新型曲面三角形边界元法及其在电场计算中的应用

New Curved Surface Trilateral BEM and Its Application in Electric Field Calculation

用边界元法计算工程三维静电场时,为了减少计算节点数同时提高计算精度,提出了新型曲面三角形边界元方法。该方法利用二阶单元剖分边界面,再利用面积比值法构造对应于二阶单元的3个顶点节点的形状函数;以二阶单元的3个顶点节点为计算节点,与二阶三角形边界元法相比,大大减少了计算量;与一阶平面三角形边界元法相比,提高了计算精度。取球形电极的电场分布计算为例进行验算,计算结果表明:与一阶剖分的平面边界元法相比,网格剖分节点相同时,新型曲面三角形边界元法的计算精度明显提高;在计算精度要求相同时,新型曲面三角形边界元法计算节点数较少。

The new curved surface trilateral BEM was put forward in this paper, in order to reduce the calculating nodes and improve the calculating precision in the engineering 3 - D electrostatic field calculation. This method used second - order element to mesh the boundary surface, and then used area ratio method to construete shape functions cor- responding to the second - order element＇ s three vertex nodes. The new curved surface trilateral BEM took the three vertex nodes of the second - order element as the calculating nodes. Hence, the new curved surface trilateral BEM can reduce the amount of the calculation, compared with the second - order trilateral BEM. Comparing with the first - order plane trilateral BEM, the new curved surface trilateral BEM can improve the calculating precision. In this paper, the e- lectric field distribution calculation of spherical electrode was given. The calculating results showed that when the grid nodes were equal, calculation precision of the new curved surface trilateral BEM was obviously improved in compared with the first- order plane trilateral BEM. And on the condition of the same precision, the new curved surface trilateral BEM required less nodes, consequently required memory can be decreased greatly.