On the Method of Moments Solutions for Volume Integral Equations With Inhomogeneous Dielectric Media

In the method of moments (MoM) for solving volume integral equations (VIEs), one usually approximates the unknown flux density with the Schaubert-Wilton-Glisson (SWG) basis function and has to assume a homogeneous material in each tetrahedral element. Also, the volume charge density is equivalently represented with a lower-order basis function, and there exist surface charges at the tetrahedral faces separating dissimilar media. These features could bring on certain numerical errors and inconvenience of implementation. In this letter, we suggest that the dyadic Green's function in the VIEs keep its original form without moving the del operator onto the basis and testing functions. In this way, the above problems can be removed although an efficient treatment for hypersingularity is required. With our technique of treating the hypersingularity, the scheme is feasible and shows certain merits as demonstrated in numerical examples.