电磁波导的通过谱计算  

Symplectic theory of electro-magnetic wave-guide

作　　者：孙雁[1] 钟万勰[1] 

机构地区：[1]上海交通大学工程力学系,上海200030

出　　处：《计算力学学报》2006年第6期663-667,共5页Chinese Journal of Computational Mechanics

基　　金：国家重大基础研究(G1999032805);国家自然科学基金(1037201910132010);教育博士点基金(20010141024)资助项目

摘　　要：将电场和磁场变量构成对偶向量,将电磁波导的基本方程导向Hamilton体系、辛几何的形式。建立电磁波导问题的变分原理,构造电磁辛有限元。通过对本征值问题的求解,确定电磁波导的传播常数。采用主-从控制方法处理不同介质的界面条件。以不同截面形状的波导和部分填充波导为例进行了计算和分析,数值算例表明,辛体系用于电磁波导分析是有效的。辛体系在应用力学中的应用已经取得了很大成功,不同学科之间的交错对于电磁波导的分析是很有利的。Electric and magnetic components are dual vectors to each other. The basic equations for electro-magnetic wave-guide problems are derived to Hamilton system formulation and symplectic geometric form. Based on the variational principle for dual variables, the electro-magnetic symplectic finite element method is derived. Then the eigenvalue problem is solved, the wavenumbers are determined. The master-slave control method is applied in inhomogeneous wave-guide problems. Two different cross-sections wave-guide problems and a rectangle inhomogeneous wave-guide problem are discussed. The numerical results demonstrate that symplectic system is useful to the wave-guide problems. The symplectic system application in applied mechanics has been successful, and a number of problems have been solved. The cross development and exchange among various disciplines will be quite beneficial to electro-magnetic wave-guide problems.

关 键 词：电磁波 波导 哈密顿体系 辛体系 界面 

分 类 号：O35[理学—流体力学] O241[理学—力学]