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<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New";mso-fareast-language:EN-US">Dear Matt! Dear Dave!
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<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New";mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New";mso-fareast-language:EN-US">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. <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New";mso-fareast-language:EN-US"><br>
From a technical viewpoint I understand how I would build a matrix that is used as a preconditioner for the Schur complement.
<br>
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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<br>
Thank you!<br>
Henrik<o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">-- <o:p>
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<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">Dipl.-Math. Henrik Büsing<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">Institute for Applied Geophysics and Geothermal Energy<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">E.ON Energy Research Center<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New"">RWTH Aachen University<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">Mathieustr. 10 | Tel +49 (0)241 80 49907<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">52074 Aachen, Germany | Fax +49 (0)241 80 49889<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">http://www.eonerc.rwth-aachen.de/GGE<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">hbuesing@eonerc.rwth-aachen.de<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New";mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b>Von:</b> Dave May <dave.mayhem23@gmail.com> <br>
<b>Gesendet:</b> Mittwoch, 25. Juli 2018 11:14<br>
<b>An:</b> Matthew Knepley <knepley@gmail.com><br>
<b>Cc:</b> Buesing, Henrik <hbuesing@eonerc.rwth-aachen.de>; PETSc <petsc-users@mcs.anl.gov><br>
<b>Betreff:</b> Re: [petsc-users] Fieldsplit - Schur Complement Reduction - Efficient Preconditioner for Schur Complement<o:p></o:p></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:<o:p></o:p></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:<o:p></o:p></p>
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<p class="MsoNormal">Dear all, <br>
<br>
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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<br>
How would I do that? <o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></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)<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></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<o:p></o:p></p>
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<p class="MsoNormal"> with something better.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Some additional info. If you want to pursue option 2, you need to do call
<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"> PCFieldSplitSetSchurPre()<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></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><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></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).<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal">Thanks,<o:p></o:p></p>
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<p class="MsoNormal"> Dave<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"> Thanks,<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"> Matt<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt">Thank you for your help!<br>
Henrik<br>
<br>
<br>
<br>
[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>
<br>
<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><o:p></o:p></p>
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<p class="MsoNormal"><span style="color:#888888"><br clear="all">
<span class="m-3725184249599076478gmail-hoenzb"><o:p></o:p></span></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span class="m-3725184249599076478gmail-hoenzb"><span style="color:#888888">--
</span><o:p></o:p></span></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 lead.<br>
-- Norbert Wiener</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="color:#888888"><o:p> </o:p></span></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><o:p></o:p></span></p>
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