三维声学多层快速多极子边界元及其应用

吴海军; 蒋伟康; 鲁文波

doi:10.7498/aps.61.054301

摘要

快速多极子边界元算法可以加速矩阵和向量乘法运算, 将传统边界元算法的计算量和内存占用量分别降为O(N log2N)和O(N), 适用于大型声学模型模拟计算. 本文发展了一种基于Burton-Miller方程的三维多层声学快速多极子边界元算法. 将新的自适应树状算法应用到对角形式的快速多极子边界元算法, 并使用最新提出的解析式源点矩计算公式, 进一步提高了快速多极子边界元的计算效率. 绝对软球体在内部共振频率处的散射声场计算, 验证了所发展算法在共振频率处求解的正确性. 与Bapat所提供的程序在多脉动球体辐射声场计算精度的比较, 验证了算法及程序在大型模型声学计算中的准确性, 同时显示了其求解的高效性. 最后, 将该算法用于车内声场及水下声学探测的分析计算.

关键词:

Abstract

It is suitable to solve the acoustic problems by using the fast multipole boundary element method (FMBEM), since the FMBEM can accelerate the matrix-vector multiplication dramatically by reducing the CPU time and memory of conventional boundary element method to O(N log2N) and O(N) respectively. We propose a 3D acoustic FMBEM based on Burton-Miller formulation in this paper. A new adaptive algorithm is applied to the diagonal form FMBEM, and a new proposed analytical moment formulation is used in the moment computation. Both of them further improve the efficiency of FMBEM. Acoustic scattering of soft sphere at resonant frequency is investigated to validate the accuracy of solution using Burton-Miller formulation. Comparisons of solution to the multi-radiating spheres problem with the one solved by Bapat's program demonstrate the accuracy and the efficiency of our algorithm in solving large-scale acoustic problems. In the end, we use our algorithm to analyze the inner sound filed of a car and dolphin acoustic scattering.

Keywords:

fast multipole boundary element method /
Burton-Miller formulation /
acoustic radiation /
acoustic scattering

作者及机构信息

1.
上海交通大学机械系统与振动国家重点实验室, 上海 200240

基金项目: 国家自然科学基金(批准号: 11074170)和机械系统与振动国家重点实验室自主课题基金(批准号: MSVMS201105)资助的课题.

Authors and contacts

1.
State Key Laboratory of Machinery System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11074170) and the Foundation of the State Key Laboratory of Mechanical System and Vibration of China.

参考文献

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[9]	Fischer M, Gauger U, Gaul L 2004 Eng. Anal. Bound. Elem. 28155
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[12]	Gaul L, Fischer M 2006 ZAMM-Z. Angew. Math. Me. 86 4
[13]	Shen L, Liu Y J 2007 Comput. Mech. 40 461
[14]	Bapat M S, Shen L, Liu Y J 2009 Eng. Anal. Bound. Elem. 331113
[15]	Bapat M S, Liu Y J 2010 CMES-Comp. Model. Eng. 58 161
[16]	Wang X R, Ji Z L 2007 J. Harbin Eng. Univ. 28 752 (in Chinese) [王雪仁, 季振林 2007哈尔滨工程大学学报 28 752]
[17]	Wang X R, Ji Z L 2008 J. Univ. Sci. Tech. Chn. 38 207
[18]	Cui X B, Ji Z L 2010 Chi. J. Comput. Phsys. 27 711 (in Chinese) [崔晓兵, 季振林 2010 计算物理 27 711]
[19]	Meng W H, Cui J Z 2008 J. Univ. Sci. Tech. Chn. 38 1332
[20]	Meng W H, Cui J Z 2010 J. Numer. Meth. Comp. Appl. 31 141(in Chinese) [孟文辉, 崔俊芝 2010数值计算与计算机应用 31 141]
[21]	Wu H J, Jiang W K 2012 Acta Acustica (accepted) (in Chinese) [吴海军, 蒋伟康 2012 声学学报 (录用)]
[22]	Wu H J, Jiang W K, Liu Y J 2012 Appl. Math. Mech. (accepted)
[23]	Wu H J, Jiang W K 2012 J. Mech. Sci. Technol. (accepted)
[24]	Liu Y J, Rizzo F J 1992 Comput. Method. Appl. M 96 271
[25]	Coifman R, Rokhlin V, Wandzura S 1993 IEEE Antenn. Propag.M 35 7
[26]	Rahola J 1996 Bit. 36 333
[27]	Driscoll J R, Healy D M 1994 Adv. Appl. Math. 15 202
[28]	Jakob-Chien R, Alpert B K 1997 J. Comput. Phys. 136 580
[29]	Chowdhury I, Jandhyala V 2006 Microwave Opt. Technol. Lett.48 1961
[30]	Chen K, Harris P J 2001 Appl. Numer. Math. 36 475

