三维静场的边界线性元解

The linear solution of the three dimensional electrostatic problem by the boundary element method

本文从三维拉普拉斯方程的基本解出发,导出了三维静场的边界积分方程。文中对三维静场边界元法作了详细讨论,推导出边界线性元法的矩阵元素的解析公式,并给出计算三维导体电容的通用计算机程序。计算实例表明,该方法精度高,计算量小,是一种十分有效的数值方法。

In this paper, the boundary integral equation to the three dimensional electrostatic problem is derived via the fundamental solution of Laplace equa- tion. A detailed discussion for the solution of the three dimensional electro- static problem by using the boundary lipear element is presented. Analytic formulas of the matrix element are derived. The common program for calcu- lating the capacitance of isolated conductors by the boundary element method is given. The solutions show that the method gives appreciable precision and takes a small amount of computation-time, so that it is quite effective.