Asymptotic Green's Functions for Source and Field Points on a Faceted Convex Surface

The uniform geometrical theory of diffraction (UTD) solution for mutual coupling is applied to a faceted conducting convex surface to predict the asymptotic Green's functions for electric and magnetic fields at a field point due to infinitesimal electric and magnetic currents at a source point, both points being on the surface. A quadratic surface mapping is used to introduce surface curvature to triangular facets. A previously developed geodesic ray tracing algorithm is applied to identify geodesic ray paths between source and field points on a faceted convex surface. The geometrical parameters extracted from the surface are used to apply the UTD solution to predict the asymptotic Green's functions. The results of the application of UTD to a faceted convex surface is validated with those of the analytical UTD solution for a circular cylinder and a sphere. This approach is applicable to arbitrary faceted convex surfaces.