Numerical solutions of integral equations for electromagnetics

Integral equations have proven their popularity for the electromagnetic analysis of radiation and scattering problems. The workhorse equations are the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE) [1,2]. The development of these equations will be reviewed in the following for perfectly conducting targets and homogeneous dielectric targets. When applied to certain closed surfaces, the original equations exhibit uniqueness difficulties at frequencies where the target surface coincides with a resonant cavity [3]. In addition, the original EFIE and MFIE also fail under certain circumstances for electrically small bodies. Alternate integral equations were proposed to remedy those situations, and these will also be summarized in the following section. In addition, we describe the numerical solution of these equations and report the progress made in recent years associated with the use of hierarchical vector basis functions, and the recent use of singular basis functions.