Infinite boundary elements for electromagnetics

Consider a two-dimensional plane wave transverse magnetic mode scattering from a perfectly electric conducting ground plane. Let the ground plane be of infinite extent and comprise two regions, a near field and a far field. In the far field, let the ground plane be flat and let us choose the co-ordinates (x, y) such that it lies on the axis y = 0. Over the interior region, let the profile of the ground plane change such that it can lie partially above and also partially below the axis y = 0. Finally, let us assume that the source of the excitation lies above the ground plane. To model this general class of problems, a method of moments electric field integral equation formulation is proposed which uses infinite boundary elements to model the far field and boundary elements to model the near field. In the far field, the field variable is approximated by the highest order terms in the far-field asymptotic expansion. The integrals over the infinite boundary elements are infinite in extent and contain oscillatory terms and hence require special integration rules. The formulation is tested for the specific problem of a semi-circular cylindrical protrusion of radius a lying above an infinite flat ground plane, such that ka = 1 where k is the wave number. This problem is chosen because it has an analytic solution in the form of a Bessel function expansion; hence, the accuracy of the formulation can be tested. In particular, the radar cross section results for various angles of incidence of the plane wave source are calculated and compared with analytic results. Copyright (c) 2007 John Wiley & Sons, Ltd.