You should use algebraic or geometric multigrid for this problem. Also use the null space command.
You should not use ICC(0) it just won’t be competitive for large problems and as Matt says is extremely sensitive to that zero eigenvalue. Barry On Apr 30, 2014, at 2:53 PM, Danny Lathouwers - TNW <[email protected]> wrote: > Dear users, > > I encountered a strange problem. I have a singular matrix P (Poisson, Neumann > boundary conditions, N=4). The rhs b sums to 0. > If I hand-fill the matrix with the right entries (non-zeroes only) things > work with KSPCG and ICC preconditioning and using the > MAT_SHIFT_POSITIVE_DEFINITE option. Convergence in 2 iterations to (a) > correct solution. So far for the debugging problem. > > My real problem computes P from D * M * D^T. If I do this I get the same > matrix (on std out I do not see the difference to all digits). > The system P * x = b now does NOT converge. > More strange is that is if I remove the zeroes from D then things do work > again. > Either things are overly sensitive or I am misusing petsc. > It does work when using e.g. the AMG preconditioner (again it is a correct > but different solution). So system really seems OK. > > Should I also use the Null space commands as I have seen in some of the > examples as well? > But, I recall from many years ago when using MICCG (alpha) preconditioning > that no such tricks were needed for CG with Poisson-Neumann. I am supposing > the MAT_SHIFT_POSITIVE_DEFINITE option does something similar as MICCG. > > For clarity I have included the code (unfortunately this is the smallest I > could get it; it’s quite straightforward though). > By setting the value of option to 1 in main.f90 the code use P = D * M * D^T > otherwise it will use the hand-filled matrix. > The code prints the matrix P and solution etc. > > Anyone any hints on this? > What other preconditioners (serial) are suitable for this problem besides > ICC/AMG? > > Thanks very much. > Danny Lathouwers > > <petsc.f90><f90_kind.f90><main.f90><Makefile>
