<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On Nov 5, 2011, at 12:25 PM, Jed Brown wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div class="gmail_quote">On Sat, Nov 5, 2011 at 10:02, Mark F. Adams <span dir="ltr"><<a href="mailto:mark.adams@columbia.edu">mark.adams@columbia.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
FYI: the yellow SIAM book on mixed FE methods by Brezi and Fortin has an excellent 2 page section on Uzawa that give, among other things, a precise recipe for Uzawa (page 99 I think) including preconditioning and a non-zero RHS for the constraint part.</blockquote>
</div><br><div>You can run Uzawa with -pc_fieldsplit_type schur and Richardson.</div><div><br></div></blockquote><div><br></div><div>Uzawa is a great algorithm, very popular, dead simple (two lines), embarrassingly robust and fast. I'm sure its easy to express in your FieldSplit stuff. This paper does a good job and going through its variants, including non-linear which I'd never seen before, and lots of convergence theory. Eq 2.5 is probably the algorithm you want to look at.</div><div><br></div><div>In the past I have not written the first line in update form like this paper and I use a Krylov solver with a rtol of ~1.e-3 for the first line of the algorithm (more like their eq 2.2).</div><div><br></div><div>They have a zero K(2,2) block but you just need to modify the second line of the algo to make it consistent.</div><div><br></div><div>Mark</div><div><br></div><div></div></div></body></html>