Meshless-based multilevel fast multipole algorithm for solving volume integral equations with complex media

Electromagnetic (EM) problems with complex media are formulated by volume integral equations (VIEs) 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 solution requires high-quality conforming meshes, resulting in a high cost in geometric discretization. In this work, a point-matching meshless method is proposed to discretize the VIEs and it uses discrete points instead of meshes to represent an object domain. Also, the method chooses the current densities as the unknown functions to be solved so that the integral kernels are free of material parameters. For electrically large problems, we incorporate it with the multilevel fast multipole algorithm (MLFMA) to accelerate the solving process. Numerical examples are presented to demonstrate the method and good results have been observed.