一种新型有限元降阶方程及其应用

本文针对流域几何结构对称，场源或边界条件非对称的工程类问题，在有限元方法的基础上，提出一种新型降低方法。这种方法在全域节点变量总数不变的前提下，将全域问题转化为拟半域问题，从而使有限元离散区域及其方程组的阶数均减少二分这一，大大节省计算机内存和ＣＰＵ时间。且编程简单，通用性强，文章最后给出计算实例。

A NEW RANKS REDUCTION APPROACH BASED ON THE FEM AND ITS APPLICATION

This paper presents a new ranks reduction approach of FEM for the problem with symmetrical geometry and asymmetrical source distribution or boundary condition. By this approach, the whole domain problem may be transformed into a fictitious half domain problem, with the total number of variables unchanged and the discreted region and ranks of the equation set reduced to half. Therefore, both storage capacity and CPU time may be reduced significantly. The method has the advantage of easy programming and generalization. An example for calculating the electric field of a metal cell is given.