A Frequency Stable Volume Integral Equation Method for Anisotropic Scatterers

Abstract

We introduce a volume integral equation method for the numerical solution of the electromagnetic scattering problem from electrically anisotropic inhomogeneous objects. The problem’s unknown, that is the sum of the conduction and polarization current densities, is decomposed in terms of its loop, star and facet components. Suitable strategies have been implemented to enforce the uniqueness of this discrete representation. Furthermore, through a convenient scaling of the unknowns, we also make the present method immune to the low-frequency breakdown problem, showing its stability regardless of the operating frequency. This approach has been extensively validated against the null-field method by analyzing the scattering from a uniaxial dielectric sphere and a uniaxial dielectric slab and comparing the scattered electric field in both the near and far zones. The condition number of the scattering problem consisting of a slab with an assigned conductivity tensor is also monitored as a function of the exciting frequency.