基于等几何分析的边界元法求解Helmholtz问题  

An Isogeometric Boundary Element Method for 3D Helmholtz Problems

作　　者：王现辉[1] 乔慧[2] 张小明[1] 谷金良[3] WANG Xianhui QIAO Hui ZHANG Xiaoming GU Jinliang(School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454003, China School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, China College of Electromechanical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China)

机构地区：[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

出　　处：《计算物理》2017年第1期61-66,共6页Chinese Journal of Computational Physics

基　　金：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);河南理工大学科学研究基金(B2014-38)

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.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.

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 

分 类 号：O241[理学—计算数学] O424[理学—数学]