Very newbie question: Dirichlet boundary conditions

Question

Hi,

I'm a newbie to Fenics (installed it yesterday) and I have a very fundamental question. I will try to make it simple. Suppose the case of the temperature distribution on a 2D square plate with constant temperatures at its four faces according to the equation ∇²T = 0. How do I specify those temperatures as BCs? Suppose the temperatures are Te = 50, Tn = 100, Tw = 150 and Ts = 75, where "e", "n", "w" and "s" are east, north, west and south faces respectively. I have seen examples where one Dirichlet boundary is specified, but don't know how to specify more than one of those BCs.

Any help is much appreciated. Thanks.

Fausto

Answer 1

Define a Dirichlet boundary condition for each side and then pass all the bcs to the solve method, i.e.

class East(SubDomain):
    def inside(self, x , on_boundary):
       return near(x[0], 1.0)

class West(SubDomain):
    def inside(self, x , on_boundary):
       return near(x[0], 0.0)

class North(SubDomain):
    def inside(self, x , on_boundary):
       return near(x[1], 1.0)

class South(SubDomain):
    def inside(self, x , on_boundary):
       return near(x[1], 0.0)

bcs = [DirichletBC(V, Constant(50), East()),
       DirichletBC(V, Constant(100), North()),
       DirichletBC(V, Constant(150), West()),
       DirichletBC(V, Constant(75), South())]

a =...
L = ...
u = Function(V)
solve(a == L, u, bcs=bcs)

Comments

Brilliant! With your hints I put together a script that worked as a charm at the first attempt. Better yet, it produced the correct answer.

The shape of the plate bugged me a little though. It's kind of twisted/bent on the borders when it should be a perfectly plane surface. I wonder where my mistake is, or what I missed.

Thanks!

Fausto