4.1.1 Boundary condition at the edges of the parallel planes

At the edges of the cavity boundary-conditions have to be considered for the solution of (4.13). The Dirichlet condition

$$U\Bigr\vert _\mathcal{C}=0 \mathcal{C},$$ (4.15)

is used for closed metallic enclosure walls. The Neumann condition

$$\vec{n}\cdot\vec{\nabla}U\Bigr\vert _\mathcal{C} =0 \mathcal{C},$$ (4.16)

is used to consider open boundaries without losses, because it enforces a vanishing current flow perpendicular to the boundary edge segment. The normal vector on the edge curve $\mathcal{C}$ is $\vec{n}$.
Other boundary conditions can be considered by the introduction of excitation ports at the boundary edge in addition to one of the two mentioned boundary conditions. PMC boundary conditions (4.16) are used in Chapter 6 together with ports at the boundary to establish an interface to the external environment of the device, which enables a separate simulation of the internal and external device domains.

C. Poschalko: The Simulation of Emission from Printed Circuit Boards under a Metallic Cover