On Thu, Feb 16, 2012 at 06:49, Thomas Witkowski < thomas.witkowski at tu-dresden.de> wrote:
> I consider a 2x2 block matrix (saddle point) with the left upper block > being singular due to Neumann boundary conditions. The whole block matrix > is still non-singular. I worked on some ideas for block preconditioning, > but there is always some problem with the singular block. All publications > I know assume the block to be definite. There is also some work on highly > singular blocks, but this is here not the case. Does some of you know > papers about block preconditioners for some class of 2x2 saddle point > problems, where the left upper block is assumed to be positive > semi-definite? > I could search, but I don't recall a paper specifically addressing this issue. In practice, you should remove the constant null space and use a preconditioner that is stable even on the singular operator (as with any singular operator). > > From a more practical point of view, I have the problem that, > independently of a special kind of block preconditioner, one has always to > solve (or to approximate the solution) a system with the singular block > with an arbitrary right hand side. But in general the right hand side does > not fulfill the compatibility condition of having zero mean. Is there a way > out of this problem? > Make the right hand side consistent by removing the null space. -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120217/dbf35d0c/attachment-0001.htm>
