[dune-fem] Has the Schur complement approach been implemented in DUNE-FEM somewhere?

[Sacconi, Andrea]

Hi,

yes, sorry, I didn't give you so many details.

Suppose I've to solve this kind of linear system:

| A    - B^T| | x | = 0
| B      C    | | y | = g

I've three classes for the corresponding (linear) operators A, B and C; if I decide to solve using a Schur complement approach, I get:

x = A^{-1} B^T y
(C + B A^{-1} B^T) y = g

How do I extract the inverse of the matrix A, given such an operator A (it's publicly derived from Operator < ... > and OEMSolver::PreconditionInterface) ?
I mean, I already know that if I do this:

B.applyTransposed (y, foo)

I can calculate foo = B^T y.
Is there something similar, kind of "applyInverse" to compute and store the temporary A^{-1} B^T ??

Hope now it's clearer.

Cheers,

Andrea
__________________________________________________________

Andrea Sacconi
PhD student, Applied Mathematics
AMMP Section, Department of Mathematics, Imperial College London,
London SW7 2AZ, UK
a.sacconi11 at imperial.ac.uk
________________________________
From: Dedner, Andreas [A.S.Dedner at warwick.ac.uk]
Sent: 17 April 2012 09:56
To: Sacconi, Andrea; dune-fem at dune-project.org
Subject: RE: [dune-fem] Has the Schur complement approach been implemented in DUNE-FEM somewhere?

Hi Andrea.

I do not quite know what you are refering to? Do you mean an
Uzawa like algorithm for Stokes?
It would help if you gave more detail on the problem youi are solving and on the
method you would like to use.
Best
Andreas
________________________________
From: dune-fem-bounces+a.s.dedner=warwick.ac.uk at dune-project.org [dune-fem-bounces+a.s.dedner=warwick.ac.uk at dune-project.org] on behalf of Sacconi, Andrea [a.sacconi11 at imperial.ac.uk]
Sent: Monday, April 16, 2012 5:01 PM
To: dune-fem at dune-project.org
Subject: [dune-fem] Has the Schur complement approach been implemented in DUNE-FEM somewhere?

Hi all,

I need to programme the Schur complement approach, with an appropriate preconditioner, to solve the linear systems I'm dealing with.
I was wondering if anybody has already implemented it, either in his own code or in the tutorials. Just not to reinvent the wheel, or to have some useful hints.

Cheers,

Andrea
__________________________________________________________

Andrea Sacconi
PhD student, Applied Mathematics
AMMP Section, Department of Mathematics, Imperial College London,
London SW7 2AZ, UK
a.sacconi11 at imperial.ac.uk
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