Fast Solution of Volume-surface Integral Equations for Conducting-anisotropic Media

Abstract

Electromagnetic problems with both conducting and anisotropic media are formulated by volume-surface integral equations (VSIEs). The conducting medium is described by a surface integral equation while the anisotropic medium is governed by volume integral equations (VIEs) and they are coupled together via produced fields. The VSIEs are usually solved by the method of moments (MoM) in which the electric current density on the conductor surface is expanded by the Rao-Wilton-Glisson basis function while the volumetric flux densities inside the anisotropic medium are represented by the Schaubert-Wilton-Glisson basis function. In this work, we use a point-matching scheme to discretize the VIEs of dielectric part and couple it with the MoM for the conducting part. We also incorporate the hybrid scheme with the multilevel fast multipole algorithm to accelerate the solving process for electrically large problems. A numerical example is provided to illustrate the approach and good results have been obtained.