FMM solutions of finite element-boundary integral implementations for antenna modeling involving curved geometries

Finite element-boundary integral formulations have been successfully applied to the analysis of cavity-backed antennas that possess fine details as is the case of with slot arrays, spirals, log-periodic and other broadband antennas. In those cases, the computational demand of the boundary-integral is large compared to that of the finite-element volume sub-system. Therefore, a fast integral method is attractive to speed-up the solution algorithm. For cavity-backed antennas recessed in an infinite ground plane, the boundary integral formulation is quite straightforward. However, if the cavity resides in a curved platform, periodic boundary conditions cannot be applied for array modeling. In this paper we present an approximate Fast Multipole Method (FMM) solution to problems involving antennas recessed on doubly curved platforms. The approach is to use the halfspace Green´s function as if the cavity resides in a flat ground plane. Clearly the limit of this approximation is applicable for geometries which are not highly curved. The region of validity of the approximation is investigated.