中文摘要：

基于电磁波导的对偶变量变分原理以及Hamilton正则方程，将含有奇异性的电磁场问题导入Hamilton体系下进行分析，通过分离变量及共轭辛本征函数向量展开法，构造出可以表征电磁场奇异性的奇异解析元。奇异元的采用克服了普通单元处理含有导电劈和介质楔的波导问题的困难，同时能够方便地与电磁对偶元相结合，保持了有限元方法的灵活性，具有较高的精度。

英文摘要：

Based on the dual variational principle and Hamilton canonical equations for electromagnetic waveguide, problems of singular electromagnetic fields are analyzed in Hamilton system. A singular analytically element is derived by using variable separation method and adjoint sysmplectic eigenfunctions expansion technique. The singular element can deal with the singularity in conducting and dielectric wedges in electromagnetic waveguides. It is easy to be implemented into dual electromagnetic element code. It is flexible, efficient and precise.