Matrix methods in potential theory and electromagnetic scattering

Abstract

Employing a conserved‐flux concept, the T‐matrix equations describing boundary‐value problems of potential theory and electromagnetic scattering are obtained without recourse to the Huygens principle or physically fictitious fields. For scattering by dielectric objects, tangential electric and magnetic fields on the surface are both represented in a single expansion, cutting the computation in half. In the low‐frequency limit the dynamical equations are shown to reduce to the static case, and numerical computations then indicate that in comparison with other approaches, the present method can achieve as much as an order of magnitude reduction in the number of equations and unknowns needed for a given accuracy. New exact relations are found between the electrostatic and magnetostatic problems, and analytical results are also obtained from the equations, with and without truncation.