用正交函数展开法解介质双球静电问题

Analysis of Electrostatic Problem of Two Dielectric Spheres by Orthogonal Harmonic Expansion

本文讨论了一般介质边界条件经逆矢径变换后的表达式，证实对介质双球静电问题若采用逆矢径变换法求解，最终将得到本征展开系数的一个无穷维线性耦合方程组，实际求解困难，本文提出用正交函数展开法求解介质双球静电问题，获得精确结果，数值结果进一步验证了Ｌａｐｌａｃｅ方程本征解的加法定理。

General dielectric boundary conditions for electrostatic problem in inversion transformation are described. It is shown that solution to electrostatic problem of two dielectric spheres with cloesd form cannot be reached by using inversion. Multiply-multipole method is applied to the problem and accurate results are obtained. The numerical results confirm the addition theorems for spherical harmonics.