[petsc-users] optimizing repeated calls to KSPsolve?

[Luke Bloy]

Hi I'm new to Petsc so excuse me if this question is naive.

I'm trying to solve the following system A x = b for x.  A is a sparse 
square matrix (2000000 by 2000000 with ~45,000,000 nonzero elements)
I'm currently using ex1 as the basis for solving the system and it is 
working quite well.

My problem is that i have a large number (~500,000)  of b vectors that I 
would like to find solutions for. My plan is to call KSPsolve repeatedly 
with each b. However I wonder if there are any solvers or approaches 
that might benefit from the fact that my A matrix does not change. Are 
there any decompositions that might still be sparse that would offer a 
speed up?

Thanks for any suggestions.
Luke