基于等几何分析的边界元法求解Helmholtz问题

计算物理 ›› 2017, Vol. 34 ›› Issue (1): 61-66.

基于等几何分析的边界元法求解Helmholtz问题

王现辉¹, 乔慧², 张小明¹, 谷金良³

1. 河南理工大学机械与动力工程学院, 焦作 454003;
2. 河南理工大学数学与信息科学学院, 焦作 454003;
3. 湖南科技大学机电工程学院, 湘潭 411201

收稿日期:2015-12-28 修回日期:2016-05-13 出版日期:2017-01-25 发布日期:2017-01-25
作者简介:王现辉(1985-),男,河南许昌,博士,讲师,从事计算声学研究,E-mail:xh_wang007@126.com
基金资助:
国家自然科学基金（U1504106），河南省高校基本科研业务费专项资金资助（NSFRF140122）和河南理工大学科学研究基金（B2014-38）

An Isogeometric Boundary Element Method for 3D Helmholtz Problems

WANG Xianhui¹, QIAO Hui², ZHANG Xiaoming¹, GU Jinliang³

1. School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454003, China;
2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, China;
3. College of Electromechanical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China

Received:2015-12-28 Revised:2016-05-13 Online:2017-01-25 Published:2017-01-25

摘要/Abstract

摘要： 将基于一类局部双变量B样条函数的等几何分析方法和Burton-Miller方法相结合，分析三维Helmholtz问题.对于某些从二维参数域映射到三维空间具有奇异点的参数曲面，该方法可以有效地避免奇异点处大量奇异与近奇异积分的计算.数值算例表明该方法具有较好的计算精度和计算效率.复杂问题的分析表明，该方法具有良好的工程应用前景.

关键词: 等几何分析, Helmholtz问题, 边界元法, CAD模型, 局部双变量B样条函数

Abstract: An isogeometric analysis based on a kind of local bivariate B-spline function and Burton-Miller method is introduced in boundary element method (BEM) for 3D Helmholtz problems.The method avoid efficiently computation of singular and nearly singular integrals aroud singular point of parametric surface.Numerical examples show that the algorithm has good performance in accuracy, efficiency and convergence.The algorithm performs isogeometric BEM (IBEM) with traditional global B-spline shape functions on CPU time and accuracy.The method has potential in engineering applications.

Key words: isogeometric analysis, Helmholtz problems, boundary element method, CAD model, local bivariate B-spline function

中图分类号:

O241
O424

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.

WANG Xianhui, QIAO Hui, ZHANG Xiaoming, GU Jinliang. An Isogeometric Boundary Element Method for 3D Helmholtz Problems[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(1): 61-66.

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