Efficient technique in low-frequency fast multipole boundary element method for plane-symmetric acoustic problems

被引:17
作者
Yasuda, Yosuke [1 ]
Higuchi, Kazutaka [1 ]
Oshima, Takuya [2 ]
Sakuma, Tetsuya [3 ]
机构
[1] Kanagawa Univ, Fac Engn, Kanagawa Ku, Yokohama, Kanagawa 2218686, Japan
[2] Niigata Univ, Fac Engn, Nishi Ku, Niigata 9502181, Japan
[3] Univ Tokyo, Grad Sch Frontier Sci, Kashiwa, Chiba 2778563, Japan
关键词
Helmholtz equation; Acoustic problems; Fast multipole method (FMM); Plane-symmetric problems; SOUND FIELD ANALYSIS; INTEGRAL-EQUATION; HELMHOLTZ-EQUATION; SCATTERING; RADIATION;
D O I
10.1016/j.enganabound.2012.04.006
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The fast multipole boundary element method (FMBEM) has been well known as a highly efficient BEM with the use of the fast multipole method (FMM). In the present paper, an efficient technique for plane-symmetric acoustic problems is proposed in the framework of an FMBEM based on the original multipole expansion theory (FMBEM for low-frequency problems: LF-FMBEM). Presented here are concrete computational procedures, which are based on the symmetries among multipole expansion coefficients for a plane-symmetric sound field produced by monopole or dipole sources. The proposed technique is straightforwardly applicable to a variety of formulations for the BEM, such as hypersingular, Burton-Miller, and indirect formulations. Numerical results show an ideal improvement of computational efficiency, with the proposed technique reducing both the computation time and required memory to about 1/2(nsym) of those using the standard LF-FMBEM, where n(sym) is the number of planes of symmetry. (c) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1493 / 1501
页数:9
相关论文
共 29 条
[1]   Adaptive fast multipole boundary element method for three-dimensional half-space acoustic wave problems [J].
Bapat, M. S. ;
Shen, L. ;
Liu, Y. J. .
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2009, 33 (8-9) :1113-1123
[2]   APPLICATION OF INTEGRAL EQUATION METHODS TO NUMERICAL SOLUTION OF SOME EXTERIOR BOUNDARY-VALUE PROBLEMS [J].
BURTON, AJ ;
MILLER, GF .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1971, 323 (1553) :201-&
[3]   A FORMULATION OF THE FAST MULTIPOLE BOUNDARY ELEMENT METHOD (FMBEM) FOR ACOUSTIC RADIATION AND SCATTERING FROM THREE-DIMENSIONAL STRUCTURES [J].
Chen, Z. -S. ;
Waubke, H. ;
Kreuzer, W. .
JOURNAL OF COMPUTATIONAL ACOUSTICS, 2008, 16 (02) :303-320
[4]   A wideband fast multipole method for the Helmholtz equation in three dimensions [J].
Cheng, Hongwei ;
Crutchfield, William Y. ;
Gimbutas, Zydrunas ;
Greengard, Leslie F. ;
Ethridge, J. Frank ;
Huang, Jingfang ;
Rokhlin, Vladimir ;
Yarvin, Norman ;
Zhao, Junsheng .
JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 216 (01) :300-325
[5]   A multipole Galerkin boundary element method for acoustics [J].
Fischer, M ;
Gauger, U ;
Gaul, L .
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2004, 28 (02) :155-162
[6]   Accelerating fast multipole methods for the Helmholtz equation at low frequencies [J].
Greengard, L ;
Huang, JF ;
Rokhlin, V ;
Wandzura, S .
IEEE COMPUTATIONAL SCIENCE & ENGINEERING, 1998, 5 (03) :32-38
[7]  
Greengard L., 1988, The Rapid Evaluation of Potential Fields in Particle Systems
[8]  
Gumerov N.A., 2004, FAST MULTIPOLE METHO
[9]   Recursions for the computation of multipole translation and rotation coefficients for the 3-D helmholtz equation [J].
Gumerov, NA ;
Duraiswami, R .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2003, 25 (04) :1344-1381
[10]   A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation [J].
Gumerov, Nail A. ;
Duraiswami, Ramani .
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2009, 125 (01) :191-205