A point-matching method for solving volume integral equations with inhomogeneous media

Volume integral equations (VIEs) are usually solved by the method of moments (MoM) with the Schaubert-Wilton-Glisson (SWG) basis function. The SWG basis function requires conformal meshes in geometric discretization and may be inconvenient for inhomogeneous problems. In this work, we propose a point-matching method for solving the VIEs without using any basis function. The method can allow an inhomogeneity of materials in each tetrahedron and may greatly facilitate the meshing of geometries. A numerical example for electromagnetic scattering by a multilayered dielectric object is presented to demonstrate the effectiveness of the method.