| 基于曲四面体单元剖分的CN E-H TDFEM方法 |
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| 引用本文： | 叶珍宝,朱剑,周海京.基于曲四面体单元剖分的CN E-H TDFEM方法[J].计算物理,2016,33(6):652-660. |
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| 作者姓名： | 叶珍宝 朱剑 周海京 |
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| 作者单位： | 1. 北京应用物理与计算数学研究所, 北京 100094;2. 南京邮电大学通信与信息工程学院, 南京 210006 |
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| 基金项目： | 国家重点基础研究发展计划(2013CB328904)，国家自然科学基金重点项目(61431014) |
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| 摘 要： | 从采用Crank-Nicolson差分格式的基于麦克斯韦旋度方程的E-H时域有限元方法出发，将展开电场和磁场的叠层矢量基函数与曲四面体单元相结合.对金属球谐振腔及介质填充的圆柱形谐振腔的数值模拟表明：相较于规则四面体单元，在剖分单元数目相同的情况下，曲四面体单元离散表面弯曲结构可以获得更高的计算精度.同时，与0.5阶基函数结合曲四面体单元相比，1.0阶基函数与曲四面体单元结合可以用更少的单元数及未知量数目来获得更高的计算精度.
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| 关 键 词： | E-H时域有限元方法 Crank-Nicolson差分 叠层矢量基函数 曲四面体单元 |
| 收稿时间： | 2015-09-25 |
| 修稿时间： | 2016-03-09 |
Crank-Nicolson E-H Time-Domain Finite-Element Method Based on Curvilinear Tetrahedral Elements |
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| YE Zhenbao,ZHU Jian,ZHOU Haijing.Crank-Nicolson E-H Time-Domain Finite-Element Method Based on Curvilinear Tetrahedral Elements[J].Chinese Journal of Computational Physics,2016,33(6):652-660. |
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| Authors: | YE Zhenbao ZHU Jian ZHOU Haijing |
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| Institution: | 1. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;2. College of Communications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing, 210006, China |
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| Abstract: | Based on E-H TDFEM method derived directly from Maxwell's curl equations, Crank-Nicolson difference scheme is implemented for time-partial differential equation to obtain an unconditionally stable algorithm. Curvilinear tetrahedral elements are applied to discretize computational domain and electric and magnetic fields are expanded with same hierarchical vector basis functions. A sphere cavity and a cylindrical cavity partially filled with dielectric rod are simulated. It shows that curvilinear tetrahedral elements can reach higher accuracy with same mesh numbers, compared with tetrahedral elements. Better results can be obtained by curvilinear tetrahedral elements combined with 1.0 order hierarchical basis functions with fewer unknowns than that combined with 0.5 order hierarchical basis functions. |
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| Keywords: | E-H time-domain finite-element method Crank-Nicolson scheme hierarchical vector basis functions curvilinear tetrahedral elements |
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