On the BEM for acoustic wave problems. (English) Zbl 1464.76096
Summary: The progress of the boundary element method (BEM) for solving acoustic wave problems is reviewed in this paper. The BEM is in a unique position among all the numerical methods available for solving acoustic wave problems. During the last few decades, research on the acoustic BEM has overcome many of the difficulties, and it is now an accurate and efficient numerical method in modeling many large-scale acoustic problems. This paper focuses on reviewing the dual boundary integral equation (BIE) formulation pioneered by Burton and Miller, treatment of the singular integrals involved in the BIEs, discretization considerations, and fast solution methods for solving the acoustic BEM equations. New directions in the research on the acoustic BEM are also discussed, with a few examples to show the potentials of the BEM in modeling aeroacoustics, acoustic metamaterials, bioacoustics, and sound rendering in computer animations.
MSC:
| 76M15 | Boundary element methods applied to problems in fluid mechanics |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 76Q05 | Hydro- and aero-acoustics |
References:
| [1] | Schenck, H. A., Improved integral formulation for acoustic radiation problems, J Acoust Soc Am, 44, 41-58 (1968) · Zbl 0187.50302 |
| [2] | Burton, A. J.; Miller, G. F., The application of integral equation methods to the numerical solution of some exterior boundary-value problems, Proc R Soc Lond Ser A, 323, 201-210 (1971) · Zbl 0235.65080 |
| [3] | Ursell, F., On the exterior problems of acoustics, Proc Camb Philos Soc, 74, 117-125 (1973) · Zbl 0259.35019 |
| [4] | Kleinman, R. E.; Roach, G. F., Boundary integral equations for the three-dimensional Helmholtz equation, SIAM Rev, 16, 214-236 (1974) · Zbl 0253.35023 |
| [5] | Jones, D. S., Integral equations for the exterior acoustic problem, Q J Mech Appl Math, 27, 129-142 (1974) · Zbl 0281.45006 |
| [6] | Meyer, W. L.; Bell, W. A.; Zinn, B. T.; Stallybrass, M. P., Boundary integral solutions of three dimensional acoustic radiation problems, J Sound Vib, 59, 245-262 (1978) · Zbl 0391.76052 |
| [7] | Seybert, A. F.; Soenarko, B.; Rizzo, F. J.; Shippy, D. J., An advanced computational method for radiation and scattering of acoustic waves in three dimensions, J Acoust Soc Am, 77, 2, 362-368 (1985) · Zbl 0574.73038 |
| [8] | Kress, R., Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering, Quart J Mech Appl Math, 38, 2, 323-341 (1985) · Zbl 0559.73095 |
| [9] | Seybert, A. F.; Rengarajan, T. K., The use of CHIEF to obtain unique solutions for acoustic radiation using boundary integral equations, J Acoust Soc Am, 81, 1299-1306 (1987) |
| [10] | Cunefare, K. A.; Koopmann, G., A boundary element method for acoustic radiation valid for all wavenumbers, J Acoust Soc Am, 85, 1, 39-48 (1989) |
| [11] | Everstine, G. C.; Henderson, F. M., Coupled finite element/boundary element approach for fluid structure interaction, J Acoust Soc Am, 87, 5, 1938-1947 (1990) |
| [12] | Martinez, R., The thin-shape breakdown (TSB) of the Helmholtz integral equation, J Acoust Soc Am, 90, 5, 2728-2738 (1991) |
| [13] | Cunefare, K. A.; Koopmann, G. H., A boundary element approach to optimization of active noise control sources on three-dimensional structures, J Vib Acoust, 113, 387-394 (1991), No. July |
| [14] | Ciskowski, R. D.; Brebbia, C. A., Boundary element methods in acoustics (1991), Kluwer Academic Publishers: Kluwer Academic Publishers New York · Zbl 0758.76036 |
| [15] | Wu, T. W., Boundary element acoustics: fundamentals and computer codes (2000), WIT Press: WIT Press Southampton · Zbl 0987.76500 |
