On Fri, Nov 4, 2011 at 10:08, Mark F. Adams <mark.adams at columbia.edu> wrote:
> Woodbury does not seem natural (ie, efficient) when A is solved > iteratively. These methods rely on multiple solves with A being almost the > same cost as one solve, most of the cost going into the matrix setup > (factorization). This is generally not the case with iterative solvers. > How does Woodbury work with inexact solves? It looks to me like there are > rank-of-B + 2 solves here. Uzawa solvers (iterate on Schur compliment) > seem better -- they work fine with inexact solves for A and you can > precondition them easily for these special matrices with explic (D - C > diag(A)^-1 B)^-1. They converge very fast, like one digit per iteration > even w/o preconditioning in my experience. I think both directions are likely useful. I vaguely recall seeing Woodbury used as a preconditioner where the low rank part was computed using an approximate A. We already have support via PCFieldSplit for the Uzawa-type iteration you describe and for the related full-space iteration. -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-dev/attachments/20111104/086d1e7a/attachment.html>
