<div><div><div class="gmail_quote"><div dir="ltr">On Wed, 25 Jul 2018 at 12:24, Buesing, Henrik <<a href="mailto:hbuesing@eonerc.rwth-aachen.de" target="_blank">hbuesing@eonerc.rwth-aachen.de</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">The problem is from two-phase flow in porous media. I have written down the equations and the operators from the 2x2 block Jacobian (see attachment).</span></p></div></div></blockquote><div dir="auto"><br></div></div></div></div><div><div><div class="gmail_quote"><div dir="auto">Have you just tried plain old multiplicative firldplit with LU as the preconditioned for the diagonal blocks?</div><div dir="auto"><br></div><div dir="auto">What are the iteration counts like?</div><div dir="auto"><br></div><div dir="auto">I think that choice should not be terrible for this system. I'd try this first before looking at Schur complements.</div></div></div></div><div><div><div class="gmail_quote"><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div lang="DE" link="blue" vlink="purple"><div class="m_-8805241891756980958m_-3643943920686596421WordSection1"><p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">
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<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">The J11 block of the Jacobian is made elliptic.
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<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New""><u></u> <u></u></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">Maybe someone could tell me how to go on from there to build a good preconditioner?
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Thank you!<br>
Henrik<u></u><u></u></span></p></div></div><div lang="DE" link="blue" vlink="purple"><div class="m_-8805241891756980958m_-3643943920686596421WordSection1">
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<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">-- <u></u>
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<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">Dipl.-Math. Henrik Büsing<u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">Institute for Applied Geophysics and Geothermal Energy<u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">E.ON Energy Research Center<u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">RWTH Aachen University<u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New""><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">Mathieustr. 10 | Tel +49 (0)241 80 49907<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">52074 Aachen, Germany | Fax +49 (0)241 80 49889<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""><a href="http://www.eonerc.rwth-aachen.de/GGE" target="_blank">http://www.eonerc.rwth-aachen.de/GGE</a><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""><a href="mailto:hbuesing@eonerc.rwth-aachen.de" target="_blank">hbuesing@eonerc.rwth-aachen.de</a><u></u><u></u></span></p>
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<p class="MsoNormal"><b>Von:</b> Dave May <<a href="mailto:dave.mayhem23@gmail.com" target="_blank">dave.mayhem23@gmail.com</a>> <br>
<b>Gesendet:</b> Mittwoch, 25. Juli 2018 11:37<br>
<b>An:</b> Buesing, Henrik <<a href="mailto:hbuesing@eonerc.rwth-aachen.de" target="_blank">hbuesing@eonerc.rwth-aachen.de</a>><br>
<b>Cc:</b> Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>>; PETSc <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>></p></div></div></div></div></div><div lang="DE" link="blue" vlink="purple"><div class="m_-8805241891756980958m_-3643943920686596421WordSection1"><div style="border:none;border-left:solid blue 1.5pt;padding:0cm 0cm 0cm 4.0pt"><div><div style="border:none;border-top:solid #e1e1e1 1.0pt;padding:3.0pt 0cm 0cm 0cm"><p class="MsoNormal"><br>
<b>Betreff:</b> Re: [petsc-users] Fieldsplit - Schur Complement Reduction - Efficient Preconditioner for Schur Complement<u></u><u></u></p></div></div></div></div></div><div lang="DE" link="blue" vlink="purple"><div class="m_-8805241891756980958m_-3643943920686596421WordSection1"><div style="border:none;border-left:solid blue 1.5pt;padding:0cm 0cm 0cm 4.0pt">
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<p class="MsoNormal">On 25 July 2018 at 10:34, Buesing, Henrik <<a href="mailto:hbuesing@eonerc.rwth-aachen.de" target="_blank">hbuesing@eonerc.rwth-aachen.de</a>> wrote:<u></u><u></u></p>
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<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">Dear Matt! Dear Dave!
</span><u></u><u></u></p>
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<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">Thank you for your messages! I pursued your option 1) and the solver I sent is what I ended up with. Thus, I would like to pursue
option 2): Find a better preconditioner than the a11 block. </span><u></u><u></u></p>
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>From a technical viewpoint I understand how I would build a matrix that is used as a preconditioner for the Schur complement.
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But, from a mathematical viewpoint I do not know what to assemble. How do I find a good preconditioner for my problem? How would I tackle such a problem?
