On Mon, Apr 19, 2010 at 7:12 AM, Jed Brown <span dir="ltr"><<a href="mailto:jed@59a2.org">jed@59a2.org</a>></span> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div class="im">On Mon, 19 Apr 2010 06:34:08 -0500, Matthew Knepley <<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>> wrote:<br>
> For Schur complement methods, the inner system usually has to be<br>
> solved very accurately. Are you accelerating a Krylov method for<br>
> A^{-1}, or just using ML itself? I would expect for the same linear<br>
> system tolerance, you get identical convergence for the same system,<br>
> independent of the number of processors.<br>
<br>
</div>Matt, run ex48 with ML in parallel and serial, the aggregates are quite<br>
different and the parallel case doesn't converge with SOR. Also, from<br>
talking with Ray, Eric Cyr, and John Shadid two weeks ago, they are<br>
currently using ML on coupled Navier-Stokes systems and usually beating<br>
block factorization (i.e. full-space iterations with<br>
approximate-commutator Schur-complement preconditioners (PCD or LSC<br>
variants) which are beating full Schur-complement reduction). They are<br>
using Q1-Q1 with PSPG or Bochev stabilization and SUPG for advection.<br></blockquote><div><br></div><div>So, to see if I understand correctly. You are saying that you can get away with</div><div>more approximate solves if you do not do full reduction? I know the theory for</div>
<div>the case of Stokes, but can you prove this in a general sense?</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
The trouble is that this method occasionally runs into problems where<br>
convergence completely falls apart, despite not having extreme parameter<br>
choices. ML has an option "energy minimization" which they are using<br>
(PETSc's interface doesn't currently support this, I'll add it if<br>
someone doesn't beat me to it) which is apparently crucial for<br>
generating reasonable coarse levels for these systems.<br></blockquote><div><br></div><div>This sounds like the black magic I expect :)</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
They always coarsen all the degrees of freedom together, this is not<br>
possible with mixed finite element spaces, so you have to trade quality<br>
answers produced by a stable approximation along with necessity to make<br>
subdomain and coarse-level problems compatible with inf-sup against the<br>
wiggle-room you get with stabilized non-mixed discretizations but with<br>
possible artifacts and significant divergence error.</blockquote><div><br></div><div>I still maintain that aggregation is a really crappy way to generate coarse systems,</div><div>especially for mixed elements. We should be generating coarse systems geometrically,</div>
<div>and then using a nice (maybe Black-Box) framework for calculating good projectors.</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<font color="#888888"><br>
Jed<br>
</font></blockquote></div><br><br clear="all"><br>-- <br>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener<br>