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<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt;mso-fareast-language:EN-US">Dear Pierre, Dear PETSc team,<o:p></o:p></span></p>
<p class="p1"><span lang="EN-US">Thank you for your response. <br>
<br>
</span>In terms of geometry, we are moving toward more complex domains with <span lang="EN-US">
more </span>refined meshes that include multiple thin channels. <span lang="EN-US">
We hav</span>e been <span lang="EN-US">experimenting</span> with the Stokes problem as a simplified case, but our main goal is to solve the high-Reynolds-number Navier–Stokes equations in these settings.<span lang="EN-US" style="mso-fareast-language:EN-US"><br>
<br>
We are currently planning to utilize a multi-node CPU architecture.<br>
<br>
</span>For the Navier–Stokes system, we have experimented with both <span lang="EN-US">
pressure-convection diffusion (</span>PCD<span lang="EN-US">)</span> and LSC preconditioners<span lang="EN-US" style="mso-fareast-language:EN-US">. In the thin channels, the PDC struggles to converge, and the LSC preconditioner is computationally slow, but
it does converge eventually. Also, for both of these preconditioners for the thin channels, the norm of the preconditioned residual is much higher than the true residual norm,
</span>which likely indicates that neither preconditioner provides a sufficiently accurate approximation of the Schur complement.<span lang="DE-CH"><o:p></o:p></span></p>
<p class="p1"><span lang="EN-US">I would appreciate any insights you may have for better preconditioning strategies.<o:p></o:p></span></p>
<p class="p1"><span lang="EN-US">Best regards,<br>
Hardik<o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">Pierre Jolivet <pierre@joliv.et><br>
<b>Date: </b>Sunday, 11 May 2025 at 20:45<br>
<b>To: </b>Hardik Kothari <hardik.kothari@corintis.com><br>
<b>Cc: </b>petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-users] Solving Stokes problem in high aspect ratio domains<o:p></o:p></span></p>
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<span style="font-size:12.0pt;font-family:"Segoe UI",sans-serif;color:black">You don't often get email from pierre@joliv.et.
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<p class="MsoNormal"><span style="font-size:12.0pt">Do you want to refine the geometry or are you fine with the current one?
<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">What kind of hardware are you planning on using (GPU, single-node…)?<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Do you have a configuration for which LSC fails or does not give you good-enough performance?<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Thanks,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Pierre<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><br>
<br>
<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">On 9 May 2025, at 9:08</span><span style="font-size:12.0pt;font-family:"Arial",sans-serif"> </span><span style="font-size:12.0pt">PM, Mark Adams <mfadams@lbl.gov> wrote:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Hi Hardik, <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">The domain shape is not critical but the element shapes are. Your 100:1 domain aspect ratio is bad if you have N^3 mesh and thus element aspect ratios of 100:1. <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">If that is the case then you probably want to look at semi-coarsening multigrid.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Mark<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">On Fri, May 9, 2025 at 9:55</span><span style="font-size:12.0pt;font-family:"Arial",sans-serif"> </span><span style="font-size:12.0pt">AM Hardik Kothari <<a href="mailto:hardik.kothari@corintis.com">hardik.kothari@corintis.com</a>>
wrote:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Dear PETSc team, <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">We are solving the Stokes equations using PETSc (via Firedrake) on a highly anisotropic 3D domain (L_x=1, L_y=0.01, L_z=0.1).<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">In this setup, standard Schur complement preconditioners using a mass inverse for pressure struggle to converge. We could solve the problem with the LSC preconditioner (solver parameters are shown in the script).
<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">We have the following questions:<o:p></o:p></span></p>
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<ul type="disc">
<li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1">
<span style="font-size:12.0pt">Why standard preconditioners struggle in such domains? <o:p></o:p></span></li><li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1">
<span style="font-size:12.0pt">Why is the preconditioned residual norm for the Schur complement system much higher than the true residual norm?<o:p></o:p></span></li><li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1">
<span style="font-size:12.0pt">Would you recommend alternative or more robust preconditioners for such geometries? <o:p></o:p></span></li></ul>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Thank you for your help. <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Best regards, <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Hardik<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="line-height:14.0pt"><b><span style="font-size:8.0pt;font-family:"Arial",sans-serif;color:#1B1464">HARDIK KOTHARI<br>
</span></b><span style="font-size:8.0pt;font-family:"Arial",sans-serif;color:#8A8A8C"><br>
<a href="mailto:hardik.kothari@corintis.com" target="_blank"><em><span style="font-family:"Arial",sans-serif;color:#8A8A8C">hardik.kothari@corintis.com</span></em></a><br>
<br>
Corintis SA<br>
EPFL Innovation Park Building C<br>
1015 Lausanne<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:7.0pt;font-family:"Arial",sans-serif;color:white">Here at Corintis we care for your privacy. That is why we have taken appropriate measures to ensure that the data you have provided to us is always secure<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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