[petsc-users] An advice on a linear system solution

[Umut Tabak]

Dear all,

For an eigenvalue solver, I was brainstorming on some ideas to solve 
some linear systems of the form:

[A B] x1 = b1
[B C] x2 = b2

Where A and C are symmetric sparse but indefinite matrices due to some 
shift operations. Namely, A = K-\sigmaM and
C = D/(\sigma)-E, where (K, M) and (D, E) are sparse symmetric stiffness 
and mass matrix pairs of the structural and fluid domains, respectively.

However, B blocks are rather sparse coupling blocks and I was wondering 
if I can use this property in order to solve this system with the 
independent factorzations of A and C blocks either directly or 
iteratively. Iterative path is more difficult I believe since the 
matrices are indefinite.

I am open to any useful ideas that can make it work or suggestions to 
kill this idea quickly.

Best regards and happy new year to all PETSc'ers.

Umut