波导本征问题的等几何分析方法

The isogeometric analysis for eigen problem of waveguide

利用等几何分析思想通过加权余量法并结合亥姆霍兹方程推导出波导本征问题的等几何分析方程,提出了一种分析波导本征问题低自由度消耗、高精度的方法。该方法消除了传统数值方法中求解域的模型非一致性,从而实现了将问题的分析计算构架于精确的模型之上。以矩形和圆形波导的本征问题分析为例,通过与解析解和其他数值方法比较表明:在同等较细网格下,等几何分析模型仅花费1156个自由度,最大误差为0.003%,相比有限元的2245个自由度和0.03%的最大误差,此方法具有自由度少、精度高、收敛速度快等优点。

In this paper,Isogeometric analysis(IGA) is extended to eigen-problem of waveguide in computational electromagnetics.The weakened equations are involved with NURBS elements from control equations in eigen problem of waveguide.Both rectangle and circular waveguide are addressed as numerical examples.The results demonstrate the proposed method consumes 1156 DOFs with 0.003 percent maximum relative error,much less than that of finite element method in the same mesh level,which consumes 2245 DOFs with 0.03 percent maximum relative error,i.e.,IGA yields more excellent results,consumes less amount of DOFs,and obtains quicker convergence than traditional method.