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

[Matthew Knepley]

On Sat, Jan 10, 2015 at 10:10 AM, Umut Tabak <u.tabak at tudelft.nl> wrote:

> 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.
>

Fieldsplit block preconditioners can be used on this type of matrix, but
success obviously depends on the
analytic character of the operators.  In particular, if we assume that we
have great PCs for the diagonal,
then B is the most important variable, and we need to know what the Schur
complement

   B^T  A^{-1} B or equiv B^T C^{-1} B

looks like.

  Thanks,

     Matt


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



-- 
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
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