dolfin team mailing list archive

["Matthew Knepley" <knepley@xxxxxxxxx>]

On Feb 11, 2008 10:27 AM, Anders Logg <logg@xxxxxxxxx> wrote:
>
> On Mon, Feb 11, 2008 at 08:05:57AM -0600, Matthew Knepley wrote:
> > On Feb 11, 2008 5:05 AM, Anders Logg <logg@xxxxxxxxx> wrote:
> > > On Mon, Feb 11, 2008 at 11:54:14AM +0100, Kristen Kaasbjerg wrote:
> > > > Hi dolfin users
> > > >
> > > > I am trying to use dolfin for the following simple
> > > > electrostatic problem:
> > > > - finding the electrostatic potential in a domain composed
> > > >   of two subdomains with different dielectric constants.
> > > >   This amounts to solving Laplace equation with appropriate
> > > >    BC's.
> > > >
> > > > One thing that I cannot figure out how to do is to tell dolfin
> > > > that I have 2 subdomains and on the internal boundary between
> > > > these two domains, the normal derivative of the potential has
> > > > a discontinuity given by the difference between the dielectric
> > > > constants.
> > > > Could anyone give me a hint of how to approach this problem
> > > > with dolfin ? I am relatively unexperienced to FEM so a nice
> > > > reference would also be welcome.
> > > >
> > > > Regards
> > > > Kristen
> > >
> > > The easiest thing to do (if there is just a coefficient in your
> > > problem that is discontinuous) is to just define a Function for the
> > > dielectric constant and make it discontinuous. Then just plug it in to
> > > your equation.
> > >
> > > Look in the demos (under src/demo/pde) for how to define a function.
> > >
> > > For example, if some parameter is 0 or 1 depending on whether x is
> > > below or above 0.5, then just do something like this in eval():
> > >
> > >   if (x[0] > 0.5)
> > >     return 1.0;
> > >   else
> > >     return 0.0;
> >
> > This is not going to give the correct answer unless you do the boundary integral
> > that comes from the integration by parts. Or am I missing something?
> >
> >    Matt
>
> I don't know. Maybe I'm ignorant but if you have -div(a*grad(u)) = f,
> then it looks to me that you may just go ahead and integrate by parts
> even if the coefficient a is discontinuous. grad(u) is already
> discontinuous (for the discretization) so I don't see the difference.

I do not agree. There is a jump term along the boundary. You can get
some solution without it, which looks alright, it is just wrong.

   Matt

> I tried to put in a discontinuous coefficient in the DOLFIN Poisson
> demo and the solution looks fine.
>
> --
>
> Anders
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What most experimenters take for granted before they begin their
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