[petsc-users] Geometric MG as Solver & Preconditioner for FEM/Spectral/FD

[Shiva Rudraraju]

> You can use one discretization for evaluating residuals, but then use an
embedded low-order discretization to apply the correction.  See "defect
correction" in Achi's multigrid guide or in Trottenberg.
Thanks Jed and Matt. Will check out these references.


On Fri, Oct 18, 2013 at 11:28 AM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> Shiva Rudraraju <rudraa at umich.edu> writes:
>
> >>I did unstructured hexes.  You still haven't said what you'll use for
> relaxation.
> >  High-order discretizations tend to have poor h-ellipticity, so they
> either
> > need heavy smoothers or a correction based on a discretization with
> better
> > h-ellipticity.
> > Quite frankly, I was not aware of the poor h-ellipticity of higher order
> > elements and I was assuming I would use the regular GS/GMRES/etc for
> > relaxation. I looked up h-ellipticity of higher order elements and now
> this
> > adds to my worries :(. I may be asking for too much here.... but what do
> > you mean by heavy smoothers? or correction based on a discretization?.
>
> You can use one discretization for evaluating residuals, but then use an
> embedded low-order discretization to apply the correction.  See "defect
> correction" in Achi's multigrid guide or in Trottenberg.
>
> The paper I mentioned earlier was doing something simpler and less
> intrusive: assemble the embedded low-order operator and feed it to
> algebraic multigrid, but evaluate residuals matrix-free using the
> high-order discretization.  But if you have a reasonable geometric
> hierarchy, the defect correction schemes are better.
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20131018/d6f1a9bb/attachment.html>