基于裁剪造型的等几何分析方法求解波导本征值问题

摘要

The geometric model and analysis model can be uniformly described by NURBS in isogeometric analysis method,so the model transformation process is avoided.However,since the analysis domain of IGA should be composed of tensor-product patches,it is difficult to deal with the issue of complex multiply connected domains.IGA based on trimming technique is constructed by NURBS geometric modeling of underlying surface and trimming curve,and then,directly map a parameter space trimmed by NURBS curve as the complicated holed structure,only one parameter space is sufficient to de-scribe arbitrary complex topology.The advantages and properties of conventional IGA are maintained,and also,the range ap-plication of IGA is enlarged.In this paper,IGA based on trimming technique is expanded to the TE waveguide eigenvalue problem.With the solution of cutoff wave number for complicated multiholes structure,the effectiveness and high accuracy of proposed method are demonstrated by corresponding numerical examples.%等几何分析方法使得几何模型和分析模型能够用NURBS统一表达，避免了模型转换过程，但由于其分析域是由张量积面片构成，很难处理截面形式复杂的多联通域问题。裁剪造型等几何分析方法通过背景曲面和裁剪曲线将复杂带孔结构作为一个被NURBS曲线裁剪后的参数区域直接映射而成，只需要一个参数空间就可以表示任意复杂的拓扑结构，该方法既保留了传统等几何分析方法的优点，又实现了对复杂多孔结构的处理。本文将裁剪造型的等几何分析方法扩展到TE波的波导本征值问题，对复杂多孔结构的截止波数进行有效求解，并通过相应的数值算例验证方法的有效性和高精度性。