中文摘要：

将电磁波导的控制方程导向了Hamilton体系、辛几何的形式.以电磁场的横向分量组成对偶向量并采用分离变量法,可以得到Hamilton算子矩阵的辛本征值问题.共轭辛正交归一关系、辛本征解展开定理等均可在此应用.对于复杂横截面和填充非均匀材料的电磁波导,提出对偶棱边元,对截面半解析离散后即可进行数值求解.对偶棱边元克服了结点基有限元求解电磁场问题的困难,与常规棱边元相比在某些方面具有一定的优势.

英文摘要：

The governing equations for the electromagnetic waveguide are derived to Hamiltonian system formulation and symplectic geometric form, and transverse electric and magnetic components are treated as dual vectors to each other. By separation of variables, we arrived at a symplectic eigenvalue problem for Hamiltonian operator matrix, which can be solved by adjoint symplectic orthonormal relationship and the symplectic eigenfunction expansion method. A dual edge element is proposed for electromagnetic waveguide with irregular cross section and inhomogeneous loaded materials. Dual edge element can surmount those difficulties related to node-based finite elements in computational electromagnetics, and our numerical examples show that dual edge element has its own merits when compared with regular edge element.