[petsc-dev] -pc_type gamg for vector PDE

[Alexander Grayver]

Hello petsc team,

I solve 3D vector Helmholtz equation like following:

\nabla \times \nabla \times E + i\omega\mu\sigma E  = -J

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