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<p class="MsoNormal">Where does your discrete saddle point system come from? <u></u>
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<p class="MsoNormal">Stokes? Navier Stokes? Something else?<u></u><u></u></p>
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<p class="MsoNormal">Maybe someone on the list can advise you.<u></u><u></u></p>
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Thank you!<br>
Henrik</span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New""> </span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New""> </span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">--
</span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">Dipl.-Math. Henrik Büsing</span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">Institute for Applied Geophysics and Geothermal Energy</span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">E.ON Energy Research Center</span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">RWTH Aachen University</span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New""> </span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-family:"Courier New""><a href="https://maps.google.com/?q=Mathieustr.+10&entry=gmail&source=g" target="_blank">Mathieustr. 10</a> | Tel +49 (0)241 80 49907</span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">52074 Aachen, Germany | Fax +49 (0)241 80 49889</span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-family:"Courier New""> </span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-family:"Courier New""><a href="http://www.eonerc.rwth-aachen.de/GGE" target="_blank">http://www.eonerc.rwth-aachen.de/GGE</a></span><u></u><u></u></p>
<p class="MsoNormal"><span style="font-family:"Courier New""><a href="mailto:hbuesing@eonerc.rwth-aachen.de" target="_blank">hbuesing@eonerc.rwth-aachen.de</a></span><u></u><u></u></p>
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<p class="MsoNormal"><b>Von:</b> Dave May <<a href="mailto:dave.mayhem23@gmail.com" target="_blank">dave.mayhem23@gmail.com</a>>
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<b>Gesendet:</b> Mittwoch, 25. Juli 2018 11:14<br>
<b>An:</b> Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
<b>Cc:</b> Buesing, Henrik <<a href="mailto:hbuesing@eonerc.rwth-aachen.de" target="_blank">hbuesing@eonerc.rwth-aachen.de</a>>; PETSc <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>><br>
<b>Betreff:</b> Re: [petsc-users] Fieldsplit - Schur Complement Reduction - Efficient Preconditioner for Schur Complement<u></u><u></u></p>
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<p class="MsoNormal">On 25 July 2018 at 09:48, Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> wrote:<u></u><u></u></p>
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<p class="MsoNormal">On Wed, Jul 25, 2018 at 4:24 AM Buesing, Henrik <<a href="mailto:hbuesing@eonerc.rwth-aachen.de" target="_blank">hbuesing@eonerc.rwth-aachen.de</a>> wrote:<u></u><u></u></p>
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<p class="MsoNormal">Dear all,
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I would like to improve the iterative solver [1]. As I understand it I would need to improve the preconditioner for the Schur complement.
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How would I do that? <u></u><u></u></p>
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<p class="MsoNormal">1) I always start from the exact thing (full Schur factorization with exact solves and back off parts until I am happy)<u></u><u></u></p>
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<p class="MsoNormal">2) Is the a11 block a good preconditioner for your Schur complement? If not, I would start by replacing that matrix<u></u><u></u></p>
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<p class="MsoNormal"> with something better.<u></u><u></u></p>
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<p class="MsoNormal">Some additional info. If you want to pursue option 2, you need to do call
<u></u><u></u></p>
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<p class="MsoNormal"> PCFieldSplitSetSchurPre()<u></u><u></u></p>
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<p class="MsoNormal"><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSetSchurPre.html#PCFieldSplitSetSchurPre" target="_blank">http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSetSchurPre.html#PCFieldSplitSetSchurPre</a><u></u><u></u></p>
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<p class="MsoNormal">with
<a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSchurPreType.html#PCFieldSplitSchurPreType" target="_blank">
PC_FIELDSPLIT_SCHUR_PRE_USER</a> (second arg) and your user defined schur complement preconditioner (last arg).<u></u><u></u></p>
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<p class="MsoNormal">Thanks,<u></u><u></u></p>
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<p class="MsoNormal"> Dave<u></u><u></u></p>
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<p class="MsoNormal"> Thanks,<u></u><u></u></p>
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<p class="MsoNormal"> Matt<u></u><u></u></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt">Thank you for your help!<br>
Henrik<br>
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[1]<br>
-ksp_max_it 100 -ksp_rtol 1e-6 -ksp_atol 1e-50 -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_precondition a11 -fieldsplit_p_w_ksp_type preonly -fieldsplit_S_n_ksp_type gmres -fieldsplit_p_w_pc_type hypre -fieldsplit_p_w_pc_hypre_type
boomeramg -fieldsplit_S_n_pc_type hypre -fieldsplit_S_n_pc_hypre_type boomeramg -fieldsplit_S_n_ksp_max_it 100 fieldsplit_S_n_ksp_rtol 1e-2<br>
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<br>
-- <br>
Dipl.-Math. Henrik Büsing<br>
Institute for Applied Geophysics and Geothermal Energy<br>
E.ON Energy Research Center<br>
RWTH Aachen University<br>
<br>
<a href="https://maps.google.com/?q=Mathieustr.+10&entry=gmail&source=g" target="_blank">Mathieustr. 10</a> | Tel +49 (0)241 80 49907<br>
52074 Aachen, Germany | Fax +49 (0)241 80 49889<br>
<br>
<a href="http://www.eonerc.rwth-aachen.de/GGE" target="_blank">http://www.eonerc.rwth-aachen.de/GGE</a><br>
<a href="mailto:hbuesing@eonerc.rwth-aachen.de" target="_blank">hbuesing@eonerc.rwth-aachen.de</a><u></u><u></u></p>
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<p class="MsoNormal"><span style="color:#888888">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments
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-- Norbert Wiener</span><u></u><u></u></p>
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<p class="MsoNormal"><span style="color:#888888"><a href="http://www.caam.rice.edu/~mk51/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a></span><u></u><u></u></p>
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