[petsc-users] Problem with -pc_type gamg

[Alexander Grayver]

Randall,

I can add few more practical notes on EM problem.

GAMG doesn't work efficiently on curl curl problems because of mentioned 
(Jed's message) reasons. One would need to consider null-space 
explicitly as in [1] or [2].
Furthermore, even mild grid stretching slows down convergence thus 
semi-coarsening is another essential thing to consider. Here you can 
find some tests:
http://proceedings.fyper.com/eccomascfd2006/documents/560.pdf

1. Hiptmair R. 1998. Multigrid method for Maxwell’s equations. SIAM 
Journal on Numerical Analysis 36, 204–225
2. Arnold D.N., Falk R.S. and Winther R. 2000. Multigrid in H(div) and 
H(curl). Numerische Mathematik 85, 197–217.

On 15.09.2012 00:18, Jed Brown wrote:
> On Fri, Sep 14, 2012 at 5:11 PM, Randall Mackie <rlmackie862 at gmail.com 
> <mailto:rlmackie862 at gmail.com>> wrote:
>
>     If you would be interested, I could dump the matrix and send it to
>     you to see if you can figure out a fix.
>     I have no idea if GAMG would even be a good preconditioner (this
>     is a ill-conditioned EM
>
>
> This is very important information. What specific EM system are you 
> solving? Is the shift, positive, negative or complex? What 
> discretization. What scale do you need to solve and how 
> performance-sensitive is the application.
>
> These problems can be huge rabbit holes for multilevel methods, 
> depending on the parameter range and necessary scale. Efficient 
> solvers will require extra work since black-box methods cannot cheaply 
> determine things like the large curl-curl null space.
>
> PETSc folks: We should make an example using auxiliary space 
> preconditioning so that we can have an FAQ on this.
>
>     problem), but
>     I have reasons to believe that MG in general, if done right, would
>     work. I was hoping to test this
>     with the GAMG preconditioner, without having to do too much work
>     on interpolation operators, etc.
>
>


-- 
Regards,
Alexander

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