Dyadic multipole-based generalized source integral equations

The approach of multipole-based generalized source integral equation (GSIE) formulations for the scattering by essentially-convex impenetrable objects is extended to dyadic problems. This is demonstrated through the two-dimensional (2-D) problem of transverse-electric (TE) scattering. For this case, the principles of multipole-based generalized source design are utilized within the framework of dyadic TE-GSIEs introduced recently for reflective shield sources. The derivation of the dyadic auxiliary contribution to the modified Green's function is presented in detail and is shown to provide similar superior low-rank compressibility of off-diagonal method-of-moments' matrix blocks as its transverse-magnetic counterpart, while maintaining error controllability. The extension enables the treatment of impedance boundary scatterers in 2-D and is a crucial stepping stone toward a full three-dimensional vector formulation that is expected to exhibit enhanced low-rank compressibility for a broad range of scatterer geometries.