Fast Solution of Volume Integral Equations Based on Meshless Discretization

Abstract

Electromagnetic problems with inhomogeneous or anisotropic penetrable media require using volume integral equations (VIEs) to describe in the integral equation approach. The VIEs are usually solved by the method of moments (MoM) with the Schaubert-Wilton-Glisson (SWG) basis function, but the implementation may not be convenient because conforming meshes are required to define the basis function. In this paper, we propose a novel meshless method to discretize the VIEs. The method uses the Green-Gauss theorem to transform a volume integral into a boundary integral so that discretizing volume domains can be removed, resulting in a truly meshless method. For electrically large problems, we incorporate the method with multilevel fast multipole algorithm (MLFMA) to accelerate the solving process. A numerical example is presented to demonstrate the approach and its effectiveness and robustness have been validated.