| [16] | Krishnasamy, G.; Rudolphi, T. J.; Schmerr, L. W.; Rizzo, F. J., Hypersingular boundary integral equations: some applications in acoustic and elastic wave scattering, J Appl Mech, 57, 404-414 (1990) · Zbl 0729.73251 |
| [17] | Amini, S., On the choice of the coupling parameter in boundary integral formulations of the exterior acoustic problem, Appl Anal, 35, 75-92 (1990) · Zbl 0663.35013 |
| [18] | Chien, C. C.; Rajiyah, H.; Atluri, S. N., An effective method for solving the hypersingular integral equations in 3-D acoustics, J Acoust Soc Am, 88, 2, 918-937 (1990) |
| [19] | Wu, T. W.; Seybert, A. F.; Wan, G. C., On the numerical implementation of a Cauchy principal value integral to insure a unique solution for acoustic radiation and scattering, J Acoust Soc Am, 90, 1, 554-560 (1991) |
| [20] | Liu, Y. J., Development and applications of hypersingular boundary integral equations for 3-D acoustics and elastodynamics (1992), Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign |
| [21] | Liu, Y. J.; Rizzo, F. J., A weakly-singular form of the hypersingular boundary integral equation applied to 3-D acoustic wave problems, Comput Methods Appl Mech Eng, 96, 271-287 (1992) · Zbl 0754.76072 |
| [22] | Yang, S.-A., Acoustic scattering by a hard and soft body across a wide frequency range by the Helmholtz integral equation method, J Acoust Soc Am, 102, 5, 2511-2520 (1997) |
| [23] | Liu, Y. J.; Chen, S. H., A new form of the hypersingular boundary integral equation for 3-D acoustics and its implementation with \(C^0\) boundary elements, Comput Methods Appl Mech Eng, 173, 3-4, 375-386 (1999) · Zbl 0946.76051 |
| [24] | Shen, L.; Liu, Y. J., An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the burton-miller formulation, Comput Mech, 40, 3, 461-472 (2007) · Zbl 1176.76083 |
| [25] | Bapat, M. S.; Shen, L.; Liu, Y. J., Adaptive fast multipole boundary element method for three-dimensional half-space acoustic wave problems, Eng Anal Bound Elem, 33, 8-9, 1113-1123 (2009) · Zbl 1244.76030 |
| [26] | Li, S.; Huang, Q., A fast multipole boundary element method based on the improved burton – miller formulation for three-dimensional acoustic problems, Eng Anal Bound Elem, 35, 5, 719-728 (2011) · Zbl 1259.76030 |
| [27] | Wu, H. J.; Liu, Y. J.; Jiang, W. K., Analytical integration of the moments in the diagonal form fast multipole boundary element method for 3-D acoustic wave problems, Eng Anal Bound Elem, 36, 2, 248-254 (2012) · Zbl 1245.76140 |
| [28] | Wu, H. J.; Liu, Y. J.; Jiang, W. K., A fast multipole boundary element method for 3D multi-domain acoustic scattering problems based on the burton – miller formulation, Eng Anal Bound Elem, 36, 5, 779-788 (2012) · Zbl 1351.74147 |
| [29] | Zheng, C.; Matsumoto, T.; Takahashi, T.; Chen, H., A wideband fast multipole boundary element method for three dimensional acoustic shape sensitivity analysis based on direct differentiation method, Eng Anal Bound Elem, 36, 3, 361-371 (2012) · Zbl 1245.74097 |
| [30] | Wu, H.; Liu, Y. J.; Jiang, W.; Lu, W., A fast multipole boundary element method for three-dimensional half-space acoustic wave problems over an impedance plane, Int J Comput Methods, 12, 1, Article 1350090 pp. (2015) · Zbl 1359.76203 |
| [31] | Cao, Y.; Wen, L.; Xiao, J.; Liu, Y. J., A fast directional BEM for large-scale acoustic problems based on the Burton-Miller formulation, Eng Anal Bound Elem, 50, 47-58 (2015) · Zbl 1403.76062 |
| [32] | Zheng, C.-J.; Chen, H.-B.; Gao, H.-F.; Du, L., Is the Burton-Miller formulation really free of fictitious eigenfrequencies?, Eng Anal Bound Elem, 59, 43-51 (2015) · Zbl 1403.76129 |
