A fast directional BEM for large-scale acoustic problems based on the Burton-Miller formulation

Engineering Analysis with Boundary Elements

Volumn 50, Issue , 2015, Pages 47-58

  Cao, Yanchuang ^a   Wen, Lihua ^a   Xiao, Jinyou ^a   Liu, Yijun ^a,b  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

^b 705 Engineering Research Center   (United States)

Author keywords

Boundary element method; Burton Miller formulation; Fast directional algorithm; Nystr m method

Indexed keywords

ACOUSTIC FIELDS; BOUNDARY ELEMENT METHOD; BOUNDARY INTEGRAL EQUATIONS; LINEAR SYSTEMS; NUMERICAL METHODS;

ACOUSTIC SCATTERING PROBLEM; BOUNDARY INTEGRAL EQUATIONS (BIE); BURTON-MILLER; DIRECTIONAL ALGORITHMS; FAST BOUNDARY ELEMENT METHOD; LARGE-SCALE ENGINEERING; M METHOD; NUMERICAL IMPLEMENTATION; ACOUSTIC PROBLEMS;

ITERATIVE METHODS; BOUNDARY ELEMENT METHOD;

EID: 84906840553     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2014.07.006     Document Type: Article

References (34)

1. A.J. Burton, and G.F. Miller The application of integral equation methods to the numerical solution of some exterior boundary-value problems Proc R Soc Lond Ser A 323 1971 201 210
2. H.A. Schenck Improved integral formulation for acoustic radiation problems J Acoust Soc Am 44 1 1968 41 58
3. I.L. Chen, J.T. Chen, and M.T. Liang Analytical study and numerical experiments for radiation and scattering problems using the CHIEF method J Sound Vib 248 5 2001 809 828 (Pubitemid 34011297)
4. L. Greengard, and V. Rokhlin A fast algorithm for particle simulation J Comput Phys 73 1987 325 348
5. L. Greengard, and V. Rokhlin A new version of the fast multipole method for the Laplace equation in three dimensions Acta Numer 6 1 1997 229 269
6. Eric Darve The fast multipole method numerical implementation J Comput Phys 160 2000 195 240
7. W. Hackbusch A sparse matrix arithmetic based on H-matrices. Part I. Introduction to H-matrices Computing 62 1999 89 108
8. G. Beylkin, R. Coifman, and V. Rokhlin Fast wavelet transforms and numerical algorithms Pure Appl Math 37 1991 141 183
9. Jinyou Xiao, Lihua Wen, and Johannes Tausch On fast matrix-vector multiplication in wavelet Galerkin BEM Eng Anal Bound Elem 33 2 2009 159 167
10. Joel R. Phillips, and Jocob K. White A precorrected-FFT method for electrostatic analysis of complicated 3-D structures IEEE Trans Comput-Aided Des Integr Circuits Syst 16 10 1997 1059 1072 (Pubitemid 127828689)
11. Jinyou Xiao, Wenjing Ye, Yaxiong Cai, and Jun Zhang Precorrected FFT accelerated BEM for large-scale transient elastodynamic analysis using frequency-domain approach Int J Numer Methods Eng 90 1 2012 116 134
12. Mario Bebendorf Approximation of boundary element matrices Numer Math 86 2000 565 589
13. Mario Bebendorf, and Sergej Rjasanow Adaptive low-rank approximation of collocation matrices Computing 70 2003 1 24
14. N. Nishimura Fast multipole accelerated boundary integral equation methods Appl Mech Rev 55 4 2002 299 324 (Pubitemid 40205891)
15. L. Shen, and Y.J. Liu An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton-Miller formulation Comput Mech 40 3 2007 461 472 (Pubitemid 46978080)
16. J.T. Chen, and K.H. Chen Applications of the dual integral formulation in conjunction fast multipole method in large-scale problems for 2D exterior acoustics Eng Anal Bound Elem 28 2004 685 709
17. Stéphanie Chaillat, Marc Bonnet, and Jean-François Semblat A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain Comput Methods Appl Mech Eng 197 2008 4233 4249
18. V. Rokhlin Diagonal forms of translation operators for the Helmholtz equation in three dimensions Appl Comput Harmon Anal 1 1993 82 93
19. Hongwei Cheng, William Y. Crutchfield, Zydrunas Gimbutas, Leslie F. Greengard, J. Frank Ethridge, and Jingfang Huang et al. A wideband fast multipole method for the Helmholtz equation in three dimensions J Comput Phys 216 2006 300 325 (Pubitemid 43632566)
20. Nail A. Gumerov, and Ramani Duraiswami A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation J Acoust Soc Am 125 1 2009 191 205
21. Lexing Ying, George Biros, and Denis Zorin A kernel-independent adaptive fast multipole algorithm in two and three dimensions J Comput Phys 196 2004 591 626 (Pubitemid 38613258)
22. William Fong, and Eric Darve The black-box fast multipole method J Comput Phys 228 23 2009 8712 8725
23. Bo Zhang, Jingfang Huang, Nikos P. Pitsianis, and Xiaobai Sun A Fourier-series-based kernel-independent fast multipole method J Comput Phys 230 15 2011 5807 5821
24. Chandrajit Bajaj, Shun-Chuan Chen, and Alexander Rand An efficient higher-order fast multipole boundary element solution for Poisson-Boltzmann- based molecular electrostatics SIAM J Sci Comput 33 2 2011 826 848
25. Lexing Ying, George Biros, and Denis Zorin A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains J Comput Phys 219 1 2006 247 275 (Pubitemid 44615404)
26. Messner Matthias, Bramas Berenger, Coulaud Olivier, Darve Eric, Optimized M2L kernels for the Chebyshev interpolation based fast multipole method, arXiv preprint, arxiv:1210.7292; 2012. p. 1-23.
27. Matthias Messner, Martin Schanz, and Eric Darve Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation J Comput Phys 231 4 2012 1175 1196
28. Achi Brandt Multilevel computations of integral transforms and particle interactions with oscillatory kernels Comput Phys Commun 65 1 1991 24 38 (Pubitemid 21665553)
29. Björn Engquist, and Lexing Ying Fast directional multilevel algorithms for oscillatory kernels SIAM J Sci Comput 29 4 2007 1710 1737
30. Paul Tsuji, and Lexing Ying A fast directional algorithm for high-frequency electromagnetic scattering J Comput Phys 230 14 2011 5471 5487
31. M. Guiggiani, G. Krishnasamy, T.J. Rudolphi, and F.J. Rizzo A general algorithm for the numerical solution of hypersingular boundary integral equations J Appl Mech 59 September 1992 604 614 (Pubitemid 23590253)
32. J. Strain Locally corrected multidimensional quadrature rules for singular functions SIAM J Sci Comput 16 4 1995 992 1017
33. Junjie Rong, Lihua Wen, and Jinyou Xiao Efficient improvement of the polar coordinate transformation for evaluating BEM singular integrals on curved elements Eng Anal Bound Elem 38 January 2014 83 93
34. Björn Engquist, and Lexing Ying Fast directional algorithms for the Helmholtz kernel J Comput Appl Math 234 2010 1851 1859