Formulation of surface integral equations for metallic, dielectric and composite objects

The surface integral equation method is one of the most popular numerical methods for the electromagnetic analysis of composite metallic and dielectric structures. In this paper, the authors seek the "optimal" surface integral equation formulations for closed metallic, homogeneous and piecewise homogeneous dielectric and composite objects by studying the properties of the integral equations. The goal is to develop formulations in which all unknown quantities are well tested in the Galerkin method and the discretized matrix equation has good spectral properties leading to rapidly converging iterative solutions. The results show that by deriving the equations so that they map the currents onto itself and are directly tested in the same space as the unknowns are expanded can significantly improve conditioning of the matrix equation.