[petsc-users] multi-grid for anisotropy

[Matthew Knepley]

On Tue, Sep 29, 2015 at 3:02 AM, Justin Chang <jychang48 at gmail.com> wrote:

> Hi all,
>
> I think I have asked a previous question related to this, and have seen
> other threads about related issues, but say I have this anisotropic
> dispersion tensor:
>
> D = (D_m + alpha_L*norm(v))*Identity + (alpha_L -
> alpha_T)*outer(v,v)/norm(v)
>
> The anisotropy of this tensor comes from the ratio of alpha_L/alpha_T and
> velocity v, and is mesh independent. That said, can tuning the multi-grid
> preconditioners parameters of GAMG/HYPRE/etc help prevent things like
> negative concentrations and violations of the discrete maximum principles?
>

In my view (Barry and Jed can tell me I am wrong), this is the job of the
interpolator. You already guarantee the bound
in your smoothers, so this is where is gets messed up. You can certainly
use your own interpolators in GMG. GAMG
is harder since it makes the aggregates, and I do not understand Hypre.

The way I imagine doing this is to setup the interpolation as a saddle
point problem, where the thing you want to enforce
is a constraint, so the interpolation is a solve instead of jsut a matrix.
This is exactly what I did for my Phd when we transferred
fluid-structure solutions from one mesh to another.

  Thanks,

     Matt


> Thanks,

-- 
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
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