[petsc-users] GAMG

[Mark Adams]

On Wed, Jun 10, 2015 at 5:02 PM, Young, Matthew, Adam <may at bu.edu> wrote:

> 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, ..."


Yea, this is confusing.  What I meant was if you have catastrophic
convergence rate then it can come from thresholding.  I should replace
"poor" with "catastrophic"


> but the previous sentence says that setting x=0.0 in -pc_gamg_threshold x
> "will result in ... generally worse convergence rates."


smaller x will generally degrade convergence rates, once you are working
"correctly" (not easy to define), but each iteration will be faster.  So
there should be a minima in terms of solve times.


> This seems to be a contradiction. Can you clarify?
>
> --Matt
> --------------------------------------------------------------
> Matthew Young
> Graduate Student
> Boston University Dept. of Astronomy
> --------------------------------------------------------------
>
>
> ________________________________________
> 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.
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20150611/492bed26/attachment.html>