KSPSetNullSpace and CG for singular systems

[Barry Smith]

    It is not the null space that is the problem.

    You are right to try the shift but
1) first run on one process using -pc_type icc -ksp_type cg - 
pc_factor_shift_positive_definite
this will keep increasing the shift until it produces a positive- 
definite preconditioner.

Run also with -ksp_view to confirm that it is using all the options  
you provided. (you can run with -help to
see the option names)

2) If you have the sequential converging then use -pc_type bjacobi - 
sub_pc_type icc -pc_factor_shift_positive_definite

Barry

On Aug 1, 2008, at 7:52 PM, Shao-Ching Huang wrote:

> Hi,
>
> I am trying to use CG to solve a singular systems (i.e. Poisson
> equation with periodic conditions on all boundaries).
>
> The code works when I use GMRES, but it diverges when I switch CG.
>
> Since the null space is a constant vector, in the code I have:
>
>   KSP ksp;
>   MatNullSpace nullspace;
>   ...
>   MatNullSpaceCreate(MPI_COMM_WORLD, PETSC_TRUE, 0, PETSC_NULL,  
> &nullspace);
>   KSPSetNullSpace(ksp, nullspace);
>   MatNullSpaceRemove(nullspace, f->p_rhs, PETSC_NULL);
>
>   KSPSetFromOptions(ksp);
>   KSPSetUp(ksp);
>   KSPSolve(ksp, f->p_rhs, f->phi);
>
> [f->p_rhs is the RHS vector. f->phi is the solution vector.]
>
> When I use "-ksp_type gmres", it converges (shown by -ksp_monitor).
>
> However, when I switch to "-ksp_type cg", it diverges.
> In this case (cg), "-ksp_converged_reason" says:
>
>  Linear solve did not converge due to DIVERGED_INDEFINITE_PC  
> iterations 1
>
> I also try adding "-sub_pc_factor_shift_nonzero 0.0000000001" but the
> CG case still fails.
>
> Am I missing some step in handling the null space when using CG?
>
> Thanks,
>
> Shao-Ching Huang
>
>