| [33] | Wu, H.; Ye, W.; Jiang, W., A collocation BEM for 3D acoustic problems based on a non-singular Burton-Miller formulation with linear continuous elements, Comput Methods Appl Mech Eng, 332, 191-216 (2018) · Zbl 1439.74488 |
| [34] | Li, J.; Chen, W.; Qin, Q., A modified dual-level fast multipole boundary element method based on the burton – miller formulation for large-scale three-dimensional sound field analysis, Comput Methods Appl Mech Eng, 340, 121-146 (2018) · Zbl 1440.65262 |
| [35] | Fu, Z.-J.; Chen, W.; Gu, Y., Burton-Miller-type singular boundary method for acoustic radiation and scattering, J Sound Vib, 333, 16, 3776-3793 (2014) |
| [36] | Pierce, A. D., Acoustics: an introduction to its physical principles and applications (1991), ASA: ASA New York |
| [37] | Liu, Y. J., Fast multipole boundary element method - Theory and applications in engineering (2009), Cambridge University Press: Cambridge University Press Cambridge |
| [38] | Liu, Y. J.; Rudolphi, T. J., Some identities for fundamental solutions and their applications to weakly-singular boundary element formulations, Eng Anal Bound Elem, 8, 6, 301-311 (1991) |
| [39] | Liu, Y. J.; Rudolphi, T. J., New identities for fundamental solutions and their applications to non-singular boundary element formulations, Comput Mech, 24, 4, 286-292 (1999) · Zbl 0969.74073 |
| [40] | Krishnasamy, G.; Rizzo, F. J.; Liu, Y. J., Boundary integral equations for thin bodies, Int J Numer Methods Eng, 37, 107-121 (1994) · Zbl 0795.73076 |
| [41] | Liu, Y. J., Analysis of shell-like structures by the boundary element method based on 3-D elasticity: formulation and verification, Int J Numer Methods Eng, 41, 541-558 (1998) · Zbl 0910.73068 |
| [42] | Krishnasamy, G.; Rizzo, F. J.; Rudolphi, T. J., Continuity requirements for density functions in the boundary integral equation method, Comput Mech, 9, 267-284 (1992) · Zbl 0755.65108 |
| [43] | Martin, P. A.; Rizzo, F. J., Hypersingular integrals: how smooth must the density be?, Int J Numer Methods Eng, 39, 687-704 (1996) · Zbl 0846.65070 |
| [44] | Krishnasamy, G.; Rizzo, F. J.; Liu, Y. J., Some advances in boundary integral methods for wave-scattering from cracks. Some advances in boundary integral methods for wave-scattering from cracks, Acta Mechanica, 3, 55-65 (1992), Springer · Zbl 0784.73023 |
| [45] | Liu, Y. J.; Rizzo, F. J., Scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation, J Acoust Soc Am, 102, 2, 926-932 (1997), No. Pt.1, August |
| [46] | Schanz, M.; Antes, H., Application of ‘operational quadrature methods’ in time domain boundary element methods, Mechanica, 32, 3, 179-186 (1997) · Zbl 0913.73075 |
| [47] | Nishimura, N., Fast multipole accelerated boundary integral equation methods, Appl Mech Rev, 55, 4, 299-324 (2002), (July) |
| [48] | Langer, S.; Schanz, M., Time domain boundary element method, (Marburg, S.; Nolte, B., Computational acoustics of noise propagation in fluids – finite and boundary element methods (2008), Springer: Springer New York), 495-516 |
| [49] | Schanz, M.; Ruberg, T.; Kielhorn, L., Time domain BEM: numerical aspects of collocation and Galerkin formulations, (Manolis, G. D.; Polyzos, D., Recent advances in boundary element Methods: a volume to honor professor Dimitri Beskos (2009), Springer) · Zbl 1161.74518 |
| [50] | Gu, X.; Li, S., Convolution quadrature time-domain boundary element method for two-dimensional aeroacoustic noise prediction, Acoust Phys, 64, 6, 731-741 (2018) |
| [51] | Gimperlein, H.; Oezdemir, C.; Stephan, E. P., Time domain boundary element methods for the neumann problem: error estimates and acoustic problems, J Comput Math, 36, 1, 70-89 (2018) |
