[petsc-users] computation of Sp for fieldsplit schur preconditioner

[Jed Brown]

Luc Berger-Vergiat <lb2653 at columbia.edu> writes:

> Hi all,
> I would like to know if there would be an easy way of computing the Sp 
> preconditioner for a fieldsplit schur complement using the following 
> formula:
> Sp=A11-A10*diag(inv(A00))*A01
> instead of
> Sp=A11-A10*inv(diag(A00))*A01

Not in general because inv(A00) is dense, thus not practically
computable.  You can use PCFieldSplitSetSchurPre to provide your own Sp.

> I think that it would be really beneficial in my case since the 
> eigenvalues of both operators are very different for my problem (see 
> ev_S_diaginv for the eigenvalues of the modified Sp and ev_S for the 
> eigenvalues of the current Sp).
>
> I do understand that this requires to compute a more complex inverse 
> while forming Sp, but I compute this inverse using a block jacobi lu due 
> to the special properties of my matrix (see jac_nonlin_nested for the 
> sparsity pattern of my matrix). So the change would actually be quite 
> minimal no? I am also actually debating whether I should compute the 
> exact S?
>
> -- 
> Best,
> Luc
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