二维半空间声学伽辽金多极边界元法

中国机械工程 ›› 2013, Vol. 24 ›› Issue (15): 2066-2071.

二维半空间声学伽辽金多极边界元法

王艳广;文桂林;陈志夫;王明

湖南大学汽车车身先进设计制造国家重点实验室，长沙，410082

出版日期:2013-08-10 发布日期:2013-08-15
基金资助:
教育部长江学者与创新团队发展计划资助项目(531105050037)；湖南大学汽车车身先进设计制造国家重点实验室自主课题资助项目(71275003)
Supported by Program for Changjiang Scholars and Innovative Research Team in University（No. 531105050037）

A Multipole Galerkin Boundary Element Method for Two Dimensional Half Space Acoustic Problems

Wang Yanguang;Wen Guilin;Chen Zhifu;Wang Ming

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha,410082

Online:2013-08-10 Published:2013-08-15
Supported by:
Supported by Program for Changjiang Scholars and Innovative Research Team in University（No. 531105050037）

摘要/Abstract

摘要：

为提高求解半空间声学问题的计算效率，将半空间格林公式引入到边界积分方程中，使用伽辽金多极边界元法求解了二维半空间声学问题。在求解半空间问题时，推导了伽辽金多极算法中矩阵向量乘积的实现过程;在求解系统线性方程组时，使用近似求逆方法对系统系数矩阵进行了预处理。数值计算结果表明：二维半空间点声源声辐射算例有效地验证了半空间伽辽金多极边界元法计算精度;与全空间镜像方法计算时间对比结果表明，半空间方法具有更高的计算效率;在求解经过近似求逆预处理的系统方程时，迭代步数显著减少了，加速了迭代求解器的收敛。最后，使用半空间的伽辽金多极边界元法求解了T形声屏障声散射问题。

关键词: 伽辽金边界元法, 快速多极方法, 半空间问题, 声学, 数值计算

Abstract:

In order to improve the computational efficiency for half space acoustic problems, a half space Green function was introduced in boundary integral equations, then the multipole Galerkin boundary element method (BEM) was used to solve the half space acoustic problems. During this process, the matrix-vector multiplication procedure was discussed, and the generalized minimal RESidual (GMRES) iterative solver pre-conditioned by approximate inverse method was employed to solve the system linear equations. The numerical results show that, the accuracy and efficiency of the multipole Galerkin BEM is validated by the half space monopole scattering problem. The approximate inverse pre-conditioner can accelerate the convergence rate of the GMRES solver, the iterative steps are reduced dramatically. Finally, the multipole Galerkin BEM was applied to solve the diffraction problem of two dimensional T shape noise barrier.

Key words: Galerkin boundary element method, fast multipole method, half space problem, acoustics;numerical calculation

中图分类号:

TB52

王艳广, 文桂林, 陈志夫, 王明. 二维半空间声学伽辽金多极边界元法[J]. 中国机械工程, 2013, 24(15): 2066-2071.

WANG Yan-An, WEN Gui-Lin, CHEN Zhi-Fu, WANG Meng. A Multipole Galerkin Boundary Element Method for Two Dimensional Half Space Acoustic Problems[J]. China Mechanical Engineering, 2013, 24(15): 2066-2071.

参考文献

[1]Chen Z S, Hofstetter G, Mang H A. A Symmetric Galerkin Formulation of the Boundary Element Method for Acoustic Radiation and Scattering [J]. J. Comput. Acoust. , 1997, 5(2): 219-241.
[2]Schenck H A. Improved Integral Formulation for Acoustic Radiation Problems[J]. J. Acoust. Soc. Am. , 1968, 44(1):41-48.
[3]Rokhlin V. Rapid Solution of Integral Equations of Scattering Theory in Two Dimensional[J]. J. Corn- put. Phys. , 1990, 86: 414-439.
[4]Rokhlin V. Diagonal Forms of Translation Operators for the Helmholtz Equation in Three Dimensions[J]. Appl. Comput. Harm. Anal., 1993,1(1): 82-93.
[5]Gumerov N A, Duraiswami R A. Broadband Fast Multipole Accelerated Boundary Element Method for the Three Dimensional Helmholtz Equation[J]. J. Acoust. Soc. Am., 2009,125(1):191-205.
[6]Wu H J, Liu Y J, Jiang tion of the Moments in W K. Analytical Integra- the Diagonal Form Fast Multipole Boundary Element Method for 3- D Acoustic Wave Problems[J]. Eng. Anal. Bound. Elem. , 2012,36: 248-254.
[7]Seybert A F, Soenarko B. Radiation and Scattering of Acoustic Waves From Bodies of Arbitrary Shape in a Three- dimension Half Space[J]. ASME Trans. J. Vib. Acoust. Stress Reliab. Des. , 1988, 110: 112-117.
[8]Burton A J, Miller G F. The Application of the In tegral Equation Methods to the Numerical Solution of Some Exterior Boundary-value Prohlems[J]. Proc. Roy. Soc. London, 1971, A323: 201-210.
[9]Labreuche C. A Convergence Theorem for the Fast Multipole Method for 2 Dimensional Scattering Problems[J]. Math. Comput. , 1998, 67:553-591.
[10]Bapat M S, Liu Y J. A New Adaptive Algorithm for the Fast Multipole Boundary Elements Method[J]. CMES-Comp. Model Eng. , 2010,58:161-183.
[11]Coifman R, Rokhlin V, Wandzura S. The Fast Multipole Method for the Wave Equation: a Pe- destrian Prescription[J]. IEEE Antennas Propa- gation Mag. , 1993,35(3) :7-12.
[12]Gyure M F, Stalzer M A. A Prescription for the Multilevel Helmholtz FMM[J]. IEEE Comput. Sci. Eng., 1998, 5(3):39-47.

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