Fast Multipole Acceleration for Solving Volume-Surface Integral Equations

Electromagnetic (EM) problems with conducting and penetrable media are formulated by volume-surface integral equations (VSIEs) which allow inhomogeneous and anisotropic materials. Traditionally, the VSIEs are solved by the method of moments (MoM) with Rao-Wilton-Glisson (RWG) and Schaubert-Wilton-Glisson (SWG) basis functions. We propose a point-matching scheme to discretize the VSIEs. The point-matching scheme does not rely on any basis and testing functions and allows the use of nonconforming meshes. Also, the integral kernels are free of material parameters by selecting current densities as unknowns. To accelerate the solution for electrically large problems, we incorporate the scheme with the multilevel fast multipole algorithm (MLFMA) and a typical numerical example is presented to validate its effectiveness.