基于Schur分解的比例边界有限元方法求解环形域静电场  

Analysis of the Electrostatic Field in Ring-type Domain by SBFEM with Schur Decomposition

作　　者：白卫峰[1] 何伟 张勇 

机构地区：[1]华北水利水电学院钢结构与工程研究院,河南郑州450011 [2]郑州市轨道交通有限公司,河南郑州450046 [3]大连理工大学建设工程学部,辽宁大连116024

出　　处：《四川大学学报（工程科学版）》2013年第1期175-182,共8页Journal of Sichuan University (Engineering Science Edition)

基　　金：国家自然科学基金资助项目(51009020);华北水利水电学院高层次人才科研启动资助项目(201109)

摘　　要：应用比例边界有限元方法求解同轴电缆(环形域)静电场边值问题。为了避免特征值方法出现的奇异问题,采用Schur分解修正原有的特征值方法。在比例边界坐标变换的基础上,利用加权余量法将环形域静电场边值问题的控制方程半弱化为关于径向坐标的2阶常微分方程的两点边值问题,引入辅助变量将其降阶为1阶常微分方程,用Schur分解方法求解此方程可获得通解,并通过边界条件确定积分常数。计算不同截面形式的同轴电缆,结果表明,Schur分解很好地避免了特征分解的奇异性问题,与其他数值方法相比,此方法适用性强,且具有精度高、数据量小、运算量小的优点。Scaled boundary finite element method （SBFEM） was applied to solve the boundary value problems of the electrostatic field in coaxial-cable, i.e. , ring-type domain. To avoid the singularity in eigenvalue method, Sehur decomposition was employed to update the original method. With scaled boundary coordinate transformation, the governing Laplace equation was semi-diseretized to set of a second-order ordinary differential equations （ ODEs ） by the weighted residual approach. Introducing auxiliary variables, the rank of ODEs was reduced to one, and the general solution of electric potential was obtained by Sehur decomposition. Integral constants were determined by the boundary conditions. Numerical examples, including coaxial-cable with various types of cross-section, were calculated and the result showed that singularity is terminated by the proposed approach in respect to Schur decomposition. Wide adaptability, excellent results and less amount of computation consumption are reached beyond other methods.

关 键 词：同轴电缆 静电场 边值问题 比例边界有限元 SCHUR分解 

分 类 号：TM151[电气工程—电工理论与新技术] O24[理学—计算数学]