广义有限差分法在静态电磁场计算中的应用  

Application of the Generalized Finite Difference Method to Static Electromagnetic Problems

作　　者：陈剑 刘春明 王茂海[2] 葛小宁 刘连光 赫蕾 Chen Jian;Liu Chunming;Wang Maohai;Ge Xiaoning;Liu Lianguang(State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power University,Beijing 102206,China;North China Branch of State Grid Power Dispatch&Control Center,Beijing 100053,China;State Key Lab of Control and Simulation of Power Systems and Generation Equipments Department of Electrical Engineering Tsinghua University,Beijing 100084,China)

机构地区：[1]新能源电力系统国家重点实验室(华北电力大学),北京102206 [2]国家电网公司华北电力调控分中心,北京100053 [3]电力系统及发电设备控制和仿真国家重点实验室(清华大学电机系),北京100084 [4]不详

出　　处：《电工技术学报》2018年第7期1579-1587,共9页Transactions of China Electrotechnical Society

基　　金：国家重点研发计划项目(2016YFC0800103)和国家自然科学基金(51677068,51577060)资助。

摘　　要：广义有限差分法是一种新型区域型无网格数值离散方法。该方法基于多元函数泰勒级数展开式和加权最小二乘拟合,将控制方程中未知参量的各阶偏导数表示为相邻节点函数值的线性组合,克服了传统有限差分法对网格的依赖性。将广义有限差分法应用于电磁场问题的数值模拟中,建立了静态电磁场问题广义有限差分法的数值离散格式。为验证所提算法的有效性,对比了该方法与有限元方法在处理规则求解域与复杂求解域电磁场问题的差异。数值算例表明,该算法稳定,效率高,计算精度高。The generalized finite difference method(GFDM)is a new type of regional meshless discrete method.Based on the multivariate Taylor series expansion and the weighted least-squares fitting,the method expressed the partial derivative of unknown parameters in the governing function to a linear combination of adjacent node function values,which overcomes the dependence of the traditional finite difference method on the mesh.In this paper,the meshless generalized finite difference method is applied to the numerical simulation of static electromagnetic field problems.And the numerical discrete scheme of the method for static electromagnetic field problem is established.In order to verify the effectiveness of the proposed algorithm,the difference between GFDM method and the finite element method in dealing with the regular domain and the complex domain is comparative analysed.The results show that the algorithm of GFDM is stable and efficient for the different solution domain,and can achieve high computational accuracy.

关 键 词：无网格法 广义有限差分法 电磁场问题 泰勒级数展开 加权最小二乘拟合 

分 类 号：TM15[电气工程—电工理论与新技术]