| [52] | Marburg, S., The Burton and Miller method: unlocking another mystery of its coupling parameter, J Comput Acoust, 24, 01, Article 1550016 pp. (2016) · Zbl 1360.76167 |
| [53] | Sladek, V.; Sladek, J.; Tanaka, M., Regularization of hypersingular and nearly singular integrals in the potential theory and elasticity, Int J Numer Methods Eng, 36, 1609-1628 (1993) · Zbl 0772.73091 |
| [54] | Chen, J. T.; Hong, H. K., Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series, Appl Mech Rev, 52, 1, 17-33 (1999) |
| [55] | Matsumoto, T.; Zheng, C.; Harada, S.; Takahashi, T., Explicit evaluation of hypersingular boundary integral equation for 3-D Helmholtz equation discretized with constant triangular element, J Comput Sci Technol, 4, 3, 194-206 (2010) |
| [56] | Zheng, C.; Matsumoto, T.; Takahashi, T.; Chen, H., Explicit evaluation of hypersingular boundary integral equations for acoustic sensitivity analysis based on direct differentiation method, Eng Anal Bound Elem, 35, 11, 1225-1235 (2011) · Zbl 1259.76035 |
| [57] | Tadeu, A.; António, J., 3D acoustic wave simulation using BEM formulations: closed form integration of singular and hypersingular integrals, Eng Anal Bound Elem, 36, 9, 1389-1396 (2012) · Zbl 1351.74137 |
| [58] | Krishnasamy, G.; Rizzo, F. J.; Liu, Y. J., Scattering of acoustic and elastic waves by crack-like objects: the role of hypersingular integral equations, (Thompson, D. O.; Chimenti, D. E., Review of progress in quantitative nondestructive evaluation (1991), Plenum Press: Plenum Press Brunswick, Maine) |
| [59] | Krishnasamy, G.; Rizzo, F. J.; Rudolphi, T. J., Hypersingular boundary integral equations: their occurrence, interpretation, regularization and computation, (Banerjee and, P. K.; etal., Developments in boundary element methods (1991), Elsevier Applied Science Publishers: Elsevier Applied Science Publishers London), Chapter 7 |
| [60] | Fukui, T., Research on the boundary element method – development and applications of fast and accurate computations (1998), Department of Global Environment Engineering, Kyoto University, Ph.D. Dissertation (in Japanese) |
| [61] | Salvadori, A., Analytical integrations of hypersingular kernel in 3D BEM problems, Comp Methods Appl Mech Eng, 190, 3957-3975 (2001) · Zbl 0987.65128 |
| [62] | Gray, L. J.; Soucie, C. S., A hermite interpolation algorithm for hypersingular boundary integrals, Int J Numer Methods Eng, 36, 2357-2367 (1993) · Zbl 0781.73074 |
| [63] | Liu, Y. J.; Rizzo, F. J., Application of overhauser \(C^{(1)}\) continuous boundary elements to ‘hypersingular’ BIE for 3-D acoustic wave problems, (Brebbia, C. A.; Gipson, G. S., Boundary elements XIII (1991), Computation Mechanics Publications), 957-966, Tulsa, OK |
| [64] | Liu, Y. J.; Mukherjee, S.; Nishimura, N.; Schanz, M.; Ye, W.; Sutradhar, A.; Pan, E.; Dumont, N. A.; Frangi, A.; Saez, A., Recent advances and emerging applications of the boundary element method, Appl Mech Rev, 64 (2012), No. March, 1-38 |
| [65] | Rokhlin, V., Rapid solution of integral equations of classical potential theory, J Comp Phys, 60, 187-207 (1985) · Zbl 0629.65122 |
| [66] | Greengard, L. F.; Rokhlin, V., A fast algorithm for particle simulations, J Comput Phys, 73, 2, 325-348 (1987) · Zbl 0629.65005 |
| [67] | Greengard, L. F., The rapid evaluation of potential fields in particle systems (1988), The MIT Press: The MIT Press Cambridge · Zbl 1001.31500 |
| [68] | Rokhlin, V., Rapid solution of integral equations of scattering theory in two dimensions, J Comput Phys, 86, 2, 414-439 (1990) · Zbl 0686.65079 |
