[petsc-users] Solving reduced system of equations with global preconditioner

[Matthew Knepley]

On Tue, Jun 5, 2018 at 6:46 PM, Adrián Amor <aamor at pa.uc3m.es> wrote:

> Hi all,
>
> I think this is a basic question that I am pretty sure that it can be done
> in PETSC but I don't know the way, so sorry for wasting your time if it's
> too basic!
>
> I have a big system of equations (say 1M of unknowns) which I divide into
> 25 blocks and I use a block-Jacobi preconditioner to get the solution from
> KSPBICG. However, I know that I can build a reduced matrix with the
> nonzeros of the big preconditioned matrix, solve this reduced problem, and
> then recover the solution for the original big system with the factorized
> matrices from block Jacobi. How can I do this with PETSC? Since using
> KSPComputeExplicitOperator and then copy blocks of this matrix to build the
> reduced surface problem in PETSC is definitely not an option.
>

Its a little hard to understand what algorithm you are describing. Do you
mean something like

  https://en.wikipedia.org/wiki/SPIKE_algorithm

We do not have that. We can do additive/multiplicative iterations on these
blocks using PCFIELDSPLIT (however the block operations would be
serialized).
If you want something direct like this, have you tried just applying
SuperLU_dist or MUMPS?

  Thanks,

    Matt


> I was doing this by hand using MUMPS to build the reduced system of
> equations, then using PETSC without preconditioner and then, recover the
> full solution. However, the burden in time and memory is not negligible so
> I wanted to explore a different way with PETSC (using maybe some ILU). I
> think that the performance in memory is going to be similar but I expect a
> better performance in time.
>
> Thanks a lot!
>
> Adrian.
>



-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20180606/024c63b2/attachment.html>