Dear all!
I have a question to solving block systems in deal.II. My (linear)
equation system looks like Ax=b where A represents a block matrix (with 9
blocks) which looks like
A = (A11 , A12, A13)
(A21, 0 , A23)
(A31, 0 , A33)
It represents the Stokes system with an additional equation (a
fluid-structure interaction problem to be exactly).
Now, I want to treat the whole system in an all-at-once approach (as
done in step-21,22,31) with a GMRES iteration. Hence, I need to build an
appropriate block preconditioner P^{-1} for the system.
My first idea was to reorder blocks of the system matrix in such a way
that I have to solve:
A_new = (A12 , A11, A13)
(0 , A21, A23)
(0 , A31, A33)
Then, to create a block preconditioner via block Gauss elimination
(procedure as in step-22, 31).
My question: Is it possible and does it make sense to create a second
system matrix A_new with the desired block structure? How can I realize
this?
Or does anyone have another idea to build an appropriate block
preconditioner for system matrix A? The goal is to use multigrid
techniques as done in step-31.
Thanks in advance and best regards,
Thomas
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