电磁场数值分析中的B样条有限元法

本文基于变分原理和B样条函数理论的应用,以矩形单元上的B样条函数作为形状函数,构造了B样条有限元法,为规则场域中电磁场分析计算问题提供了一种理想的数值计算方法。本法与通常的有限元法相比,不仅可得更高精度的位函数数值解,而且基函数的一阶导数连续,使场量计算精度也相当理想。此外,计算量和所需计算机内存容量都显著减少。文中,在不同媒质交界处,成功地引用B样条重节点理论,解决了多种媒质场域内电磁场求解问题。同时,还采用变形的B样条函数基解决了强加边界条件的处理问题。本文提供的方法通过典型示例的解析解予以验证。

The B-Spline Finite Element Method for Electromagnetic Field Analysis

A B-Spline finite element method based on variational Principle and B-Spline theory is presented.It provides a very effective method for solving electromagnetic field problems in regular regions.The B-Spline functions for rectangular elements are used as shape functions.Compared With the usual finite element method,it can give not only much more accurate potential function,but also more accurate field vectors due to the continuity of the first detrivati-ve of base functions.Moreover,both the computing time and the required storage capacity are greatly reduced.The authors successfully use B-Spline theory of multiple nodes at the interface of different media to solve piecewise homogenous space problems.At the same time,the changed B-Spline basis is used to deal with the imposed boundary conditions.The method presented in this paper is illustrated by sveral typical examples.