dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

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;

-- 
Anders