[petsc-users] Mixed matrices MatMatMult

[Luc Berger-Vergiat]

Ok,
this work is still part of my Schur complement approach using the full 
schur but with a block diagonal A00^-1.
I implemented the computation of A00^-1 by extracting each diagonal 
block and inverting them individually.
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...).

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.
Decreasing that cost would be nice (I attached the output of 
-log_summary for reference).
I think I need to look for the objects that are not Destroyed too.

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:

        [ A00  A01  A02 ]  --> IS(0)
A = [ A10  A11  A12 ]  --> IS(1)
        [ A20  A21  A22 ]  --> IS(2)

How can I use IS(1) and IS(2) to track:

S =   [ A11  A12 ]  _  [ A10] * [A00]^-1 * [ A01 A02 ]  = [ S11  S12 ]  
--> IS(1)'
          [ A21  A22 ]     [ 
A20]                                          = [ S21  S22 ]  --> IS(2)'

or is there a simple way to compute IS(1)' and IS(2)' based on IS(1) and 
IS(2)?

Thanks!

Best,
Luc

On 03/26/2015 04:12 PM, Matthew Knepley wrote:
> On Thu, Mar 26, 2015 at 3:07 PM, Luc Berger-Vergiat 
> <lb2653 at columbia.edu <mailto:lb2653 at columbia.edu>> wrote:
>
>     Hi all,
>     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?
>
>
> I am afraid you are currently stuck with the latter.
>
>   Thanks,
>
>     Matt
>
>
>     -- 
>     Best,
>     Luc
>
>
>
>
>
> -- 
> What most experimenters take for granted before they begin their 
> experiments is infinitely more interesting than any results to which 
> their experiments lead.
> -- Norbert Wiener

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20150326/74911791/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: time.log
Type: text/x-log
Size: 11655 bytes
Desc: not available
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20150326/74911791/attachment-0001.bin>