| [69] | Rokhlin, V., Diagonal forms of translation operators for the helmholtz equation in three dimensions, Appl Comput Harmon Anal, 1, 1, 82-93 (1993) · Zbl 0795.35021 |
| [70] | Epton, M.; Dembart, B., Multipole translation theory for the three dimensional laplace and helmholtz equations, SIAM J Sci Comput, 16, 865-897 (1995) · Zbl 0852.31006 |
| [71] | Koc, S.; Chew, W. C., Calculation of acoustical scattering from a cluster of scatterers, J Acoust Soc Am, 103, 2, 721-734 (1998) |
| [72] | Greengard, L. F.; Huang, J.; Rokhlin, V.; Wandzura, S., Accelerating fast multipole methods for the Helmholtz equation at low frequencies, IEEE Comput Sci Eng, 5, 3, 32-38 (1998) |
| [73] | Tournour, M. A.; Atalla, N., Efficient evaluation of the acoustic radiation using multipole expansion, Int J Numer Methods Eng, 46, 6, 825-837 (1999) · Zbl 1041.76548 |
| [74] | Darve, E., The fast multipole method I: error analysis and asymptotic complexity, SIAM J Numer Anal, 38, 1, 98-128 (2000) · Zbl 0974.65033 |
| [75] | Darve, E., The fast multipole method: numerical implementation, J Comput Phys, 160, 1, 195-240 (2000) · Zbl 0974.78012 |
| [76] | Yasuda, Y.; Sakuma, T., A technique for plane-symmetric sound field analysis in the fast multipole boundary element method, J Comput Acoust, 13, 1, 71-85 (2005) · Zbl 1137.76434 |
| [77] | Gumerov, N. A.; Duraiswami, R., Recursions for the computation of multipole translation and rotation coefficients for the 3-D helmholtz equation, SIAM J Sci Comput, 25, 4, 1344-1381 (2003) · Zbl 1072.65157 |
| [78] | Darve, E.; Havé, P., Efficient fast multipole method for low-frequency scattering, J Comput Phys, 197, 1, 341-363 (2004) · Zbl 1073.65133 |
| [79] | Fischer, M.; Gauger, U.; Gaul, L., A multipole galerkin boundary element method for acoustics, Eng Anal Bound Elem, 28, 155-162 (2004) · Zbl 1049.76042 |
| [80] | Chen, J. T.; Chen, K. H., Applications of the dual integral formulation in conjunction with fast multipole method in large-scale problems for 2D exterior acoustics, Eng Anal Bound Elem, 28, 6, 685-709 (2004) · Zbl 1130.76375 |
| [81] | Gumerov, N. A.; Duraiswami, R., Fast multipole methods for the helmholtz equation in three dimensions (2004), Elsevier: Elsevier Amsterdam |
| [82] | Cheng, H.; Crutchfield, W. Y.; Gimbutas, Z.; Greengard, L. F.; Ethridge, J. F.; Huang, J.; Rokhlin, V.; Yarvin, N.; Zhao, J., A wideband fast multipole method for the helmholtz equation in three dimensions, J Comput Phys, 216, 1, 300-325 (2006) · Zbl 1093.65117 |
| [83] | Gumerov, N. A.; Duraiswami, R., A broadband fast multipole accelerated boundary element method for the three dimensional helmholtz equation, J Acoust Soc Am, 125, 1, 191-205 (2009) |
| [84] | Saad, Y.; Schultz, M., A generalized minimal residual algorithm for solving nonsymmetric linear system, SIAM J Stat Comput, 7, 856-869 (1986) · Zbl 0599.65018 |
| [85] | Liu, Y. J.; Nishimura, N., The fast multipole boundary element method for potential problems: a tutorial, Eng Anal Bound Elem, 30, 5, 371-381 (2006) · Zbl 1187.65134 |
| [86] | Ying, L.; Biros, G.; Zorin, D., A kernel-independent adaptive fast multipole algorithm in two and three dimensions, J Comput Phys, 196, 2, 591-626 (2004) · Zbl 1053.65095 |
| [87] | Engquist, B.; Ying, L., Fast directional algorithms for the helmholtz kernel, J Comput Appl Math, 234, 6, 1851-1859 (2010) · Zbl 1379.65103 |
| [88] | Fong, W.; Darve, E., The black-box fast multipole method, J Comput Phys, 228, 23, 8712-8725 (2009) · Zbl 1177.65009 |
| [89] | Cui, X. B.; Ji, Z. L., Fast multipole boundary element approaches for acoustic attenuation prediction of reactive silencers, Eng Anal Bound Elem, 36, 7, 1053-1061 (2012) · Zbl 1351.76137 |
