论文部分内容阅读
本文讨论具垂向光滑变化的非均匀介质中电磁场延拓的数学物理问题及稳定化的算法原理。首先从电磁场的基本方程出发,导出了垂向非均匀介质下磁场的垂直分量所满足的二阶偏微分方程,并且依照实际背景将场的延拓问题化归为解相应二阶椭圆型方程的Cauchy问题。接着利用Fourier变换方法得到了场延拓的形式表达式,然后给出了几种特殊垂向非均匀介质下场延拓的精确解析公式。最后,应用正则化方法建立了场延拓的稳定化的公式,给出了所得公式的离散化形式,同时指出了相应正则化参数的选择原则。
In this paper, we discuss the math-physics problems of electromagnetic field extension in non-uniform media with vertical and smooth changes and the principle of the algorithm. First of all, based on the basic equations of the electromagnetic field, the second-order partial differential equations satisfied by the vertical components of the magnetic field in the vertical inhomogeneous medium are deduced and the continuation problem of the field is classified as corresponding second-order elliptic equations according to the actual background Cauchy problem. Then, using Fourier transform method, the formal expression of field extension is obtained, and then the exact analytical formulas of several special vertical inhomogeneous media field continuation are given. Finally, the method of regularization is used to establish the field-stabilizing formula, and the discretization of the formula is given. At the same time, the selection principle of the regularization parameter is pointed out.