| 钟万勰,孙雁.电磁共振腔辛有限元法[J].计算力学学报,2004,21(2):129~134 |
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| 电磁共振腔辛有限元法 |
| Symplectic finite element method for electromagnetic resonant cavity |
| 修订日期：2003-11-17 |
| DOI：10.7511/jslx20042025 |
| 中文关键词: 电磁共振腔 电磁波 对偶变量 有限元法 本征值 变量离散分析 集成光学 |
| 英文关键词:electro-magnetic,finite element,duality system,resonance cavity,eigenvalue,W-W algorithm. |
| 基金项目:国家重大基础研究(G1999032805)，国家自然科学基金(10372019,10132010)，教育博士点基金(20010141024)资助项目. |
| 钟万勰 孙雁 |
| [1]大连理工大学工程力学系,辽宁大连116023 [2]上海交通大学工程力学系,上海200030 |
| 摘要点击次数: 1833 |
| 全文下载次数: 8 |
| 中文摘要: |
| 将电磁场的基本方程导向了对偶方程形式。给出了推导电磁场有限元所需相应的对偶变量变分原理。为了有限元列式的保辛，交分原理被积函数可导向对于对偶变量为对称的形式。交分原理的边界积分项对于相邻单元互相抵消。对偶变量有限元推导可避免所谓的C1连续性问题。采用对偶变量离散分析了共振腔本征值问题，离散后再消去一类变量可导出普通的广义本征值问题而求解。算例表明了对偶变量有限元分析的有效性。 |
| 英文摘要: |
| In present paper, the fundamental equations of electromagnetic field are written in the form of duality system. The variational principle for dual variables is derived for electromagnetic finite element method. To maintain the symplectic conservation conditions of FEM formulation, the integrand is rewritten symmetrically for duality variables. The boundary integral terms of variational principle are cancelled mutually for the adjacent elements. The dual variable FEM formulation can avoid the difficulty of continuity condition. The FEM analysis for dual variables is applied to the solution of eigenproblems of resonant cavity and the generalized eigenvalues are solved numerically. Numerical examples demonstrate the effectiveness of the dual finite element method. |
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