Jed, I've wanted to scrap this approach for a long time, but moving away from these GFM-type treatments is not a choice that I've been allowed to follow through on for various reasons which are out of my control.
On Wed, Mar 20, 2013 at 4:55 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote: > > On Wed, Mar 20, 2013 at 4:51 PM, John Mousel <john.mousel at gmail.com>wrote: > >> Right now, Mehrdad and I are just passing the constant vector. The >> problem is that the null space is extremely expensive to compute. Something >> like 5-20 times the cost of solving the Poisson equation itself depending >> on the problem size. What we have tried in the past is to find a single >> solution to Atrans*n = 0 and pass this as the nullspace. It's had success >> at making the true residual drop in unison with the preconditioned >> residual. However, because we are working with moving boundary problems, >> the null space is changing each time step. In order to get around this, we >> have decided to try to avoid giving the null space, and see if we get an >> accurate answer, and we do get pretty much the same answer when we only >> require preconditioned residual convergence. This is obviously less than >> robust, but we've yet to find a way to get the null space in an efficient >> manner. I tried programming up a GASM type algorithm where BiCG/ILU is used >> near the interface where the solution is not smooth, and GAMG is used far >> away where the changes in the null vector are very very small, but that >> didn't have much success. > > > It's not usually a good idea to choose a spatial discretization that is > singular with a complicated null space. Proving that an iteration remains > in the benign space is one of the first things demanded from such > discretizations. If you can't find a way to iterate in the null space or > otherwise project it out, then I would seriously reconsider your choice of > this discretization. > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20130320/54920bfe/attachment.html>
