Iterative solution to the scattering by hemispherical bosses on a conducting surface

Analytic solution to the problem of scattering of a plane electromagnetic wave by a system of hemispherical bosses on a perfectly conducting surface has-a variety of engineering applications. For example, the electromagnetic scattering by three-dimensional rough surfaces or partially buried objects can be simulated by a system of spheres [1]. Exact analytic solution to the problem of scattering by a system of hemispherical bosses has been obtained by using the translational addition theorem for vector spherical wave functions [1]. The required computer time and memory to invert the resulting system matrix increases rapidly with the number of hemispherical bosses. In this paper we replace the array of hemispherical bosses by full spheres in the absence of the conducting plane, but with the given incident plane wave and also a supplementary, image plane wave, chosen such that the boundary conditions for the total field are satisfied at all points where the conducting plane is located in the original problem. Next, we apply the iterative solution where it requires the held scattered by each sphere due only to the primary and secondary incident fields, which acts as an incident field on the other spheres [2]. Hence this iterative process continues until the solution converges. Numerical results are plotted for the normalized backscattering cross section patterns for various angles of incidence.<>