Electric and magnetic combined source integral equations for electromagnetic transmission problems

Various combined source integral equation (CSIE) formulations are developed for the analysis of electromagnetic scattering by three-dimensional arbitrarily shaped homogeneous penetrable objects. The considered CSIE formulations include the classical “electric” CSIE proposed by Mautz and Harrington in 1979, and its dual “magnetic” CSIE as well as mixed “electric–magnetic” and “magnetic–electric” CSIE formulations. Novel discretization schemes by utilizing the primary (Rao–Wilton–Glisson, RWG) and the dual (Buffa–Christiansen, BC) functions are applied to convert the integral equations into matrix equations. These schemes avoid the numerical problems that would appear if the CSIE formulations were discretized with the conventional Galerkin method using the RWG functions only.