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<p class="MsoNormal"><span style="font-size:11.0pt">Barry, thanks very much for the insight, and you are right!<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">For the purpose of sharing information, in case anyone is interested, here are some details.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">The problem at hand is a *<b>nearly</b>* incompressible flow problem, such that part of the diagonal Jacobian term (d(rho)_dp) is very close to but not truly zero.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">I have noticed that Option-2 complained about zero pivot, and I can see that the diagonal Jacobian term is zero by outputting the Jacobian.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Option-1 was Ok, and I can see that the diagonal Jacobian term is very small but non-zero.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">So you are right, they behave very similarly but produces a tiny bit of difference.<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">Best,<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="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="color:black">From:
</span></b><span style="color:black">Barry Smith <bsmith@petsc.dev><br>
<b>Date: </b>Sunday, August 24, 2025 at 3:30</span><span style="font-family:"Arial",sans-serif;color:black"> </span><span style="color:black">PM<br>
<b>To: </b>Zou, Ling <lzou@anl.gov><br>
<b>Cc: </b>Stefano Zampini <stefano.zampini@gmail.com>, PETSc <petsc-users@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-users] Understanding 'snes' object<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-line-height-alt:.75pt"><span style="font-size:1.0pt;color:white">You should have very similar behavior, but not identical behavior. The Jacobian-vector product will produce slightly different values with the two approaches, which
means that the computed residual norms displayed with -ksp_monitor -snes_monitor<o:p></o:p></span></p>
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<p class="MsoNormal"> You should have very similar behavior, but not identical behavior. The Jacobian-vector product will produce slightly different values with the two approaches, which means that the computed residual norms displayed with -ksp_monitor -snes_monitor
etc will be somewhat different. With long runs that involve many nonlinear solves the differences in the norms computed will become nontrivial and you will start getting different iteration counts, but the solutions computed should remain very similar.<o:p></o:p></p>
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<p class="MsoNormal"> Barry<o:p></o:p></p>
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<p class="MsoNormal">On Aug 23, 2025, at 10:03<span style="font-family:"Arial",sans-serif"> </span>AM, Zou, Ling via petsc-users <petsc-users@mcs.anl.gov> wrote:<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Thank you both Jed and Stefano.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Then, somehow, I may have introduced inconsistence in my code, because I expected they have exactly the same behavior.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Best,</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-Ling</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b>From:<span class="apple-converted-space"> </span></b>Stefano Zampini <<a href="mailto:stefano.zampini@gmail.com">stefano.zampini@gmail.com</a>><br>
<b>Date:<span class="apple-converted-space"> </span></b>Friday, August 22, 2025 at 4:42<span style="font-family:"Arial",sans-serif"> </span>PM<br>
<b>To:<span class="apple-converted-space"> </span></b>Zou, Ling <<a href="mailto:lzou@anl.gov">lzou@anl.gov</a>><br>
<b>Cc:<span class="apple-converted-space"> </span></b>PETSc <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] Understanding 'snes' object<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:1.0pt;color:white">Il giorno sab 23 ago 2025 alle ore 00:</span><span style="font-size:1.0pt;font-family:"Arial",sans-serif;color:white"> </span><span style="font-size:1.0pt;color:white">25 Zou, Ling via petsc-users
<petsc-users@</span><span style="font-size:1.0pt;font-family:"Arial",sans-serif;color:white"> </span><span style="font-size:1.0pt;color:white">mcs.</span><span style="font-size:1.0pt;font-family:"Arial",sans-serif;color:white"> </span><span style="font-size:1.0pt;color:white">anl.</span><span style="font-size:1.0pt;font-family:"Arial",sans-serif;color:white"> </span><span style="font-size:1.0pt;color:white">gov>
ha scritto: Hi all, Can someone please help me understand the output of the following two outputs using ‘-snes_view’? Option 1: SNES Object: 1</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">Il giorno sab 23 ago 2025 alle ore 00:25 Zou, Ling via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>> ha scritto:<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Hi all,</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Can someone please help me understand the output of the following two outputs using ‘-snes_view’?</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Option 1:</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="m-7958132393732476812p1"><span class="m-7958132393732476812s1">SNES Object: 1 MPI process</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">type: newtonls</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">maximum iterations=15, maximum function evaluations=10000</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">tolerances: relative=1e-08, absolute=1e-50, solution=1e-08</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">total number of linear solver iterations=5</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">total number of function evaluations=14</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">norm schedule ALWAYS</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"><span style="color:#00B050"> </span></span><span class="apple-converted-space"><span style="color:#00B050"> </span></span><span class="m-7958132393732476812s1"><span style="color:#00B050">Jacobian
is built using finite differences with coloring</span></span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Option 2:</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812s1">SNES Object: 1 MPI process</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">type: newtonls</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">maximum iterations=50, maximum function evaluations=10000</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">tolerances: relative=1e-08, absolute=1e-50, solution=1e-08</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">total number of linear solver iterations=8</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">total number of function evaluations=17</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"> </span><span class="apple-converted-space"> </span><span class="m-7958132393732476812s1">norm schedule ALWAYS</span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"><span style="color:#00B050"> </span></span><span class="apple-converted-space"><span style="color:#00B050"> </span></span><span class="m-7958132393732476812s1"><span style="color:#00B050">Jacobian
is applied matrix-free with differencing</span></span><o:p></o:p></p>
<p class="m-7958132393732476812p1"><span class="m-7958132393732476812apple-converted-space"><span style="color:#00B050"> </span></span><span class="apple-converted-space"><span style="color:#00B050"> </span></span><span class="m-7958132393732476812s1"><span style="color:#00B050">Preconditioning
Jacobian is built using finite differences with coloring</span></span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Does it mean that</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<ul type="disc">
<li class="m-7958132393732476812msolistparagraph" style="mso-list:l0 level1 lfo1">
<span style="font-size:11.0pt">Option 1 uses Newton’s method, such that J du = b is solved with J being explicitly constructed?</span><o:p></o:p></li></ul>
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<p class="MsoNormal">yes<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> <span style="font-size:10.0pt"><o:p></o:p></span></p>
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<ul type="disc">
<li class="m-7958132393732476812msolistparagraph" style="mso-list:l2 level1 lfo2">
<o:p></o:p></li><li class="m-7958132393732476812msolistparagraph" style="mso-list:l2 level1 lfo2">
<span style="font-size:11.0pt">Option 2 uses matrix free method, such that J du = b is solved with J v ~ (F(u + dv) – F(u)) / h when needed, e.g., in a Krylov method.</span><o:p></o:p></li></ul>
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<p class="MsoNormal"> <span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">yes, and the preconditioner is constructed using an explicitly constructed Jacobian matrix<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> <span style="font-size:10.0pt"><o:p></o:p></span></p>
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<ul type="disc">
<li class="m-7958132393732476812msolistparagraph" style="mso-list:l1 level1 lfo3">
<o:p></o:p></li></ul>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Thanks,</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-Ling</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><br clear="all">
<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> <span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span class="gmailsignatureprefix">--</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">Stefano<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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