[petsc-users] GAMG

[Young, Matthew, Adam]

Jed,
When expanding the LHS, the anti-symmetric kappa terms cause mixed second-order derivatives to cancel, leaving n[\partial_{xx} + \partial_{yy} + (1+\kappa^2)\partial_{zz}]\phi + lower-order terms. Since n (density) and kappa are non-negative, I thought this would mean the operator is still elliptic. You're right that there is unavoidable anisotropy in the direction of the magnetic field.

Mark,
I'll look for that Trottenberg, et al. book. Thanks for the reference. Regarding the manual, the last sentence of the first paragraph in "Trouble shooting algebraic multigrid methods" says "-pc_gamg_threshold 0.0 is the most robust option ... and is recommended if poor convergence rates are observed, ..." but the previous sentence says that setting x=0.0 in -pc_gamg_threshold x "will result in ... generally worse convergence rates." This seems to be a contradiction. Can you clarify?

--Matt
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Matthew Young
Graduate Student
Boston University Dept. of Astronomy
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________________________________________
From: Jed Brown [jed at jedbrown.org]
Sent: Wednesday, June 10, 2015 12:42 PM
To: Mark Adams; Young, Matthew, Adam; PETSc users list
Subject: Re: [petsc-users] GAMG

Mark Adams <mfadams at lbl.gov> writes:

> Yes, lets get this back on the list.
>
> On Wed, Jun 10, 2015 at 12:01 PM, Young, Matthew, Adam <may at bu.edu> wrote:
>
>>  Ah, oops - I was looking at the v 3.5 manual. I am certainly interested
>> in algorithmic details if there are relevant papers. My main interest right
>> now is determining if this method is appropriate for my problem.
>>
>
> Jed mentioned that this will not work well out of the box, as I recall.  It
> looks like very high anisotropy.

It looks like a hyperbolic term.  If you only look at the symmetric part
of the tensor, then you get anisotropy (1 versus 1 + \kappa^2 ≅ 10000),
but we also have a big nonsymmetric contribution.