A new approach , the multipole theory ( mt ) method , is briefly described for analysis of waveguide eigenvalue problems . the essential concept is to represent the solution of the waveguide partial differential equation by the generalized mt formula of 2 - d helmholtz equation . the applied rules and the procedure of the mt method are also introduced . by calculating and analyzing some engineering problems , it is shown that the mt method is an effective approach for analysis of waveguide eigenvalue problems 本文利用多极理论分析波导本征值问题.给出用多极理论分析波导本征值问题的使用规则和实施方法.实例计算结果表明，用多极理论分析波导本征值问题，不仅具有较高的计算精度，而且可以很方便地应用于波导工程问题的设计与计算，多极理论是一种有效的波导本征值分析方法
First of all , the algorithm base on the boundary problem of helmholtz equation and finite - difference technique , calculate the field in “ cold ” cavity and disperse the helmholtz equation , as a result of the formula : ax = x . secondly , according to the eigenvalue of matrix theory and applied iterative methods , eigenmode adopt a numerical approach which allows the improved chebyshev polynomial iteration which based on the power method to extract the isolated eigenmode in the spectrum . finally , we resolve the problem of compatibility in software and insert the eigenmode module into the chipic which will have the function of eigenmode analysis 具体的说: ( 1 )首先以电磁理论中的亥姆霍兹方程的边值问题理论和计算电磁学中的有限差分法为基础,计算冷腔中的场分布并离散亥姆霍兹方程,得到标准的本征值问题: ax = x ; ( 2 )然后根据矩阵理论中的eigenvalue问题和数值计算中的迭代方法,采用改进后的chebyshev多项式,在power迭代法的基础上对ax = x进行多项式迭代,实现对频谱中孤立本征模的萃取; ( 3 )最后将用fortran语言编制的eigenmode模块加入到chipic软件中,解决了eigenmode模块与chipic主代码的兼容问题,从而实现了chipic软件的模式分析功能。
