A meshless scheme for solving volume integral equations with inhomogeneous media

The solutions of Volume integral equations (VIEs) rely on the discretization of volumetric domains which is usually tedious. Also, the method of moments (MoM) with the the Schaubert-Wilton-Glisson (SWG) basis function does not allow a discontinuous inhomogeneity of material in tetrahedral elements and has to assume a homogeneous material in each tetrahedron for continuously inhomogeneous media. We propose a novel meshless scheme which can avoid the problems in the MoM based on the Green-Gauss theorem for solving the VIEs with inhomogeneous media. Numerical examples for EM scattering by inhomogeneous objects are presented to illustrate the scheme.