| [90] | Li, J.; Chen, W.; Fu, Z., A modified dual-level algorithm for large-scale three-dimensional laplace and helmholtz equation, Comput Mech, 62, 4, 893-907 (2018) · Zbl 1459.65229 |
| [91] | Hackbusch, W., A sparse matrix arithmetic based on \(H\)-matrices. Part I: introduction to \(H\)-matrices, Computing, 62, 2, 89-108 (1999) · Zbl 0927.65063 |
| [92] | Bebendorf, M., Approximation of boundary element matrices, Numer Math, 86, 4, 565-589 (2000) · Zbl 0966.65094 |
| [93] | Bebendorf, M.; Rjasanow, S., Adaptive low-rank approximation of collocation matrices, Computing, 70, 1-24 (2003) · Zbl 1068.41052 |
| [94] | Rjasanow, S.; Steinbach, O., The fast solution of boundary integral equations (2007), Springer: Springer Berlin · Zbl 1119.65119 |
| [95] | Bebendorf, M., Hierarchical Matrices: a means to efficiently solve elliptic boundary value problems (2008), Springer-Verlag: Springer-Verlag Berlin · Zbl 1151.65090 |
| [96] | Brancati, A.; Aliabadi, M. H.; Benedetti, I., Hierarchical adaptive cross approximation GMRES technique for solution of acoustic problems using the boundary element method, CMES Comput Model Eng Sci, 43, 2, 149-172 (2009) · Zbl 1232.65158 |
| [97] | Brunner, D.; Junge, M.; Rapp, P.; Bebendorf, M.; Gaul, L., Comparison of the fast multipole method with hierarchical matrices for the Helmholtz-BEM, CMES Comput Model Eng Sci, 58, 2, 131-158 (2010) · Zbl 1231.74454 |
| [98] | Martinsson, P. G.; Rokhlin, V., A fast direct solver for boundary integral equations in two dimensions, J Comput Phys, 205, 1, 1-23 (2005) · Zbl 1078.65112 |
| [99] | Greengard, L.; Gueyffier, D.; Martinsson, P.-G.; Rokhlin, V., Fast direct solvers for integral equations in complex three-dimensional domains, Acta Numer, 18, 243-275 (2009) · Zbl 1176.65141 |
| [100] | Ho, K.; Greengard, L., A fast direct solver for structured linear systems by recursive skeletonization, SIAM J Sci Comput, 34, 5, A2507-A2532 (2012) · Zbl 1259.65062 |
| [101] | Ambikasaran, S.; Darve, E., An O(NlogN) fast direct solver for partial hierarchically semi-separable matrices, J Sci Comput, 57, 3, 477-501 (2013) · Zbl 1292.65030 |
| [102] | Lai, J.; Ambikasaran, S.; Greengard, L., A fast direct solver for high frequency scattering from a large cavity in two dimensions, SIAM J Sci Comput, 36, 6, 887-903 (2014) · Zbl 1319.78008 |
| [103] | Corona, E.; Martinsson, P.-G.; Zorin, D., An O(N) direct solver for integral equations on the plane, Appl Comput Harmon Anal, 38, 2, 284-317 (2015) · Zbl 1307.65180 |
| [104] | Coulier, P.; Pouransari, H.; Darve, E., The inverse fast multipole method: using a fast approximate direct solver as a preconditioner for dense linear systems, SIAM J Sci Comput, 39, 3, 761-796 (2015) · Zbl 1365.65068 |
| [105] | Huang, S.; Liu, Y. J., A new fast direct solver for the boundary element method, Comput Mech, 60, 3, 379-392 (2017) · Zbl 1412.65234 |
| [106] | Tosh, A.; Liever, P.; Owens, F.; Liu, Y. J., A high-fidelity CFD/BEM methodology for launch pad acoustic environment prediction, (Proceedings of the 18th AIAA/CEAS aeroacoustics conference (33rd AIAA aeroacoustics conference) (2012), AIAA: AIAA Colorado Springs), Paper Number: AIAA 2012-2107 |
| [107] | Wu, T. W.; Lee, L., A direct boundary integral formulation for acoustic radiation in a subsonic uniform flow, J Sound Vib, 175, 1, 51-63 (1994) · Zbl 0945.76542 |
| [108] | Lighthill, M. J., On sound generated aerodynamically. I. General theory, Proc R Soc Lond A Math Phys Sci, 211, 1107, 564-587 (1952) · Zbl 0049.25905 |
