Whoops, sorry I missed this.
It looks like you have a largish \omega\mu\sigma because, as Jed mentioned, one
would not expect GAMG to work well for the curl-curl part.
A few things to try:
1) '-pc_gamg_type sa' will provide what should be a better solver for SPD
problems.
2) Try:
-pc_type hypre ! instead of -pc_type gamg
-pc_hypre_type boomeramg
-pc_hypre_boomeramg_strong_threshold 0.6
3) You say 'staggard' but I just see E here. Do you have E on faces? I forget
how staggering works here. If E is cell centered then you have a system of 3x3
blocks (with the right ordering) and GAMG might benefit from setting the block
size to tell it this:
MatSetBlockSize(mat,3);
And Jed's answer addresses your 2nd question about null-space. These solvers
will degrade as \omega\mu\sigma gets smaller.
Mark
On Jan 19, 2012, at 5:37 PM, Jed Brown wrote:
> On Wed, Jan 18, 2012 at 08:22, Alexander Grayver <agrayver at gfz-potsdam.de>
> wrote:
> Hello petsc team,
>
> I solve 3D vector Helmholtz equation like following:
>
> \nabla \times \nabla \times E + i\omega\mu\sigma E = -J
>
> Multigrid methods for curl-curl problems are pretty specialized. ML and Hypre
> have support for specific discretizations, I don't know if they support an
> imaginary shift. The PETSc interface to these packages does not currently
> support their special Maxwell interfaces.
>
> The methods are generally based on edge relaxation or auxiliary space
> preconditioning, see Hiptmair or Arnold, Falk, and Winther for the
> mathematical background.
>
>
> I use structured staggered grid and FD. The solution is a vector that
> consists of three parts E = {Ex Ey Ez}. The operator is symmetric matrix with
> complex numbers on diagonal.
> I'm interested in solving this system with iterative techniques. I applied
> newly presented gamg and it gives promising results, but all I did is just:
> -ksp_type tfqmr -pc_type gamg
>
> I played with different ksp_type and gamg options which are listed on PCGAMG
> doc page, but nothing improved convergence.
> Could you please guide me a bit through usage of this technique?
> The precise questions are:
> 1. Do I have to do something to say petsc that my equation is a vector
> equation? Is it important for gamg pc?
> 2. Should I take into account null-space using KSPSetNullSpace? Since it is
> well known that as \omega or \sigma get small, null-space of geometric term
> (curl curl operator) starts to dominate and system gets more ill-conditioned.
> 3. Which options for gamg may improve convergence in my case?
>
>
> Thanks a lot in advance.
>
> --
> Regards,
> Alexander
>
>
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