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

[Adrián Amor]

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.

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.
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