基于等几何分析方法求解任意截面波导本征问题  

Isogeometric Analysis on Eigenvalues of Waveguide with Arbitrary Cross-section

作　　者：张勇 林皋[1] 胡志强[1] 刘俊[1] 

机构地区：[1]大连理工大学建设工程学部,辽宁大连116024

出　　处：《计算物理》2012年第4期534-542,共9页Chinese Journal of Computational Physics

基　　金：中德科学基金(GZ566);国家自然科学基金(90510018;90915009;51009019;51109134)资助项目

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.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.

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 

分 类 号：TM151[电气工程—电工理论与新技术] O24[理学—计算数学]