[petsc-users] singular matrix solve using MAT_SHIFT_POSITIVE_DEFINITE option

[Barry Smith]

  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 <D.Lathouwers at tudelft.nl> 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>