中文摘要：

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。

英文摘要：

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.