THE FAST MULTIPOLE METHOD OF THREE DIMENSIONAL ELECTROMAGNETIC WAVE VOLUME INTEGRAL EQUATION(3DV-FMM)
三维电磁波体积分方程的快速多极子算法

In this paper, a Fast Multipole Method (FMM) is developed to solving the scattered fields from three dimensional (3D) inhomogeneous dielectric scatterers. This generalized FMM is applied to the volume integral equation (3DV-FMM). The discrete formula of the volume integral equation was derived by the basic FMM and multi-level FMM. The FMM approach significantly reduces both the complexity of a matrix-vector multiplying and memory requirement. In calculation, the delta function is chosen as the basis and perfect convergence to the FMM results is achieved. As a typical example, the bistatic RCS of cubic scatterers with homogeneous, or inhomogeneous permittivity is calculated numerically. Distribution of electric currents on the cross-section of a dielectric cube is also obtained. Comparing with conventional moment method, the results of 3DV-FMM are exactly matched. However, the computer memory and CPU time are greatly reduced by using the 3DV-FMM. This method is applicable to the forward numerical simulation for 3D electromagnetic inverse problem.