Vector Generalized Source Integral Equation Formulations in Two Dimensions

Toward the development of three-dimensional (3-D) generalized source integral equation (GSIE) formulations for electromagnetic (EM) scattering, the GSIE approach is extended for describing the two-dimensional (2-D) transverse electric (TE) surface scattering by essentially-convex objects. The TE-GSIE uses reflective convex shields with a complex surface impedance to form an auxiliary contribution to the modified Green’s dyadic (MGD). Following the source model approach, the auxiliary contributions are realized by using longitudinal magnetic current sources. It is shown that the impedance should be chosen such that the MGD exhibits a deep shadow behind the shields and strong attenuation of broadside interactions while maintaining adequacy of the formulation. For these cases, enhanced rank-deficiency of the off-diagonal moment matrix blocks, in various admissibility settings, and slow scaling of the rank, which are required for fast low-rank (LR) compression-based solvers, are demonstrated.