施引文献

[1]	Rokhlin V 1985 J. Comput. Phys. 60 187
[2]	Greengard L, Rokhlin V 1987 J. Comput. Phys. 73 325
[3]	Rokhlin V 1993 Appl. Comput. Harmon. A 1 82
[4]	Sakuma T, Yasuda Y 2002 Acta Acust. United AC. 88 513
[5]	Yasuda Y, Sakuma T 2003 Acta Acust. (Stuttgart) 89 28
[6]	Amini S, Profit A T J 2003 Eng. Anal. Bound. Elem. 27 547
[7]	Burton A J, Miller G F 1971 P. Roy. Soc. Lond. A Mat. 323 201
[8]	Chen J T, Chen K H 2004 Eng. Anal. Bound. Elem. 28 685
[9]	Fischer M, Gauger U, Gaul L 2004 Eng. Anal. Bound. Elem. 28155
[10]	Fischer M, Gaul L 2005 J. Comput. Acoust. 13 87
[11]	Fischer M, Gaul L 2005 Int. J. Numer. Meth. Eng. 62 1677
[12]	Gaul L, Fischer M 2006 ZAMM-Z. Angew. Math. Me. 86 4
[13]	Shen L, Liu Y J 2007 Comput. Mech. 40 461
[14]	Bapat M S, Shen L, Liu Y J 2009 Eng. Anal. Bound. Elem. 331113
[15]	Bapat M S, Liu Y J 2010 CMES-Comp. Model. Eng. 58 161
[16]	Wang X R, Ji Z L 2007 J. Harbin Eng. Univ. 28 752 (in Chinese) [王雪仁, 季振林 2007哈尔滨工程大学学报 28 752]
[17]	Wang X R, Ji Z L 2008 J. Univ. Sci. Tech. Chn. 38 207
[18]	Cui X B, Ji Z L 2010 Chi. J. Comput. Phsys. 27 711 (in Chinese) [崔晓兵, 季振林 2010 计算物理 27 711]
[19]	Meng W H, Cui J Z 2008 J. Univ. Sci. Tech. Chn. 38 1332
[20]	Meng W H, Cui J Z 2010 J. Numer. Meth. Comp. Appl. 31 141(in Chinese) [孟文辉, 崔俊芝 2010数值计算与计算机应用 31 141]
[21]	Wu H J, Jiang W K 2012 Acta Acustica (accepted) (in Chinese) [吴海军, 蒋伟康 2012 声学学报 (录用)]
[22]	Wu H J, Jiang W K, Liu Y J 2012 Appl. Math. Mech. (accepted)
[23]	Wu H J, Jiang W K 2012 J. Mech. Sci. Technol. (accepted)
[24]	Liu Y J, Rizzo F J 1992 Comput. Method. Appl. M 96 271
[25]	Coifman R, Rokhlin V, Wandzura S 1993 IEEE Antenn. Propag.M 35 7
[26]	Rahola J 1996 Bit. 36 333
[27]	Driscoll J R, Healy D M 1994 Adv. Appl. Math. 15 202
[28]	Jakob-Chien R, Alpert B K 1997 J. Comput. Phys. 136 580
[29]	Chowdhury I, Jandhyala V 2006 Microwave Opt. Technol. Lett.48 1961
[30]	Chen K, Harris P J 2001 Appl. Numer. Math. 36 475

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