Meshfree Solutions of Volume Integral Equations for Electromagnetic Scattering by Anisotropic Objects

Volume integral equations (VIEs) are indispensable for solving inhomogeneous or anisotropic electromagnetic (EM) problems by integral equation approach. The solution of VIEs strongly relies on the discretization of volume integral domains, and tetrahedral elements in discretization are usually preferred for arbitrary geometric shapes. Unlike discretizing a surface domain, discretizing a volume domain is very inconvenient in practice, and special commercial software is needed in general even for a simple and regular geometry. To release the burden of descretizing volume domains, especially to remove the constraint of mesh conformity in the traditional method of moments (MoM), we propose a novel meshfree scheme for solving VIEs in this paper. The scheme is based on the transformation of volume integrals into boundary integrals through the Green-Gauss theorem when integral kernels are regularized by excluding a small cylinder enclosing the observation node. The original integral domain represented by the object is also expanded to a cylindrical domain circumscribing the object to facilitate the evaluation of boundary integrals. The singular integrals over the small cylinder are specially handled with singularity subtraction techniques. Numerical examples for EM scattering by inhomogeneous or anisotropic objects are presented to illustrate the scheme, and good results are observed.