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Ok,<br>
this work is still part of my Schur complement approach using the
full schur but with a block diagonal A00^-1.<br>
I implemented the computation of A00^-1 by extracting each diagonal
block and inverting them individually.<br>
This works quite well and does not cost some much, especially since
I can still use threads to accelerate this process (I might send a
question about this in the future...).<br>
<br>
At the moment the most expensive part of the procedure is inverting
S (I'm using LU at the moment to make sure that everything is
implemented correctly) and the second most expensive procedure is
MatMatMult. I'm doing two of these: A10 * A00^-1 and then a right
multiplication by A01.<br>
Decreasing that cost would be nice (I attached the output of
-log_summary for reference).<br>
I think I need to look for the objects that are not Destroyed too.<br>
<br>
Finally I now would like to split the Schur complement into two
submatrices. I have an IS that tracks location of these sub-matrices
in the global system:<br>
<br>
[ A00 A01 A02 ] --> IS(0)<br>
A = [ A10 A11 A12 ] --> IS(1)<br>
[ A20 A21 A22 ] --> IS(2)<br>
<br>
How can I use IS(1) and IS(2) to track:<br>
<br>
S = [ A11 A12 ] _ [ A10] * [A00]^-1 * [ A01 A02 ] = [ S11 S12
] --> IS(1)'<br>
[ A21 A22 ] [
A20] = [ S21 S22 ] -->
IS(2)'<br>
<br>
or is there a simple way to compute IS(1)' and IS(2)' based on IS(1)
and IS(2)?<br>
<br>
Thanks!<br>
<pre class="moz-signature" cols="72">Best,
Luc</pre>
<div class="moz-cite-prefix">On 03/26/2015 04:12 PM, Matthew Knepley
wrote:<br>
</div>
<blockquote
cite="mid:CAMYG4GniTA0jX7+JWT=Rvi5bt+XHHTqcaBaofOz5NgwThz_c7w@mail.gmail.com"
type="cite">
<div dir="ltr">
<div class="gmail_extra">
<div class="gmail_quote">On Thu, Mar 26, 2015 at 3:07 PM, Luc
Berger-Vergiat <span dir="ltr"><<a
moz-do-not-send="true" href="mailto:lb2653@columbia.edu"
target="_blank">lb2653@columbia.edu</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">Hi all,<br>
I want to multiply two matrices together, one is MATAIJ
and the second is MATBAIJ, is there a way to leverage the
properties of the blocked matrix in the BAIJ format or
should I just assemble the BAIJ matrix as AIJ?</blockquote>
<div><br>
</div>
<div>I am afraid you are currently stuck with the latter.</div>
<div><br>
</div>
<div> Thanks,</div>
<div><br>
</div>
<div> Matt</div>
<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex"><span
class="HOEnZb"><font color="#888888"><br>
-- <br>
Best,<br>
Luc<br>
<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>
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