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Message #06132
Laplace equation in 2D
Dear Dolfin developers
I am trying to learn to use dolfin for a relatively simple
problem, but there are a couple of things that I haven't been able
to figure out from the manual.
What I am trying to do is solving Laplace equation in the geometry
illustrated below (in 2D) in order to find the electrostatic potential:
_________
| |
| |
_________|_______|_________
| Dielectric |
|__________________________|
V = const
I have Dirichlet BC on all boundaries.
1) How do you deal with the internal boundary between the dielectric
and vacuum in FEM ? Here the solution has a discontinuity in the
normal derivative.
2) The variational form of Laplace equation is:
a = dot(grad(v), grad(u))*dx = 0
However, the LinearPDE function takes both an "a" and an "L"
(see eg the poisson demo.py). What am I missing here ?
3) Having obtained a solution, how do I get its value at an arbitrary
position ? Have tried the eval attribute, but it complains about
the input type (I tried with an array).
I hope that you have time to clarify these things for me.
Thanks in advance.
Kristen Kaasbjerg
PS: I am using the python wrappers.