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Solving Thin-Body Acoustic Problems Over an Impedance Plane with a Fast Multipole Indirect Boundary Element Method

Meng-Hui Liang

Institute of Sound and Vibration Research, Hefei University of Technology, Hefei, Anhui 230009, P. R. China

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Yong-Bin Zhang

Institute of Sound and Vibration Research, Hefei University of Technology, Hefei, Anhui 230009, P. R. China

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Chang-Jun Zheng

https://orcid.org/0000-0002-5383-7029

Institute of Sound and Vibration Research, Hefei University of Technology, Hefei, Anhui 230009, P. R. China

E-mail Address: cjzheng@hfut.edu.cn

Corresponding author.

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Shuai Wang

Institute of Sound and Vibration Research, Hefei University of Technology, Hefei, Anhui 230009, P. R. China

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, and

Chuan-Xing Bi

Institute of Sound and Vibration Research, Hefei University of Technology, Hefei, Anhui 230009, P. R. China

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https://doi.org/10.1142/S2591728522400060Cited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue on the Occasion of the 30th Anniversary of the Journal of Theoretical and Computational Acoustics
Edited by Michael D. Collins, Steffen Marburg and Andrew N. Norris

Abstract

This paper presents a fast multipole indirect boundary element solver for the thin-body acoustic problems over an infinite impedance plane. The half-space impedance Green’s function involving a complex line source to approximate the porous ground effects is employed in the indirect boundary integral equation (IBIE), which makes that both mass-like and spring-like impedance conditions on the infinite plane are explicitly satisfied. A nonsingular IBIE formulation is derived to implement the fast multipole method (FMM) easily. The image relations of multipole moments are used to avoid the computation and translation of multipole/local expansion coefficients in the image domain. To deal with the numerical instability in the local translation of image multipole moments, a half-space tree structure is elaborately constructed for the FMM. The validity of the method is testified by a benchmark example and the potential of the method is investigated by the numerical simulation of noise barriers with different geometrical configurations.

Keywords:

