How to solve an eigenvalue problem?

Hello,

This is my first time to use COMSOL. I want to solve an eigenvalue problem on a geometry : a unit square with a circle inside. I attached file.

div ( ep^(-1)* grad u)=lambda * u

where ep =1 outside the circle and ep=(1-lambda^(-1))^(-1) inside circle ,

u is continuous on the interior boundary (the boundary of circle) , and

n (ep * grad u) |_outside = n (ep* grad u) |_inside on the interior boundary.

on the boundary of the square,

u is periodic on the up and down sides, and is Floquet periodic on the left and right sides, i.e., u(x_left)=u(x_right)*exp^(i*k), k is a specific real number, for example k=1.

My questions are
1) how to set the interior boundary condition?

2) it is a nonlinear eigenvalue problem. I don't know if the software can solve it. Because it always gives me the error message : undefined value found.

3) how to set the Floquet boundary condition?


Sorry for so many problems. But it really bothered me a lot.
I am using 4.2 version. Please check my attachment.


Thanks a lot.

Yue