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<p>For our case, the Schur complement becomes a curl curl problem by designed. So we expect it is going to be scalable. We are still experimenting boomeramg, which seems be working, but would like to switch to AMS later if possible. </p>
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<p>The question is, can we use AMS for dmstag where dofs in our case lives on edges? One thing we are not so sure is the discrete gradient operator. We were told by our local expert that it needs to be scaled properly instead of 1 and -1. We are wondering if
there are some examples using AMS beyond dmda, maybe in firedrake or dmstag? (Actually, in firedrake, we recently got AMS working with the lowest order RT space for a different project). Any example along the line would be useful.</p>
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<p>Thanks,</p>
<p>Qi</p>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Barry Smith <bsmith@petsc.dev><br>
<b>Sent:</b> Thursday, April 22, 2021 12:12:56 PM<br>
<b>To:</b> Matthew Knepley<br>
<b>Cc:</b> Jorti, Zakariae; Tang, Qi; petsc-users@mcs.anl.gov; Tang, Xianzhu<br>
<b>Subject:</b> [EXTERNAL] Re: [petsc-users] PCFIELDSPLIT with BoomerAMG preconditioning on a Schur Complement</font>
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Schur complements are generally dense, unless your original matrix has specific structure that you know of, it is unlikely hypre AMG will work well on the Schur complement.
<div class=""><br class="">
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<div class=""> Barry</div>
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<blockquote type="cite" class="">
<div class="">On Apr 20, 2021, at 5:26 PM, Matthew Knepley <<a href="mailto:knepley@gmail.com" class="">knepley@gmail.com</a>> wrote:</div>
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<div dir="ltr" class="">On Tue, Apr 20, 2021 at 4:33 PM Jorti, Zakariae via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" class="">petsc-users@mcs.anl.gov</a>> wrote:<br class="">
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<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex; border-left:1px solid rgb(204,204,204); padding-left:1ex">
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<p class="">Hello,</p>
<p class=""><br class="">
</p>
<p class="">I have a block matrix A,</p>
<p class=""><br class="">
</p>
<p class="">[A_{00} A_{01}]</p>
<p class="">[A_{10} A_{11}] , </p>
<p class=""><br class="">
</p>
<p class="">and <span class="" style="font-size:12pt">a</span><span class="" style="font-size:12pt">m trying to use PCFIELDSPLIT as a preconditioner on</span><span class="" style="font-size:12pt"> it. The preconditioner has this shape: </span></p>
<p class=""><span class="" style="font-size:12pt"><br class="">
</span></p>
<p class="">[inv(A_{00}) 0 ]</p>
<p class="">[ 0 -ksp(S)] ;</p>
<p class=""><br class="">
</p>
<p class="">where S is the Schur Complement matrix: </p>
<p class="">S = <span class="" style="font-size:12pt">A_{11} - </span><span class="" style="font-size:12pt">A_{10} * inv(</span><span class="" style="font-size:12pt">A_{00}</span><span class="" style="font-size:12pt">) * </span><span class="" style="font-size:12pt">A_{01},</span></p>
<p class=""><span class="" style="font-size:12pt">that I get by calling: </span></p>
<p class=""><br class="">
</p>
<p class="">MatGetSchurComplement(A, isrow0, iscol0, isrow1, iscol1, MAT_INITIAL_MATRIX, &S, MAT_SCHUR_COMPLEMENT_AINV_DIAG, MAT_IGNORE_MATRIX, NULL);</p>
<div class=""><br class="">
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<p class=""><span class="" style="font-size:12pt">I would like to set BoomerAMG preconditioner for </span>ksp(S). So, I am calling:</p>
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<p class="">PCFieldSplitGetSubKSP(pc, &n, &subksp);</p>
<p class="">KSPSetOperators(subksp[1], S, S);</p>
<p class="">KSPGetPC(<span class="" style="font-size:12pt">subksp[1],</span><span class="" style="font-size:12pt"> subpc</span><span class="" style="font-size:12pt">);</span></p>
<p class=""><span class="" style="font-size:12pt">PCSetType(subpc,"boomeramg");</span></p>
<p class=""><span class="" style="font-size:12pt"><br class="">
</span></p>
<p class=""><span class="" style="font-size:12pt">but I end up getting the following error:</span></p>
<p class=""><span class="" style="font-size:12pt"><br class="">
</span></p>
<p class="">[0]PETSC ERROR: No support for this operation for this object type</p>
<p class="">[0]PETSC ERROR: Mat type schurcomplement</p>
<p class="">[0]PETSC ERROR: See <a href="https://www.mcs.anl.gov/petsc/documentation/faq.html" target="_blank" class="">
https://www.mcs.anl.gov/petsc/documentation/faq.html</a> for trouble shooting.</p>
<p class="">[0]PETSC ERROR: Petsc Release Version 3.14.2, Dec 03, 2020 </p>
