| 基于等几何分析的边界元法求解Helmholtz问题 |
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| 引用本文： | 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. |
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| 作者姓名： | 王现辉 乔慧 张小明 谷金良 |
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| 作者单位： | 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 |
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| 基金项目： | 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） |
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| 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.
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| 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 |
| 收稿时间： | 2015-12-28 |
| 修稿时间： | 2016-05-13 |
An Isogeometric Boundary Element Method for 3D Helmholtz Problems |
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| 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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| Authors: | WANG Xianhui QIAO Hui ZHANG Xiaoming GU Jinliang |
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| Institution: | 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 |
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| 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. |
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| Keywords: | isogeometric analysis Helmholtz problems boundary element method CAD model local bivariate B-spline function |
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