<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p.msonormal0, li.msonormal0, div.msonormal0
{mso-style-name:msonormal;
mso-margin-top-alt:auto;
margin-right:0cm;
mso-margin-bottom-alt:auto;
margin-left:0cm;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
span.m4832964853800348607m-3725184249599076478gmail-hoenzb
{mso-style-name:m_4832964853800348607m-3725184249599076478gmail-hoenzb;}
span.E-MailFormatvorlage19
{mso-style-type:personal-reply;
font-family:"Courier New";
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri",sans-serif;
mso-fareast-language:EN-US;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:70.85pt 70.85pt 2.0cm 70.85pt;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="DE" link="blue" vlink="purple">
<div class="WordSection1">
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New";mso-fareast-language:EN-US">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).
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-family:"Courier New";mso-fareast-language:EN-US">The J11 block of the Jacobian is made elliptic.
<o:p></o:p></span></p>
<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">Maybe someone could tell me how to go on from there to build a good preconditioner?
<br>
<br>
Thank you!<br>
Henrik<o:p></o:p></span></p>
<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"><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 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>
<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"><b>Von:</b> Dave May <dave.mayhem23@gmail.com> <br>
<b>Gesendet:</b> Mittwoch, 25. Juli 2018 11:37<br>
<b>An:</b> Buesing, Henrik <hbuesing@eonerc.rwth-aachen.de><br>
<b>Cc:</b> Matthew Knepley <knepley@gmail.com>; 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>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<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:<o:p></o:p></p>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm">
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New"">Dear Matt! Dear Dave!
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New""> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><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><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New""><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?
</span><o:p></o:p></p>
</div>
</div>
</blockquote>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">Where does your discrete saddle point system come from? <o:p>
</o:p></p>
</div>
<div>
<p class="MsoNormal">Stokes? Navier Stokes? Something else?<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">Maybe someone on the list can advise you.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm">
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New""><br>
Thank you!<br>
Henrik</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New""> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New""> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New"">--
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New"">Dipl.-Math. Henrik Büsing</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New"">Institute for Applied Geophysics and Geothermal Energy</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New"">E.ON Energy Research Center</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New"">RWTH Aachen University</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="font-family:"Courier New""> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Courier New""><a href="https://maps.google.com/?q=Mathieustr.+10&entry=gmail&source=g">Mathieustr. 10</a> | Tel +49 (0)241 80 49907</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Courier New"">52074 Aachen, Germany | Fax +49 (0)241 80 49889</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Courier New""> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><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><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Courier New""><a href="mailto:hbuesing@eonerc.rwth-aachen.de" target="_blank">hbuesing@eonerc.rwth-aachen.de</a></span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Courier New""> </span><o:p></o:p></p>
<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" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><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 11:14<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<o:p></o:p></p>
</div>
</div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">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>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt">
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">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>
</div>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt">
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">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.
<br>
<br>
How would I do that? <o:p></o:p></p>
</blockquote>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">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>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">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>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> with something better.<o:p></o:p></p>
</div>
</div>
</div>
</blockquote>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Some additional info. If you want to pursue option 2, you need to do call
<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> PCFieldSplitSetSchurPre()<o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><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>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">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>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">
<o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Thanks,<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> Dave<o:p></o:p></p>
</div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt">
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> Thanks,<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> Matt<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt">
<p class="MsoNormal" style="mso-margin-top-alt:auto;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>
</blockquote>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#888888"><br clear="all">
</span><o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="m4832964853800348607m-3725184249599076478gmail-hoenzb"><span style="color:#888888">--
</span></span><o:p></o:p></p>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><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>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#888888"> </span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#888888"><a href="http://www.caam.rice.edu/~mk51/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
</div>
</blockquote>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</blockquote>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
</div>
</div>
</div>
</body>
</html>