三维电磁波体积分方程的快速多极子算法

该文提出用快速多极子方法(FMM)求解三维非均匀介质散射体的电磁散射，将以往边界方程的FMM推广到三维矢量电磁波体积分方程(3DV-FMM)，推导了一级和多级快速多极子的三维体积分离散公式。这一方法减少了计算机存储要求，并从量级上降低了共轭梯度迭代求解的矩量法的计算量。在计算中，选用函数作基函数，达到相当好的收敛性．本文用3DV-FMM数值计算了三维均匀和非均匀介质立方体，多个介质体的双站散射截面(RCS)，以及任一剖面上的等效电流体密度分布。计算结果与矩量法相吻合，但在计算内存和CPU时间上要节省得多。本文的方法也可为三维电磁波逆散射的反演算法研究给出正向模拟的快速计算。

THE FAST MULTIPOLE METHOD OF THREE DIMENSIONAL ELECTROMAGNETIC WAVE VOLUME INTEGRAL EQUATION(3DV-FMM)

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.