求解多层媒质中点源电场问题的复镜像法

求解点源与半无限大均匀媒质的电场问题可利用经典镜像法。若媒质分层均匀，则经典镜像法需要无穷多个镜像来模拟这种电场问题，这给分析计算带来一定的困难。本文所介绍的复镜像法是采用任意函数的有限项指数级数Ｐｒｏｎｙ展开来定义镜像的大小和位置，而替代经典镜像法中采用无限项Ｔａｉｌｏｒ级数展开方法。仅利用几个复镜像便可以得到高精度的计算结果。对于一般的２层媒质问题，利用８个复镜像可以达到１千个经典镜像的计算精度。

Complex image method for calculating electrostatic field in multilayer media

The classic image method has been widely used in the calculation of the field produced by point sources with an infinite homogeneous medium. However, an infinite number of images must be employed in the calculation of the field with multi layer media, which results in many difficulties. The complex image method introduced in this paper can determine the amplitude and the location of images by Prony's algorithm that develops a function into an exponential series with finite terms rather than Tailor's development with infinite terms employed in the classic image method. In general, the complex image method employs a few images to give a high accurate result. For example, solving the two layer problem, eight complex images give a accurate result that one thousand classic images can provide.