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

[Luc Berger-Vergiat]

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

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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