References

1. T. Ishizuka and K. Fujiwara, Performance of noise barriers with various edge shapes and acoustical conditions, Appl. Acoust. 65 (2004) 125–141. Crossref, Google Scholar
2. R. Seznec, Diffraction of sound around barriers: Use of the boundary elements technique, J. Sound. Vib. 73 (1980) 195–209. Crossref, Google Scholar
3. Y. Kawai and T. Terai, The application of integral equation methods to the calculation of sound attenuation by barriers, Appl. Acoust. 31 (1990) 101–117. Crossref, Google Scholar
4. K. Attenborough, Sound propagation close to the ground, Annu. Rev. Fluid Mech. 34 (2002) 51–82. Crossref, Google Scholar
5. T. F. W. Embleton, Tutorial on sound propagation outdoors, J. Acoust. Soc. Am. 100 (1996) 31–48. Crossref, Google Scholar
6. R. Piscoya and M. Ochmann, Boundary elements for noise barriers above an impedance ground, in Proc. INTER-NOISE 2016 (Hamburg, Germany, 2016), pp. 4357–4362. Google Scholar
7. K. M. Li, W. K. Lui and G. H. Frommer, The scattering of sound by a hard sphere above an impedance ground, Acta Acust. United Ac. 90 (2004) 251–262. Google Scholar
8. T. F. W. Embleton, J. E. Piercy and N. Olson, Outdoor sound propagation over ground of finite impedance, J. Acoust. Soc. Am. 59 (1976) 267–277. Crossref, Google Scholar
9. D. G. Albert, Observations of acoustic surface waves in outdoor sound propagation, J. Acoust. Soc. Am. 113 (2003) 2495–2500. Crossref, Google Scholar
10. L. A. D. Lacerda, L. C. Wrobel, H. Power and W. J. Mansur, A novel boundary integral formulation for three-dimensional analysis of thin acoustic barriers over an impedance plane, J. Acoust. Soc. Am. 104 (1998) 671–678. Crossref, Google Scholar
11. H. Wu, Y. Liu, W. Jiang and W. Lu, A fast multipole boundary element method for three-dimensional half-space acoustic wave problems over an impedance plane, Int. J. Comp. Methods 12 (2015) 1350090. Link, Google Scholar
12. C.-J. Zheng, W.-Y. Liu, Y.-B. Zhang, C.-X. Bi, H.-F. Gao and H.-B. Chen, Simulation of sound propagation over an infinite impedance plane by using a fast multipole BEM, J. Theor. Comput. Acoust. 28 (2020) 2050020. Link, Google Scholar
13. S. Marburg, Boundary element method for time-harmonic acoustic problems, in Computational Acoustics, M. Kaltenbacher (ed.) (Springer, Switzerland, 2018), pp. 69–158. Crossref, Google Scholar
14. Y. Liu, On the BEM for acoustic wave problems, Eng. Anal. Bound. Elem. 107 (2019) 53–62. Crossref, Google Scholar
15. T. W. Wu (ed.), Boundary Element Acoustics: Fundamentals and Computer Codes, Advances in Boundary Elements Series (WIT, UK, 2000). Google Scholar
16. M. Ochmann and R. Piscoya, Theory and Application of Acoustic Sources using Complex Analysis (Springer, Germany, 2021). Crossref, Google Scholar
17. R. Piscoya and M. Ochmann, Acoustical Green’s function and boundary element techniques for 3D half-space problems, J. Comput. Acoust. 25 (2017) 1730001. Link, Google Scholar
18. I. C. Mathews and R. A. Jeans, An acoustic boundary integral formulation for open shells allowing different impedance conditions, top and bottom surfaces, J. Sound Vib. 300 (2007) 580–588. Crossref, Google Scholar
19. C. Laurens, A. Onur, V. Dirk and D. Wim, An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains, Comput. Method. Appl. Mech. 316 (2017) 186–208. Crossref, Google Scholar
20. Y.-H. Wu, C.-Y. Dong and H.-S. Yang, A 3D isogeometric FE-IBE coupling method for acoustic-structural interaction problems with complex coupling models, Ocean. Eng. 218 (2020) 108183. Crossref, Google Scholar
21. L. Greengard and V. Rokhlin, A fast algorithm for particle simulations, J. Comput. Phys. 73 (1987) 325–348. Crossref, Google Scholar
22. C. Zheng, T. Matsumoto, T. Takahashi and H. Chen, A wideband fast multipole boundary element method for three dimensional acoustic shape sensitivity analysis based on direct differentiation method, Eng. Anal. Bound. Elem. 36 (2012) 361–371. Crossref, Google Scholar
23. N. Gumerov, R. Adelman and R. Duraiswami, Fast multipole accelerated indirect boundary elements for the Helmholtz equation, Proc. Meet. Acoust. 19 (2013) 015097. Crossref, Google Scholar
24. G. Taraldsen, The complex image method, Wave Motion 43 (2005) 91–97. Crossref, Google Scholar
25. A. R. Okoyenta, H. Wu, X. Liu and W. Jiang, A short survey on Green’s function for acoustic problems, J. Theor. Comput. Acoust. 28 (2020) 1950025. Link, Google Scholar
26. R. Piscoya and M. Ochmann, Implementation of different formulas for special Green’s functions in a 3D half-space BEM, J. Theor. Comput. Acoust. 26 (2018) 1850051. Google Scholar
27. M. O’Neil, L. Greengard and A. Pataki, On the efficient representation of the half-space impedance Green’s function for the Helmholtz equation, Wave Motion 51 (2014) 1–13. Crossref, Google Scholar
28. M. Ochmann, The complex equivalent source method for sound propagation over an impedance plane, J. Acoust. Soc. Am. 116 (2004) 3304–3311. Crossref, Google Scholar
29. W. L. Li, T. W. Wu and A. F. Seybert, A half-space boundary element method for acoustic problems with a reflecting plane of arbitrary impedance, J. Sound Vib. 171 (1994) 173–184. Crossref, Google Scholar
30. M. A. Nobile and S. I. Hayek, Acoustic propagation over an impedance plane, J. Acoust. Soc. Am. 78 (1985) 1325–1336. Crossref, Google Scholar
31. X. Di and K. E. Gilbert, An exact Laplace transform formulation for a point source above a ground surface, J. Acoust. Soc. Am. 93 (1993) 714–720. Crossref, Google Scholar
32. 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. A 323 (1971) 201–210. Crossref, Google Scholar
33. C.-J. Zheng, H.-B. Chen, H.-F. Gao and L. Du, Is the Burton–Miller formulation really free of fictitious eigenfrequencies?, Eng. Anal. Bound. Elem. 59 (2015) 43–51. Crossref, Google Scholar
34. M. A. Epton and B. Dembart, Multipole translation theory for the three-dimensional Laplace and Helmholtz equations, SIAM. J. Sci. Comput. 16 (1995) 865–897. Crossref, Google Scholar
35. N. Nishimura, Fast multipole accelerated boundary integral equation methods, Appl. Mech. Rev. 55 (2002) 299–324. Crossref, Google Scholar
36. C.-J. Zheng, H.-B. Chen and L.-L. Chen, A wideband fast multipole boundary element method for half-space/plane-symmetric acoustic wave problems, Acta Mech. Sin. 29 (2013) 219–232. Crossref, Google Scholar
37. C. Zheng, T. Matsumoto, T. Takahashi and H. Chen, Explicit evaluation of hypersingular boundary integral equations for acoustic sensitivity analysis based on direct differentiation method, Eng. Anal. Bound. Elem. 35 (2011) 1225–1235. Crossref, Google Scholar
38. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, Mathematical Tables (Dover Publications, New York, 1972). Google Scholar
39. Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 7 (1986) 856–869. Crossref, Google Scholar
40. T. W. Wu, A direct boundary element method for acoustic radiation and scattering from mixed regular and thin bodies, J. Acoust. Soc. Am. 97 (1995) 84–91. Crossref, Google Scholar
41. A. Mohsen, R. Piscoya and M. Ochmann, The application of the dual surface method to treat the nonuniqueness in solving acoustic exterior problems, Acta Acust. united Ac. 97 (2011) 699–707. Crossref, Google Scholar
42. J. W. Lee, J. T. Chen and C. F. Nien, Indirect boundary element method combining extra fundamental solutions for solving exterior acoustic problems with fictitious frequencies, J. Acoust. Soc. Am. 145 (2019) 3116–3132. Crossref, Google Scholar
43. Y. H. Wu, C. Y. Dong and H. S. Yang, Isogeometric indirect boundary element method for solving the 3D acoustic problems, J. Comput. Appl. Math. 363 (2020) 273–299. Crossref, Google Scholar

Vol. 30, No. 03

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History

Received 23 June 2022

Revised 5 August 2022

Accepted 5 August 2022

Published: 30 September 2022

Information

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Solving Thin-Body Acoustic Problems Over an Impedance Plane with a Fast Multipole Indirect Boundary Element Method

Abstract

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