[petsc-users] Solving a sequence of linear systems stored on disk with MUMPS

[Thibaut Appel]

Dear PETSc users,

I need to solve several linear systems successively, with LU 
factorization, as part of an iterative process in my Fortran application 
code.

The process would solve M systems (A_m)(x_m,i) = (b_m,i) for m=1,M at 
each iteration i, but computing the LU factorization of A_m only once.
The RHSs (b_m,i+1) are computed from all the different (x_m,i) and all 
depend upon each other.

The way I envisage to perform that is to use MUMPS to compute, 
successively, each of the LU factorizations (m) in parallel and store 
the factors on disk, creating/assembling/destroying the matrices A_m on 
the go.
Then whenever needed, read the factors in parallel to solve the systems. 
Since version 5.2, MUMPS has a save/restore feature that allows that, 
see http://mumps.enseeiht.fr/doc/userguide_5.2.1.pdf p.20, 24 and 58.

In its current state, the PETSc/MUMPS interface does not incorporate 
that feature. I'm an advanced Fortran programmer but not in C so I don't 
think I would do an amazing job having a go inside 
src/mat/impls/aij/mpi/mumps/mumps.c.

I was picturing something like creating as many KSP objects as linear 
systems to be solved, with some sort of flag to force the storage of LU 
factors on disk after the first call to KSPSolve. Then keep calling 
KSPSolve as many times as needed.

Would you support such a feature?

Thanks for your support,

Thibaut