Maybe some related question: Most textbooks write that the compatibility condition to solve a system with constant null space is that the right hand side has zero mean value. Today I read part of the Multigrid-book written by Trottenberg, and there the condition is written in a different form (eq 5.6.22 on page 185): the integral of the right hand side must be equal on the whole domain and on the boundary. Does any of you have an explanation for this condition? Is there a book/paper that considers the compatibility condition in more details?
Thomas Am 16.02.2012 12:49, schrieb Thomas Witkowski: > 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? > > 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? > > Thomas
