模拟镜像法求解平板导体涡流场格林函数

Simulated Image Method for Evaluating Green's Function of An Infinite Uniform Conducting Plate

为快速精确计算均匀无限大平板导体涡流场的格林函数,提出了模拟镜像方法（SIM）。对于垂直电偶极子,SIM将格林函数表示成复镜像与模拟镜像之和。对于水平电偶极子,SIM将格林函数表示成复镜像与模拟镜像之和。模拟镜像的位置由经典镜像或复镜像方法给出,其强度通过广义逆方法逼近格林函数的截断误差部分来确定,因考虑了偶极子高阶镜像作用,故当导体板的厚度与其透入深度为任意比值时,SIM的计算结果都十分精确。

In order to evaluate Green's function of an infinite uniform conducting plate rapidly and accurately, the simulated image method (SIM) is presented. When dealing with the vertical electric dipole, the Green's function is expressed analytically by the sum of two terms, i. e. finite number of classical images and simulated images by SIM. As for the horizontal electric dipole, SIM decomposes the Green's function into the complex images and the simulated images respectively. The location of simulated images are given by the classical image method or the complex image method, and the intensity of those are determined by approximating the truncation error of Green's function using the generalized inversion method based on the singularity value decomposition. The numerical results of SIM are very precise in the case of the different thickness of the conducting plate, because the contributions of the high order dipole image are take into account elaborately. The simulated image method is a subtle candidate solution, when a lot of the Green's functions have to be evaluated again and again, saying the problem of the eddy current nondestructive testing.