<p class="">[0]PETSC ERROR: ./mimeticcurleuler2 on a arch-linux-c-debug named nid00140 by zjorti Tue Apr 20 12:23:34 2021</p>
<p class="">[0]PETSC ERROR: Configure options CC=cc CXX=CC FC=ftn COPTFLAGS=-g CXXOPTFLAGS=-g FOPTFLAGS=-g --download-hypre --with-debugging=1 --with-cxx-dialect=C++11</p>
<p class="">[0]PETSC ERROR: #1 MatGetRow() line 561 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/mat/interface/matrix.c</p>
<p class="">[0]PETSC ERROR: #2 MatConvert_Basic() line 53 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/mat/utils/convert.c</p>
<p class="">[0]PETSC ERROR: #3 MatConvert() line 4254 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/mat/interface/matrix.c</p>
<p class="">[0]PETSC ERROR: #4 PCSetUp_HYPRE() line 231 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ksp/pc/impls/hypre/hypre.c</p>
<p class="">[0]PETSC ERROR: #5 PCSetUp() line 1009 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ksp/pc/interface/precon.c</p>
<p class="">[0]PETSC ERROR: #6 KSPSetUp() line 406 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ksp/ksp/interface/itfunc.c</p>
<p class="">[0]PETSC ERROR: #7 KSPSolve_Private() line 658 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ksp/ksp/interface/itfunc.c</p>
<p class="">[0]PETSC ERROR: #8 KSPSolve() line 889 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ksp/ksp/interface/itfunc.c</p>
<p class="">[0]PETSC ERROR: #9 PCApply_FieldSplit_Schur() line 1133 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ksp/pc/impls/fieldsplit/fieldsplit.c</p>
<p class="">[0]PETSC ERROR: #10 PCApply() line 444 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ksp/pc/interface/precon.c</p>
<p class="">[0]PETSC ERROR: #11 KSP_PCApply() line 283 in /global/u1/z/zjorti/Software/petsc-3.14.2/include/petsc/private/kspimpl.h</p>
<p class="">[0]PETSC ERROR: #12 KSPInitialResidual() line 65 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ksp/ksp/interface/itres.c</p>
<p class="">[0]PETSC ERROR: #13 KSPSolve_GMRES() line 245 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ksp/ksp/impls/gmres/gmres.c</p>
<p class="">[0]PETSC ERROR: #14 KSPSolve_Private() line 719 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ksp/ksp/interface/itfunc.c</p>
<p class="">[0]PETSC ERROR: #15 KSPSolve() line 889 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ksp/ksp/interface/itfunc.c</p>
<p class="">[0]PETSC ERROR: #16 SNESSolve_KSPONLY() line 51 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/snes/impls/ksponly/ksponly.c</p>
<p class="">[0]PETSC ERROR: #17 SNESSolve() line 4569 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/snes/interface/snes.c</p>
<p class="">[0]PETSC ERROR: #18 TSTheta_SNESSolve() line 185 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ts/impls/implicit/theta/theta.c</p>
<p class="">[0]PETSC ERROR: #19 TSStep_Theta() line 223 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ts/impls/implicit/theta/theta.c</p>
<p class="">[0]PETSC ERROR: #20 TSStep() line 3757 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ts/interface/ts.c</p>
<p class="">[0]PETSC ERROR: #21 TSSolve() line 4154 in /global/u1/z/zjorti/Software/petsc-3.14.2/src/ts/interface/ts.c</p>
<p class=""><span class="" style="font-size:12pt"><br class="">
</span></p>
<p class=""><span class="" style="font-size:12pt">Am I doing something </span>wrong here? How can I fix this?</p>
</div>
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</blockquote>
<div class="">It really is best to do this with options. It will take a lot of programming to replicate what you can do.</div>
<div class=""><br class="">
</div>
<div class="">You are trying to precondition an implicit matrix (S) with Boomeramg, which needs explicit entries. You can tell PCFIELDSPLIT to build an</div>
<div class="">explicit matrix for the Schur complement:</div>
<div class=""><br class="">
</div>
<div class=""> <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSetSchurPre.html" class="">
https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSetSchurPre.html</a></div>
<div class=""><br class="">
</div>
<div class=""> Thanks,</div>
<div class=""><br class="">
</div>
<div class=""> Matt <br class="">
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<p class="">Many thanks.</p>
<p class=""><br class="">
</p>
<p class="">Best regards,</p>
<p class=""><br class="">
</p>
<p class="">Zakariae Jorti</p>
<p class=""><span class="" style="font-size:12pt"><br class="">
</span></p>
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<div class="">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br class="">
-- Norbert Wiener</div>
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<div class=""><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank" class="">https://www.cse.buffalo.edu/~knepley/</a><br class="">
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