[CIG-CS] Particle problems and Semi-Lagrangian Schemes for Gamr

[Matthew Knepley]

2011/5/31 Walter Landry <walter at geodynamics.org>

> Back to the list.
>
> mspieg <mspieg at ldeo.columbia.edu> wrote:
> > Hi Walter,
> >   Mike is quite right, I've been using Semi-Lagrangian methods for ages
> in
> > both finite volume, and more recently finite element calculations.  They
> have
> > a lot of nice properties, but can be computationally expensive in
> elements
> > (depending on how they're implemented).  However, because they advect
> > continuous fields, they will scale linearly with your degrees of freedom
> (or
> > possibly quadrature points) (and they don't have CFL stability issues).
>
> This is very interesting.  What do you mean that they are expensive in
> elements?  I would expect the cost of advection would be dwarfed by
> the cost of solving Stokes.
>

I suspect you are correct for the exceedingly simple geometry of GALE. If
GAMR
is just octrees, you are also right AND there is code for this in PETSc
already.

   Matt


> Also, I found Katz et. al. [1], which includes a mid-ocean ridge
> model.  That uses finite volumes.  Do you have any results for a
> finite-element semi-lagrangian scheme I can look at?
>
> > I actually have a demonstration T-Dependent viscosity Rayleigh-Benard
> problem
> > with semi-lagrangian advection implemented in hybrid FEniCS/PETSc codes
> if
> > you're interested.
>
> Cheers,
> Walter Landry
> walter at geodynamics.org
>
>
> [1] Numerical simulation of geodynamic processes with the Portable
>    Extensible Toolkit for Scientific Computation
>    R.F. Katz, M.G. Knepley, B. Smith, M. Spiegelman, E.T. Coon,
>    Physics of the Earth and Planetary Interiors 163 (2007) 52�#|68
>
> _______________________________________________
> CIG-CS mailing list
> CIG-CS at geodynamics.org
> http://geodynamics.org/cgi-bin/mailman/listinfo/cig-cs
>
>


-- 
What most experimenters take for granted before they begin their experiments
is infinitely more interesting than any results to which their experiments
lead.
-- Norbert Wiener
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://geodynamics.org/pipermail/cig-cs/attachments/20110531/5bd0e253/attachment.htm