三维模型电磁感应的数值解法

本文讨论了“虚点”和“虚微商”概念带来的矛盾和困难后,摒弃了电导率突变界面的模型,改用电导率渐变的模型去研究三维电磁感应的近似计算方法。在基本方程中考虑了电导率梯度项▽σ, ▽²B+1/σ（▽σ）×（▽×B）=i（4πσω）B. 文章的主要内容是给出有限差分法求解三维电磁感应问题的一般方程组。同时也作了一个简单的实例计算,以检验方程组运算的可行性。

ON THE FINITE DIFFERENCE METHOD OF THREE-DIMENSIONAL ELECTROMAGNETIC INDUCTION PROBLEM

The difficulties encountered by using the fictitious values or fictitious derivatives for deriving the finite difference equations of three-dimensional induction are discussed. The conductivity model with sharp boundaries is abandoned and replaced by that in which the conductivity is a smoothly-varying function of position. In this paper the general equation of the three-dimensional electromagnetic induction iswhere ▽σ , the gradient of the conductivity, cannot be omittedThe main part of this paper deals with the generally required finitedifference formulae in detail. Then, a simple numerical calculation is given to illustrate the application of the general equation.