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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.
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Keywords:
- fast multipole boundary element method /
- Burton-Miller formulation /
- acoustic radiation /
- acoustic scattering
[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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[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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