Well-conditioned Muller formulation for electromagnetic scattering by dielectric objects

Numerical solution of electromagnetic scattering by homogeneous dielectric objects with the method of moments (MoM) and Rao-Wilton-Glisson (RWG) basis functions is discussed. It is shown that the low-frequency breakdown associated to the MoM solution of scattering by dielectric objects can be avoided by the classical Muller formulation without the loop-tree or loop-star basis functions. Two variations of the Muller formulation, T-Müller and N-Muller, are considered. It is demonstrated that only the N-Muller formulation with the Galerkin method and RWG functions gives stable solution. Discretization of the N-Muller formulation leads to a well-conditioned matrix equation and rapidly converging iterative solutions on a wide frequency range from very low frequencies to microwave frequencies. At zero frequency, the N-Muller formulation decouples into the electrostatic and magnetostatic integral equations.