| [109] | Ffowcs-Williams, J. E.; Hawkings, D. L., Sound generation by turbulence and surfaces in arbitrary motion, Philos Trans R Soc Lond Ser A Math Phys Sci, 264, 1151, 321-342 (1969) · Zbl 0182.59205 |
| [110] | Papamoschou, D., Prediction of jet noise shielding, (Proceedings of the 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition (2010), American Institute of Aeronautics and Astronautics) |
| [111] | Papamoschou, D.; Mayoral, S., Modeling of jet noise sources and their diffraction with uniform flow, (Proceedings of the 51st AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition (2013), American Institute of Aeronautics and Astronautics) |
| [112] | Wolf, W. R.; Lele, S. K., Acoustic analogy formulations accelerated by fast multipole method for two-dimensional aeroacoustic problems, AIAA J, 48, 10, 2274-2285 (2010) |
| [113] | Wolf, W. R.; Lele, S. K., Aeroacoustic integrals accelerated by fast multipole method, AIAA J, 49, 7, 1466-1477 (2011) |
| [114] | Wolf, W. R.; Azevedo, J. L.F.; Lele, S. K., Convective effects and the role of quadrupole sources for aerofoil aeroacoustics, J Fluid Mech, 708, 502-538 (2012) · Zbl 1275.76187 |
| [115] | Mao, Y.; Xu, C., Accelerated method for predicting acoustic far field and acoustic power of rotating source, AIAA J, 54, 2, 603-615 (2016) |
| [116] | Alomar, A.; Angland, D.; Zhang, X., Extension of roughness noise to bluff bodies using the boundary element method, J Sound Vib, 414, 318-337 (2018) |
| [117] | Gorishnyy, T.; Maldovan, M.; Ullal, C.; Thomas, E., Sound ideas, Phys World, 12, 1-6 (2005) |
| [118] | Liang, Z.; Li, J., Extreme acoustic metamaterial by coiling up space, Phys Rev Lett, 108, 11, Article 114301 pp. (2012) |
| [119] | Ma, G.; Sheng, P., Acoustic metamaterials: from local resonances to broad horizons, Sci Adv, 2, 2, Article e1501595 pp. (2016) |
| [120] | Cummer, S. A.; Christensen, J.; Alù, A., Controlling sound with acoustic metamaterials, Nat Rev Mater, 1, 16001 (2016) |
| [121] | Pennec, Y.; Vasseur, J. O.; Djafari-Rouhani, B.; Dobrzyński, L.; Deymier, P. A., Two-dimensional phononic crystals: examples and applications, Surf Sci Rep, 65, 8, 229-291 (2010) |
| [122] | Henríquez, V. C.; Andersen, P. R.; Jensen, J. S.; Juhl, P. M.; Sánchez-Dehesa, J., A numerical model of an acoustic metamaterial using the boundary element method including viscous and thermal losses, J Comput Acoust, 25, 04, Article 1750006 pp. (2017) · Zbl 06775142 |
| [123] | Li, F.-L.; Wang, Y.-S.; Zhang, C.; Yu, G.-L., Boundary element method for band gap calculations of two-dimensional solid phononic crystals, Eng Anal Bound Elem, 37, 2, 225-235 (2013) · Zbl 1351.74118 |
| [124] | Mey, F. D.; Reijniers, J.; Peremans, H.; Otani, M.; Firzlaff, U., Simulated head related transfer function of the phyllostomid bat phyllostomus discolor, J. Acoust. Soc. Am., 124, 4, 2123-2132 (2008) |
| [125] | Mehrgardt, S.; Mellert, V., Transformation characteristics of the external human ear, J Acoust Soc Am, 61, 6, 1567-1576 (1977) |
| [126] | Wang, J.-H.; Qu, A.; Langlois, T. R.; James, D. L., Toward wave-based sound synthesis for computer animation, ACM TransGraph, 37, 4, 1-16 (2018), SIGGRAPH 2018 |
| [127] | Chadwick, J.; An, S.; James, D. L., Harmonic shells: a practical nonlinear sound model for near-rigid thin shells, ACM Trans Graph, 28, 5, 119:1-119:10 (2009), SIGGRAPH 2009 |
| [128] | Zheng, C.; James, D. L., Rigid-body fracture sound with precomputed soundbanks, ACM Trans Graph, 29, 3, 1-13 (2010), SIGGRAPH 2010 |
| [129] | Zheng, C.; James, D. L., Toward high-quality modal contact sound, ACM Trans Graph, 30, 4, 1-11 (2011), SIGGRAPH 2011 |
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