三维静电场球坐标系曲面边界元法仿真精度分析

Simulation Accuracy Analysis of Surface Boundary Element Method in 3D Electrostatic Field Spherical Coordinate System

摘要: 三维电场的仿真数值计算精度与模型网格的选择和密度有密切关系，相关研究较少，已公开发表的研究成果中数值计算的网格划分大多靠经验，缺少网格剖分规范。基于球坐标系的曲面边界元法以曲面单元离散求解的模型表面，可以减少平面单元的拟合误差。对球面划分不同区域分别进行三角形网格和四边形网格剖分，对不同网格剖分面积和密度进行控制，讨论不同区域网格对仿真计算精度的影响，给出球面模型兼顾计算内存及计算时间下的最佳剖分方法。讨论了不同极点位置对球面积分的影响，结论可以广泛应用于工程实际。

Abstract: The numerical calculation accuracy of the 3D electric field simulation is closely related to the selection and density of the model grid elements. There are few related researches, and most numerical calculations meshes in published research results rely on experience, and there is a lack of mesh selection specifications. The surface boundary element method based on the spherical coordinate system uses the surface elements to discretely solve the model surface, which can reduce the fitting errors of the plane elements. Triangular meshing and quadrilateral meshing are divided into different areas of the spherical surface, and the area and density of different meshes are controlled. The influence of different meshes on the simulation calculation accuracy is discussed. The spherical model is given to take into account the calculation memory and calculation time. The best subdivision method is established. Discussed the influence of different positions of the poles on the area of the ball, the conclusion can be widely used in engineering calculation.