基于MATLAB的静态场边值问题求解方法

A Methods For Solving Electromagnetic Static Boundary Value Problem Based on MATLAB

以MATLAB作为计算工具,分别采用解析法、有限差分法和有限单元法解决了静态电磁场边值问题,然后将三种方法求得的计算结果可视化并进行比较分析.解析法的可视化过程采用将自变量离散后代入解析解,求出位函数的离散值,用MATLAB编程将结果可视化;有限差分法和有限单元法是根据不同的算法直接求解微分方程,采用MATLAB编程和PDE工具箱将结果可视化.文章阐述了三种求解方法的原理,分别给出了求解的具体步骤和程序,指出利用不同方法借助MATLAB处理静态电磁场的边值问题在教学中具有推广意义.

The research solved the static electromagnetic field boundary value problems using three different methods and taking MATLAB as computations aids. And all the three results were visualized and compared. In analytical method, the function of discrete values were achieved after the discrete independent variables being putting into the post - analytical solution, then running MATLAB to visualize it; in the finite difference and the finite element method, a different algorithm was used for solving differential equations directly, and the results were visualized by PDE toolbox and the programming of MATLAB. The article gave the principles of three methods, steps and process in detail. In addition, it also illustrated the use of different methods of dealing value problem based on MATLAB in engineering education