球形电极三维静电场的球面三角形边界元算法

Spherical Surface Triangular BEM of Spherical Electrode in 3-D Electrostatic Fields

针对电力设备中球形电极的电场强度计算问题,提出了球面三角形边界元方法。在该方法中,定义了球面三角形单元上的形状函数。边界元积分严格取为球面积分,求解函数在球面单元上沿大圆弧线性插值,边界元的外法线方向严格取为球面法线方向。算例计算结果表明,与平面三角形边界元相比,在网格剖分情况相同时,球面三角形边界元的计算精度显著提高;在计算精度要求相同时,采用球面三角形边界元计算,节点数可以大幅度减少,从而对计算机内存需求明显减少,总体计算时间也相应减少。

The spherical surface triangular BEM is put forward to be used to calculate electric field intensity of spherical electrodes in 3-D electrostatic fields. In this method, the shape functions on the spherical surface triangular elements are defined. The element integral is strictly carried through on the spherical surface, and the solved function is linearly interpolated on spherical surface element along the great arc, and directions of outward normal line to element and spherical surface are strictly unanimous. The calculated results show that the precision of the spherical surface triangular BEM is obviously higher than plane triangular BEM on the condition of the same nodes; and on the condition of the same precision the spherical surface triangular BEM requires less nodes, consequently required memory and calculated time can be decreased greatly.