We will consider the half filled waveguide given in Figure 4.1, “Inhomogeneous Waveguide Geometry”. The waveguide has square sides with length 1. The lower half is filled with a dielectric whose relative permittivity is 4.0. This is an inhomogeneous waveguide. We will solve for the electric field in the waveguide.

Figure 4.1. Inhomogeneous Waveguide Geometry

The input file is given below. I think it is pretty straight forward.

# points - all fixed
6
0 0 0 0 1
1 1 0 0 1
2 1 0.5 0 1
3 1 1 0 1
4 0 1 0 1
5 0 0.5 0 1
# edges - all Dirichlet except edge 6
7
0 0 1 1
1 1 2 1
2 2 3 1
3 3 4 1
4 4 5 1
5 5 0 1
6 5 2 0
# boundaries
2
# outer boundary
6 1 1 1 0
0
1
2
3
4
5
# dielectric boundary, mu=1, epsilon=4
4 1 1 4.0 0
0
1
6
5

We will discuss how to change permittivity and permeability in the next section.