<html>
<head>
<meta content="text/html; charset=utf-8" http-equiv="Content-Type">
</head>
<body bgcolor="#FFFFFF" text="#000000">
Dear Matt,<br>
<br>
sorry but I think I haven't understood points 2 and 3 you mentioned.
Could you be a bit more specific?<br>
<br>
Thanks<br>
Elias<br>
<br>
<div class="moz-cite-prefix">On 28.05.2015 18:02, Matthew Knepley
wrote:<br>
</div>
<blockquote
cite="mid:CAMYG4Gk-QAbk=95jpjH_GOBmfaFLOOfEamrA3TmXcuTjKs5Lcw@mail.gmail.com"
type="cite">
<div dir="ltr">
<div class="gmail_extra">
<div class="gmail_quote">On Thu, May 28, 2015 at 10:47 AM,
Elias Karabelas <span dir="ltr"><<a
moz-do-not-send="true"
href="mailto:elias.karabelas@medunigraz.at"
target="_blank">elias.karabelas@medunigraz.at</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">Dear
Members,<br>
<br>
I want to solve a Block System arising from the
Discretization of a stabilized Finite Element Formulation
of the Stokes System.<br>
<br>
I have the following Block Structure<br>
<br>
A -B^T<br>
B C<br>
<br>
The Preconditioner I intend to use is a block
preconditioner of the Form<br>
<br>
A -B^T<br>
S<br>
<br>
where S is an approximation of the Schur Complement. For
applying the inverse of the schur complement I want to use
a Stabilized Least Squares Commutator in the form<br>
<br>
S^-1 = (B diag(Q)^-1 B^T + C_1)^-1 (B diag(Q)^-1 A
diag(Q)^-1 B^T + C_2) (B diag(Q)^-1 B^T + C_1)^-1<br>
<br>
where Q is the mass matrix and C_1 and C_2 are some
additional stabilization matrices.<br>
<br>
I got from the Manual, that I can use the PCFieldSplit
preconditioner for generating the general Block
preconditioner as indicated above. And I also found that I
can define some arbitrary PC with PCSHELL. My question is,
if it is possible to use PCSHELL to define the action of
S^-1 as indicated above.<br>
</blockquote>
<div><br>
</div>
<div>1) Use FieldSplit is the right PC to start with. Make
sure you can do something simple like </div>
<div><br>
</div>
<div> A -B^T</div>
<div> C + B diag(A)^{-1} B^T</div>
<div><br>
</div>
<div>with it before we do the more complicated thing.</div>
<div><br>
</div>
<div>2) You will want to implement a PC for the (1,1) block.
You can use a PCSHELL, which is simpler to setup, but</div>
<div> that means you will have to manually pull out the
FieldSplit KSP and set it. If instead you define your own</div>
<div> PC implementation, its more boilerplate code, but
you could specify this PC from the command line without</div>
<div> any FieldSplit specific code in your application.</div>
<div><br>
</div>
<div>3) Your PC will get two matrices, the
MatSchurComplement, and the preconditioning matrix. If you
set Q as the</div>
<div> preconditioning matrix, or really if you set</div>
<div><br>
</div>
<div> A 0</div>
<div> 0 Q</div>
<div> </div>
<div>as the global preconditioning matrix, then the subsolve
for (1,1) will get the Schur Complement and Q, and I think</div>
<div>that is enough to build your Stabilized LSC PC.</div>
<div><br>
</div>
<div>Let me know if this makes sense to you.</div>
<div><br>
</div>
<div> Thanks,</div>
<div><br>
</div>
<div> Matt</div>
<div><br>
</div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
Kind Regards<span class="HOEnZb"><font color="#888888"><br>
Elias Karabelas<br>
<br>
-- <br>
Elias Karabelas, Ph.D.<br>
<br>
Medical University of Graz<br>
Institute of Biophysics<br>
Harrachgasse 21/IV<br>
8010 Graz, Austria<br>
<br>
Phone: <a moz-do-not-send="true"
href="tel:%2B43%20316%20380%207759"
value="+433163807759" target="_blank">+43 316 380
7759</a><br>
Email: <a moz-do-not-send="true"
href="mailto:elias.karabelas@medunigraz.at"
target="_blank">elias.karabelas@medunigraz.at</a><br>
Web : <a moz-do-not-send="true"
href="http://forschung.medunigraz.at/fodok/staff?name=EliasKarabelas"
target="_blank">http://forschung.medunigraz.at/fodok/staff?name=EliasKarabelas</a><br>
<br>
</font></span></blockquote>
</div>
<br>
<br clear="all">
<div><br>
</div>
-- <br>
<div class="gmail_signature">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</div>
</div>
</div>
</blockquote>
<br>
<pre class="moz-signature" cols="72">--
Elias Karabelas, Ph.D.
Medical University of Graz
Institute of Biophysics
Harrachgasse 21/IV
8010 Graz, Austria
Phone: +43 316 380 7759
Email: <a class="moz-txt-link-abbreviated" href="mailto:elias.karabelas@medunigraz.at">elias.karabelas@medunigraz.at</a>
Web : <a class="moz-txt-link-freetext" href="http://forschung.medunigraz.at/fodok/staff?name=EliasKarabelas">http://forschung.medunigraz.at/fodok/staff?name=EliasKarabelas</a> </pre>
</body>
</html>