dolfin team mailing list archive

["Garth N. Wells" <g.n.wells@xxxxxxxxxx>]

Anders Logg wrote:
> Yes, look at the demo in src/demo/pde/dg/. (It contained some test
> code before that I just removed.)
>
> Yes, you can take the avg() and jump() of an arbitrary function (but
> there may be some limitations that I can't recall right now).
>
> It currently only works in 2D. In 3D, it only works in principle but
> not in practice... :-)
>
> What is currently holding us back from getting everything in place is
>
>     (1) Decide on a numbering scheme for the mesh and write this down
>         firmly in the manual
>
>     (2) Implement this in FFC and DOLFIN
>
>     (3) Porting FFC to generate UFC code

There is another problem. The approach using the tensor contraction is 
not practical, especially for vector equations. FFC generate 96 cases 
(in 3D) which takes way too long and produces very large output.

Garth

> /Anders
>
>
> On Mon, Jan 29, 2007 at 04:08:06PM +0100, Johan Hoffman wrote:
> > Is there a demo-form file available for using these operators? Can one
> > take the avg and jump of an arbitrary function?
> >
> > /Johan
> >
> >
> >
> > > What we have implemented for DG is the ability to define integrals
> > > over interior facets that have contributions from both sides of the
> > > facet, so you can write
> > >
> > >     v('+')*v('-')*avg(v)*jump(u, n)...
> > >
> > > It's a little different from what you have in that the integral is
> > > over all interior facets in the mesh, not just along some given
> > > surface.
> > >
> > > Perhaps you could extract all the cells in the mesh that border to the
> > > common surface, so instead of having some interior surface, you have
> > > an interior mesh that contains the surface and each interior facet in
> > > that mesh connects to exactly two cells, one on each side.
> > >
> > > /Anders
> > >
> > >
> > > On Thu, Jan 18, 2007 at 09:24:01AM +0100, Johan Hoffman wrote:
> > > > Garth and Anders,
> > > >
> > > > I am interested in solving a problem where I a priori specifies an inner
> > > > surface (aligned with cell faces) where the solution is discontinuous.
> > > > The
> > > > coupling of the solution over the discontinuity is taken cared of by a
> > > > surface integral over that inner surface (like a penalty term).
> > > >
> > > > For this I expect to need:
> > > >
> > > > (1) a data structure with "double nodes" at a predefined surface (=
> > > > collection of nodes/faces).
> > > >
> > > > (2) for the nodes on the surface; the ability to assemble only
> > > > contribution from either side of the surface for the "double nodes"
> > > > respectively (where the two sides of the surface may be represented by a
> > > > MeshFunction for example).
> > > >
> > > > (3) a surface integral defined over an inner surface.
> > > >
> > > > I suspect that some parts of (1)-(3) is already in place, as part of the
> > > > DG work? What remains to be done to handle this problem?
> > > >
> > > > /Johan
> > > >
> > > >
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