曲边多角形区域上不连续介质问题基于直接边界积分方程的机械求积法

Mechanical quadrature methods for discontinuous media problem based on the direct boundary integral equations on polygonal regions

作者提出了多角形区域上不连续介质问题▽.(γ(x)▽u(x))=0基于直接边界积分方程的机械求积法.作者首先导出了多角形不连续介质问题的等价直接边界积分方程组,然后采用三角周期变换,去除边界积分方程组解在角点的奇异性,利用Sidi-Israeli求积法则,构造机械求积法.数值结果表明该算法简单、有效,计算量低且具有高精度.

This paper presents a mechanical quadrature method based on the direct boundary integral equations（BIE） for the discontinuous media problem △↓（γ（x）△↓u（x））=0 on polygonal regions. First, the authors suggest an equivalent direct BIE for the discontinuous media problem, and then use triangle periodical variable transformation to remove the singularity of the solutions of the BIE at the corners of the boundary. Finally we obtain the mechanical quadrature methods by using the Sidi-Israeli＇s rule. Numercial results show that our methods possess high accuracy, less computational complexity, and the algorithm is very simple.