电磁边界差分离散格式的变分法

Variational Method of Obtaining Difference Equations on Electromagnetic Medium Interfaces

本文基于变分原理的有限差分近似,对任意矩形网络离散的分层均介介质场域中Poisson方程和Helmholtz方程的介质交界面边界条件进行处理,得到了统一的边界差分离散格式。本文方法还推广于圆形域和轴对称场。本文公式具有普遍性和统一性,推导过程简单、规范。基于变分原理,有限差方法可以象有限无法,用于处理任意边界条件和介质连接条件,而总体矩阵的形成要比有限无法容易得到。

Electromagnetic boundary conditions of Poisson' s and Helmhotz's equations in layered isotropic media are treated by using variational principle and FD approximation in this paper,and unified formulae are obtained on arbitrary rectangular meches. This method is also used to circular region and axisymmetric field.