span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> 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.</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div><p class="xmsonormal" style="margin-right: 0in; margin-left: 0in; font-size: 10pt; font-family: Aptos, sans-serif; margin-bottom: 12pt;"><span style="font-size: 12pt;"> </span><o:p></o:p></p></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">On Mar 28, 2024, at 1:14</span><span style="font-size: 12pt; font-family: Arial, sans-serif;"> </span><span style="font-size: 12pt;">PM, Zou, Ling <</span><a href="mailto:lzou@anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">lzou@anl.gov</span></a><span style="font-size: 12pt;">> wrote:</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div><div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Thank you, Barry.</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; 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><div><div><div><div style="margin: 0in; font-size: 10pt; 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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">PS1:<span class="xapple-converted-space"> </span></span><span style="font-size: 12pt;">-ksp_norm_type unpreconditioned did not work as the true residual did not go down, even with 300 linear iterations.</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; 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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-Ling</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div></div><div id="x_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="xmsonormal" style="margin-right: 0in; margin-left: 0in; font-size: 10pt; font-family: Aptos, sans-serif; margin-bottom: 12pt;"><b><span style="font-size: 12pt;">From:<span class="xapple-converted-space"> </span></span></b><span style="font-size: 12pt;">Barry Smith <</span><a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">bsmith@petsc.dev</span></a><span style="font-size: 12pt;">><br><b>Date:<span class="xapple-converted-space"> </span></b>Thursday, March 28, 2024 at 11:14 AM<br><b>To:<span class="xapple-converted-space"> </span></b>Zou, Ling <</span><a href="mailto:lzou@anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">lzou@anl.gov</span></a><span style="font-size: 12pt;">><br><b>Cc:<span class="xapple-converted-space"> </span></b>Zhang, Hong <</span><a href="mailto:hzhang@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">hzhang@mcs.anl.gov</span></a><span style="font-size: 12pt;">>,<span class="xapple-converted-space"> </span></span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">petsc-users@mcs.anl.gov</span></a><span class="xapple-converted-space"><span style="font-size: 12pt;"> </span></span><span style="font-size: 12pt;"><</span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 12pt;">><br><b>Subject:<span class="xapple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?</span><o:p></o:p></p></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; 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="xapple-converted-space"> </span></span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerStart</span><o:p></o:p></div></div></div></div></div><div id="x_pfptBannerwwham91"><div id="x_pfptBannerwwham91"><div id="x_pfptBannerwwham91"><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><b><span style="font-size: 12pt; font-family: Arial, sans-serif;">This Message Is From an External Sender</span></b><o:p></o:p></div></div></div></div></div><div id="x_pfptBannerwwham91"><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><span style="font-size: 12pt; font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: rgb(208, 216, 220);"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerEnd</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> 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.</span><o:p></o:p></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> 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.</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> Barry</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div><div><div><p class="xmsonormal" style="margin-right: 0in; margin-left: 0in; font-size: 10pt; font-family: Aptos, sans-serif; margin-bottom: 12pt;"><span style="font-size: 12pt;"> </span><o:p></o:p></p></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">On Mar 28, 2024, at 11:43</span><span style="font-size: 12pt; font-family: Arial, sans-serif;"> </span><span style="font-size: 12pt;">AM, Zou, Ling via petsc-users <</span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 12pt;">> wrote:</span><o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div><div><div><div><div><div><div><div style="margin: 0in; font-size: 10pt; 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><div><div><div><div style="margin: 0in; font-size: 10pt; 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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div></div></div><div><div><div><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?</span><o:p></o:p></div></div></div></div></div><div><div><div><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.</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">-Ling</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">NL Step =</span></span><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">0, fnorm =</span></span><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">NL Step =</span></span><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">1, fnorm =</span></span><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">NL Step =</span></span><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">2, fnorm =</span></span><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">NL Step =</span></span><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">3, fnorm =</span></span><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">NL Step =</span></span><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;">4, fnorm =</span></span><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: white;"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif; background: black;"><span class="xapple-converted-space"><span style="font-size: 9pt; font-family: "Andale Mono"; color: rgb(180, 36, 25);"> </span></span><span class="xs1"><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div></div></div><div id="x_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="xmsonormal" style="margin-right: 0in; margin-left: 0in; font-size: 10pt; font-family: Aptos, sans-serif; margin-bottom: 12pt;"><b><span style="font-size: 12pt;">From:<span class="xapple-converted-space"> </span></span></b><span style="font-size: 12pt;">Zhang, Hong <</span><a href="mailto:hzhang@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">hzhang@mcs.anl.gov</span></a><span style="font-size: 12pt;">><br><b>Date:<span class="xapple-converted-space"> </span></b>Wednesday, March 27, 2024 at 4:59 PM<br><b>To:<span class="xapple-converted-space"> </span></b></span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">petsc-users@mcs.anl.gov</span></a><span class="xapple-converted-space"><span style="font-size: 12pt;"> </span></span><span style="font-size: 12pt;"><</span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 12pt;">>, Zou, Ling <</span><a href="mailto:lzou@anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">lzou@anl.gov</span></a><span style="font-size: 12pt;">><br><b>Subject:<span class="xapple-converted-space"> </span></b>Re: Does ILU(15) still make sense or should just use LU?</span><o:p></o:p></p></div><div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">Ling,</span><o:p></o:p></div></div></div></div></div></div><div><div><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.</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">Hong</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></div></div></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="84%" align="center"></span></div><div id="x_divRplyFwdMsg"><div><div><div><div><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 <</span><a href="mailto:petsc-users-bounces@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 11pt; font-family: Calibri, sans-serif;">petsc-users-bounces@mcs.anl.gov</span></a><span style="font-size: 11pt; font-family: Calibri, sans-serif;">> on behalf of Zou, Ling via petsc-users <</span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 11pt; font-family: Calibri, sans-serif;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 11pt; font-family: Calibri, sans-serif;">><br><b>Sent:</b> Wednesday, March 27, 2024 4:24 PM<br><b>To:</b> </span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 11pt; font-family: Calibri, sans-serif;">petsc-users@mcs.anl.gov</span></a><span class="xapple-converted-space"><span style="font-size: 11pt; font-family: Calibri, sans-serif;"> </span></span><span style="font-size: 11pt; font-family: Calibri, sans-serif;"><</span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 11pt; font-family: Calibri, sans-serif;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 11pt; font-family: Calibri, sans-serif;">><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><div><div><div><div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;"> </span><o:p></o:p></div></div></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><o:p></o:p></p><p><span style="font-size: 11pt; font-family: Helvetica;"> </span><o:p></o:p></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><o:p></o:p></p><p><span style="font-size: 11pt; font-family: Helvetica;"> </span><o:p></o:p></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></div></div></div></div></div></div></div></div></div></div></blockquote></div></div></div></div></div></div></div></div></div></div></div></div></blockquote></div><br></body></html>