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/20130320/272642cf/attachment.html>
