How can I get different boundry conditions for the same geometry?

I'm investigating the skin effect in heterogenous conductors so I'm trying to draw proper geometry for the problem in PDEtoolbox GUI (R2013a) V1.2. I'm using nested two circles to demonstrate cros-section of a conductor. If I set formula C1+C2 I can not asssign a boundry value for the second material. If I set formula C1-C2 I can assign a boundary value for the second material this time but the mesh is not generated in C2 however I need the inner area also. How can I draw this geometry and assign two different boundary conditions for each material? In other words is it possible to solve combined PDEs for different boundary conditions in PDEtoolbox GUI?

Answer 1

[Bill Greene]

First let me make a comment about geometry construction in PDE Toolbox. C1+C2 says that you want to perform the analysis on a region that contains both C1 and C2 (I believe this is what you want). C1-C2 says that you want to perform the analysis on a region with a circular hole with size of C2 in the center (not what you want).

Now I'll comment on boundary conditions. No boundary condition is needed at the boundary between the two materials because the finite element solution approach in PDE Toolbox is based on a "weak form" of the differential equations (see this page for details http://www.mathworks.com/help/pde/ug/elliptic-pdes.html) Basically, the weak form contains no derivatives of the coefficient matrix to cause problems at material interfaces. Because a boundary condition on an "internal" boundary like the one between C1 and C2 is almost never needed in practice, there isn't a simple way in PDE Toolbox to apply such a boundary condition.

Bill