摘要
为了精确计算三维静电场中球形电极表面的电场强度,提出了基于球坐标变换的球面曲边三角形边界元法。该方法中积分的区域为球面,求解函数采用球面上球坐标线性插值,单元的外法线方向为严格的球面法线方向。计算结果表明,与平面直边单元相比,在网格剖分节点相同时,球面曲边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,球面曲边三角形边界元法节点数较少,具有计算速度快,占用计算机内存少等优点。
In order to calculate the electric field intensities of spherical electrodes in 3-D electrostatic fields precisely, the spherical surface curve triangular BEM which is based on spherical coordinates transformation is put forward. Firstly, owing to the spherical coordinates system being an orthogonal system, the spherical surface in rectangular coordinates system is transformed to rectangular region in （φ,θ） plane which is an abstract plane. Except two polar points , one-to-one mapping is built up from spherical surface in rectangular coordinates system to rectangular region in （φ,θ） plane. From differential area variable on spherical surface to differential area variable on （φ,θ） plane, Jacobian is given. Secondly, according to the one-to-one mapping relation, if the spherical surface is meshed by triangular elements corresponding nodes on （φ,θ） plane are connected lines which form plane straight side triangles. These plane straight side triangles correspond to spherical surface curve triangles. Thus integrals on spherical surface curve triangles can be obtained by calculating integrals on plane straight side triangles in （φ,θ） plane. And the problem that the spherical surface elements whose one node is polar point correspond to elements in （φ,θ） plane is solved. Thirdly, because unknown function is linearly interpolated along spherical coordinates on （φ,θ） plane, according to the one-to-one mapping relation, unknown function is linearly interpolated along spherical coordinates on spherical surface. Finally, directions of outward normal line to element and spherical surface are strictly unanimous, and formulae of the unit normal vector of spherical surface are given. The calculating results show that, on the conditions of the same meshing, compared with high precise finite element（FE） results, the spherical surface curve triangular BEM results are consistent with FEs, whereas results of the plane straight side triangles which are also in rectangular coordinates system have big errors. Hence compared with plane straight side BEM, on the condition of the same nodes the precision of the spherical surface curve triangular BEM is higher obviously, and on the condition of the same precision the spherical surface curve triangular BEM requires less nodes, consequently required memory and calculated time can be decreased greatly.
出处
《高电压技术》
EI
CAS
CSCD
北大核心
2007年第3期117-120,共4页
High Voltage Engineering
关键词
三维静电场
计算
边界元法
球面曲边三角形
球形电极
球坐标
3-D electrostatic field
calculation
boundary element method
spherical surface curve triangle
spherical electrode
spherical coordinate
