Isogeometric Analysis for the Waveguide Eigenvalue Problem Based on the NURBS Patch Splicing Technique

WANG Feng; LIN Gao; LIU Jun; LI Jian-bo

doi:10.3969/j.issn.0372-2112.2016.01.029

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Isogeometric Analysis for the Waveguide Eigenvalue Problem Based on the NURBS Patch Splicing Technique

更新时间：2025-07-16

- Isogeometric Analysis for the Waveguide Eigenvalue Problem Based on the NURBS Patch Splicing Technique
- Acta Electronica Sinica Vol. 44, Issue 1, Pages: 200-205(2016)
- 作者机构：
  
  1. 大连理工大学水利工程学院,辽宁,大连,116024
  2. 南京水利科学研究院水文水资源与水利工程科学国家重点实验室,江苏,南京,210098
  3. 大连理工大学水利工程学院,辽宁,大连,116024
  4. 南京水利科学研究院水文水资源与水利工程科学国家重点实验室,江苏,南京,210098
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2016.01.029
  CLC： TN814
- Published：2016
- 稿件说明：
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WANG Feng, LIN Gao, LIU Jun, et al. Isogeometric Analysis for the Waveguide Eigenvalue Problem Based on the NURBS Patch Splicing Technique[J]. Acta Electronica Sinica, 2016, 44(1): 200-205.
DOI：

WANG Feng, LIN Gao, LIU Jun, et al. Isogeometric Analysis for the Waveguide Eigenvalue Problem Based on the NURBS Patch Splicing Technique[J]. Acta Electronica Sinica, 2016, 44(1): 200-205. DOI： 10.3969/j.issn.0372-2112.2016.01.029.

摘要

基于NURBS的等几何分析方法集成了计算机辅助设计(CAD)和有限元方法的优点

CAD模型、网格划分和数值仿真均采用同样的几何描述.然而

由于单个NURBS曲面片拓扑的局限性

单片等几何分析方法难以处理介质分布不均匀以及截面形式复杂的多连通区域问题.本文基于面片拼接

将等几何分析方法用来求解此类问题的波导本征值.细分前后

NURBS曲面片拼接处的控制点和网格必须匹配.通过Galerkin法来离散波导本征值问题的Helmholtz控制方程

计算结果表明该方法具有自由度消耗小、精度高、收敛速度快等优点.

Abstract

Isogeometric analysis (IGA) based on the non-uniform rational B-splines (NURBS) has integrated the advantages of Computer Aided Design (CAD) and the finite element method (FEM).The main feature of IGA is the usage of one common geometry representation for creating CAD models

for meshing

and for numerical simulation.However

IGA based on one single NURBS patch is difficult to deal with the inhomogeneous mediums and complex multiply connected domains because of the limitation of the NURBS patch topology.In this paper

IGA based on the patch splicing is used to solve the waveguide eigenvalue problem of this kind.The control points and meshes of different patches must coincide on the interface

even after refinement.The Helmholtz governing equation can be discreted using the Galerkin procedure.Numerical examples are presented to show that IGA possesses the advantages of better convergence on a per-degree-of-freedom and high accuracy.

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