[petsc-users] Schur complement with a preconditioner
Umut Tabak
u.tabak at tudelft.nl
Thu Jul 25 12:29:01 CDT 2013
Dear all,
I have a system that I would like to solve for multiple rhs,
represented in block notation as
[ A C ] x1 b1
=
[ C^T B ] x2 b2
I could solve the system
(B - C^TA^{-1}C)x2 = bupdated
with Minres algorithm in MATLAB by using the Incomplete Factorization of
B in decent iteration counts, like 43. The problem is that B is not SPD
and it has one negative eigenvalue. That is the reason to use MINRES.
Just as a try, I saved the matrix represented by (B - C^TA^{-1}C) in
sparse format and used the hypre euclid preconditioner in PETSc which
resulted in 25 iterations to convergence. But since for large problems,
this approach is not viable, I was wondering if that is possible to use
the complete cholesky factorization of B+alpha*diag(B) where alpha is
given as
alpha = max(sum(abs(A),2)./diag(A))-2
as a preconditioner for the above schur complement. Or in general use an external preconditioner
for the matrix operator.
Any pointers are appreciated.
Best,
Umut
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