有限元法求解电磁场问题的误差分析  

Error analysis of finite element method in solving electromagnetic problems

作　　者：吴雅祥 刘仲武[1] 王开祥 WU Ya-xiang;LIU Zhong-wu;WANG Kai-xiang(School of Materials Science and Engineering,South China University of Technology,Guangzhou 510640,China;FoShan ShunDe Midea Electrical Heating Appliances Manufacturing Co Ltd,Foshan 528311,China)

机构地区：[1]华南理工大学材料科学与工程学院,广东广州510640 [2]佛山市顺德区美的电热电器制造有限公司,广东佛山528311

出　　处：《磁性材料及器件》2019年第1期21-25,39,共6页Journal of Magnetic Materials and Devices

基　　金：国家自然科学基金资助项目(51774146)

摘　　要：有限元方法目前已广泛应用于分析结构复杂的电磁场问题,但对于有限元方法可能存在的误差却鲜有研究。通过对比圆形载流线圈中心轴线上的磁感应强度,分析了有限元法对二维和三维电磁场问题进行求解时的误差。对静态磁场问题和涡流问题分析表明,有限元方法对二维电磁场问题求解精度较高,并且可以方便地通过细化网格划分进一步提高求解精度;三维电磁场问题在求解域较小的情况下误差较大,且无法通过细化网格减小误差。此外分析了求解域大小对求解精度的影响,并得出了求解域设置应满足的条件。Finite element method(FEM)has been widely used in the analysis of complicated electromagnetic problems.However,there are few studies on the possible errors of finite element method.By comparing the magnetic induction intensity on the center axis of the circular current carrying coil,the error of finite element method in solving 2D and 3D electromagnetic problems was analyzed.The results of static magnetic field analysis and eddy current analysis shows that finite element method is more accurate for 2D electromagnetic field problem,and can conveniently improve the accuracy by refining the mesh;for 3D electromagnetic field problems,large error will occur while the solution domain is small,and cannot be eliminated through grid refinement.In addition,the influence of region size on the accuracy of the solution was analyzed,and the condition that the region of the solution should be satisfied is obtained.

关 键 词：电磁场问题 求解 有限元法 相对误差 

分 类 号：TM153[电气工程—电工理论与新技术]