Electric field integral equations for electromagnetic scattering problems with electrically small and electrically large regions

Numerically stable electric field integral equations (EFIE) are presented for electromagnetic scattering problems that may include both electrically small geometrically complex and electrically large regions. A reduced integrand is achieved by implementing quasi-static assumptions in the electrically small regions, full-wave methods in the electrically large regions, and applying appropriate coupling relations between the regions. Use of the method provides computational efficiency as well as insight into the conditions under which the electromagnetic fields within electrically small regions of the problem can be assumed to be primarily capacitive or inductive in nature. The theoretical development of the method is highlighted in this communication and then applied to examples of electrically small, inductively-loaded, and capacitively-loaded monopole antennas. The accuracy of the results is verified with two independent methods.