边界元法的边界效应问题

本文采用两种新方法来处理边界元法的边界效应问题。首先,用线性元的降低高次奇异性法。与一般边界元相比,使边界效应大为缓和。其次,用抛弃基本解的插值法。它能得到一般边界元法无法求得更靠近边界的内点值。将两种方法结合起来的混合法,则可得到更为满意的结果。作者编制了线性元降低高次奇异性法程序。用它对工程实例进行计算,结果证明了本文方法的优越性。

The Boundary Effect problem in Boundary Element Method

Two new methods are used to deal with the boundary effect problem in B. E. M.. Firstly, the reducing high singularity method of Linear B. E. M. is adopted. Comparing with the ordinary B. E. M., it has greatly relaxed the boundary effect. Secondly, the inserting method of giving up the fundamental solutions for differential equation can be used to obtain the results of points inside the area of further nearing the boundary, which can not be obtained by ordinary B. E. M.. If the two methods are united as a mixed one, the more satisfactory results can be obtained. The author has also compiled a computer program of the reducing high singularity method of linear B. E. M.. The results of adopting the program to compute the engineering problemshave proved the superiority of the methods used in this paper.