[petsc-dev] -pc_type gamg for vector PDE

[Jed Brown]

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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