Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods

In this paper, formulation of the surface integral equations for solving electromagnetic scattering by dielectric and composite metallic and dielectric objects with iterative methods is studied. Four types of formulations are considered: T formulations, N formulations, the combined field integral equation formulation, and the Müller formulation. By studying properties of the integral equations and their testing in the Galerkin method, “optimal” forms for each formulation type are derived. Numerical examples demonstrate that the developed new formulations lead to clear improvements in the convergence rates when the matrix equations are solved iteratively with the generalized minimal residual method. Both the Rao-Wilton-Glisson and Trintinalia-Ling (TL) basis functions are used in expanding the unknown electric and magnetic surface current densities. In particular, the first-order TL basis functions are required in the N formulations to maintain the solution accuracy when the surfaces include sharp edges.