基于有限元的磁暴感应地电场区域分解中位函数多值性分析  

Analysis of Multi Valuedness of Potential Function in Domain Decomposition of Geomagnetic Storm-induced Geoelectric Field Based on Finite Element

作　　者：陶瑞祥 王泽忠[1] TAO Ruixiang;WANG Zezhong(Beijing Key Laboratory of High Voltage&EMC,North China Electric Power University, Beijing 102206,China)

机构地区：[1]华北电力大学高电压与电磁兼容北京市重点实验室,北京102206

出　　处：《华北电力大学学报（自然科学版）》2018年第2期10-15,共6页Journal of North China Electric Power University：Natural Science Edition

基　　金：国家重点研发计划项目(2016YFC0800100);中央高校基本科研业务费专项资金资助项目(2017XS007)

摘　　要：在应用区域分解法求解多尺度磁暴感应地电场过程中,在求解得到的磁暴感应地电场中感应电流分布相同的前提下,基于有限元的区域分解法求解得到的位函数值与有限元直接求解得到的位函数值存在较大差异,这说明磁暴感应地电场求解过程中的位函数存在多值性。以基于有限元的区域分解法求解分解模型和有限元法直接求解整体模型两种算法,通过节点单元和棱边单元分别求解多尺度磁暴感应地电场,具体阐述位函数求解结果的多值性。通过对比发现,两种单元计算得到的矢量磁位不存在多值性,而电位存在多值性。针对电位计算结果的多值性,分析并验证了边界条件对电位多值性的影响,发现电位耦合是导致棱边单元电位多值性的原因,但节点单元电位的多值性没有因为取消电位耦合而消失。分析结果可为计算交变电磁场问题时的单元选择方面提供参考。In the process of solving the multi-scale geomagnetic storm-induced geoelectric field by using domain decomposition,on the premise that the induced current distribution in the geomagnetic storm-induced geoelectric field was the same,the potential function values calculated by the Domain Decomposition Method(DDM)based on the Finite Element Method(FEM)were quite different from those obtained by the direct solution of FEM.This illustrates that the potential function in the geomagnetic field induced by magnetic storm is multi-valued.By using the Domain Decomposition Method(DDM)based on the Finite Element Method(FEM)and direct solution of FEM,this paper solved the multi-scale geomagnetic storm-induced geoelectric field respectively through the node element and the edge element and provided a detailed statement of the multi valuedness of potential function.By comparison,it is found that the vector magnetic potential calculated by the two kinds of elements has no multi-valued property,while the potential is multi-valued.In view of the result,the paper analyzed and verified the influence of boundary conditions on the multi valuedness of potential.The results show that potential coupling is the cause of multi valuedness of potential of edge element but the multi valuedness of potential of the node element does not disappear after removing potential coupling.The analyses results can be a reference for the selection of elements in calculating alternative electromagnetic fields.

关 键 词：有限元 区域分解 磁暴 感应地电场 位函数 多值性 

分 类 号：TM152[电气工程—电工理论与新技术]