Approximate Boundary Conditions for Thin Structures

In wave propagation problems thin structures are often replaced by boundaries of zero thickness, in order to reduce the numerical mesh. The reduction of thickness has to be incorporated in the approximate boundary condition applied to the interface. This paper presents a modification of an approximate boundary condition originally introduced by Mitzner. The modified Mitzner condition can be applied to the boundary of zero thickness and it is more general and accurate than the commonly used impedance boundary condition. For frequency domain solvers the condition is as easy to implement as the impedance boundary condition. It is tested and compared to the impedance boundary condition for planar and cylindrical structures. The new condition is exact at normal incidence on a planar structure.