基于等几何分析方法求解任意截面波导本征问题

计算物理 ›› 2012, Vol. 29 ›› Issue (4): 534-542.

基于等几何分析方法求解任意截面波导本征问题

张勇, 林皋, 胡志强, 刘俊

大连理工大学建设工程学部, 辽宁大连, 116024

收稿日期:2011-09-02 修回日期:2012-02-10 出版日期:2012-09-25 发布日期:2012-09-25
作者简介:张勇(1983-),男,湖北十堰,博士生,从事等几何分析的数值计算的研究及应用,E-mail:zymarchine@gmail.com
基金资助:
中德科学基金(GZ566);国家自然科学基金(90510018,90915009,51009019,51109134)资助项目

Isogeometric Analysis on Eigenvalues of Waveguide with Arbitrary Cross-section

ZHANG Yong, LIN Gao, HU Zhiqiang, LIU Jun

Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China

Received:2011-09-02 Revised:2012-02-10 Online:2012-09-25 Published:2012-09-25

摘要/Abstract

摘要： 基于等几何分析方法具有自由度花费少、高精度、高阶连续性等特点,通过加权余量法对椭圆波导本征问题的亥姆霍兹方程等几何离散得出等几何分析方程.解决了传统数值方法的求解域与几何模型的非一致性问题,实现了将问题的分析计算构架于精确几何模型基础之上.分析任意截面波导的本征问题,对不同偏心率的椭圆波导以及三角形和五边形波导的截止波数的求解结果显示等几何分析方法求解波导本征问题的高效及高精度特性.与传统方法相比,此方法以较少的自由度消耗便会达到较高的求解精度,并且数值解的收敛率较快.

关键词: 波导本征问题, 等几何分析, 非均匀有理B样条, 椭圆波导, 三角形波导, 五边形波导

Abstract: Isogeometric analysis(IGA) is applied to eigenvalue problem of waveguide with arbitrary cross-section.Weakened equations are involved with NURBS elements from governing equation of waveguide.The computational model in IGA is inherited from a design model in CAD system,which is beyond traditional numerical method with remodeling procedure.Elliptical waveguides with various eccentricities,triangular and pentagon waveguides are addressed as numerical examples.It demonstrates that the preseut method is feasible for eigenvalue analysis of waveguide with either elliptical or polygonal cross-section.Moreover,it yields excellent results with fewer DOFs,and obtains quicker convergence than traditional method.

Key words: waveguide eigenvalue problem, isogeometric analysis, NURBS, elliptical waveguide, triangular waveguide, pentagonal waveguide

中图分类号:

张勇, 林皋, 胡志强, 刘俊. 基于等几何分析方法求解任意截面波导本征问题[J]. 计算物理, 2012, 29(4): 534-542.

ZHANG Yong, LIN Gao, HU Zhiqiang, LIU Jun. Isogeometric Analysis on Eigenvalues of Waveguide with Arbitrary Cross-section[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 29(4): 534-542.

[1]	王现辉, 乔慧, 张小明, 谷金良. 基于等几何分析的边界元法求解Helmholtz问题[J]. 计算物理, 2017, 34(1): 61-66.
[2]	陈德祥, 徐自力, 刘石, 冯永新. Navier-Stokes方程的最小二乘等几何方法[J]. 计算物理, 2014, 31(3): 285-291.
[3]	张立东, 李椿萱. 结构型网格分块生成技术[J]. 计算物理, 2001, 18(4): 325-328.