New formulation and iterative solution for low-frequency volume integral equation

Abstract

An alternative E-field volume integral equation (VIE) is given for low-frequency applications. This low-frequency VIE is first solved at electrostatics using the method of moments (MoM) and then corrected by adding the contribution of the vector potential term. The reason why E-field VIE does not break down at low frequencies and even at statics is also explained. The issue of low-frequency inaccuracy is discussed as well. In addition, it can be proven by the extinction theorem that solving static VIE is equivalent to solving Poisson's equation. This low-frequency VIE can be solved more efficiently than directly solving the original VIE because the volume integral is replaced by a surface integral so that unknown count in the matrix equation can be reduced. Numerical results by this new low-frequency VIE agree well with those by Mie series. The applicable frequency range of this method is also discussed by investigating the behavior of eigenvalues. Last, low-frequency inaccuracy is also observed for the scattering of a dielectric sphere under the illumination of an axis-symmetric wave.