On Mon, Feb 11, 2008 at 08:05:57AM -0600, Matthew Knepley wrote: > On Feb 11, 2008 5:05 AM, Anders Logg <[EMAIL PROTECTED]> 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 tried to put in a discontinuous coefficient in the DOLFIN Poisson demo and the solution looks fine. -- Anders _______________________________________________ DOLFIN-dev mailing list [email protected] http://www.fenics.org/mailman/listinfo/dolfin-dev
