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Fundamental Equations of Acoustics Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Boundary Element Method for Time-Harmonic Acoustic Problems

Author : Steffen Marburg

Published in: Computational Acoustics

Publisher: Springer International Publishing

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Abstract

This chapter presents an introduction to the solution of time-harmonic acoustic problems by a boundary element method (BEM). Specifically, the Helmholtz equation with admittance boundary conditions is solved in 3d. The chapter starts with a derivation of the Kirchhoff–Helmholtz integral equation from a residual formulation of the Helmholtz equation. The discretization process with introduction of basis and test functions is described and shown for the collocation and the Galerkin method. Thereafter, only collocation is used. The next section describes the application of field sources and incident wave fields on behalf of a particular solution. This is followed by a discussion on field point evaluation and a detailed description on the evaluation of the system matrix entries. The latter starts with the integral free terms, continues with an adaptive integration strategy for regular and quasi-singular integrals and finishes with an integration strategy for singular integrals. Subsequent sections discuss the choice of boundary elements and the methods to deal with the well-known non-uniqueness problem in BEM. While it has become obvious for the former problem that discontinuous Lagrangian elements perform the best, in the latter case the author is convinced that the Burton and Miller method is the only safe and efficient choice to avoid irregular frequencies. The next subsection explains the motivation for and the basic idea of fast boundary element techniques and it concludes with a discussion about the cases when these fast techniques are actually reasonable. A section on structure fluid interaction is not just describing the so-called mortar formulation but also shows that a (non-local) boundary admittance may contain the complete information about the interaction between fluid and structure. The final two subsections deal with symmetric and periodic problems on the one side and with panel contribution analysis on the other side. Throughout this chapter, numerous different examples are presented. In some cases, the author chose simple one-dimensional examples which may be solved analytically. Other examples are rather industrial applications such as sedan cabin compartments, diesel engine radiation, a tire noise problem and the computation of common room acoustic measures for a music recording studio.

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previous chapter Non-conforming Finite Elements for Flexible Discretization with Applications to Aeroacoustics
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Literature
Adey, R. A., Niku, S. M., Baynham, J., & Burns, P. (1995). Predicting acoustic contributions and sensitivity. Application to vehicle structures. In C. A. Brebbia (Ed.), Computational acoustics and its environmental applications (pp. 181–188). Southampton: Computational Mechanics Publications.
Atkinson, K. E. (1997). The numerical solution of integral equations of the second kind (1st ed.). Cambridge: Cambridge University Press.CrossRefMATH
Baumgart, J., Marburg, S., & Schneider, S. (2007). Efficient sound power computation of open structures with infinite/finite elements and by means of the Padé-via-Lanczos algorithm. Journal of Computational Acoustics, 15, 557–577.MathSciNetCrossRefMATH
Bebendorf, M. (2008). Hierarchical matrices: A means to efficiently solve elliptic boundary value problems. Berlin: Springer.MATH
Bebendorf, M., Kuske, C., & Venn, R. (2015). Wideband nested cross approximation for Helmholtz problems. Numerische Mathematik, 130, 1–34.MathSciNetCrossRefMATH
Bernardi, C., Maday, Y., & Patera, A. T. (1994). A new nonconforming approach to domain decomposition: The mortar element method. In H. Brezis and J.-L. Lions(Eds.), Nonlinear partial differential equations and their applications (Vol. 11, pp. 13–51). Pitman, New York: College de France Seminar.
Bespalov, A. (2000). On the usage of a regular grid for implementation of boundary integral methods for wave problems. Russian Journal of Numerical Analysis and Mathematical Modelling, 15, 469–488.MathSciNetCrossRefMATH
Bork, I. (2000). A comparison of room simulation software - the 2nd round robin on room acoustical computer simulation. Acta Acustica united with Acustica, 86, 943–956.
Bork, I. (2005a). Report on the 3rd round robin on room acoustical computer simulation - Part I: Measurements. Acta Acustica united with Acustica, 91, 740–752.
Bork, I. (2005b). Report on the 3rd round robin on room acoustical computer simulation - Part II: Calculations. Acta Acustica united with Acustica, 91, 753–763.
Brakhage, H., & Werner, P. (1965). Über das Dirichlet’sche Außenraumproblem für die Helmholtz’sche Schwingungsgleichung. Archiv der Mathematik, 16, 325–329.CrossRefMATH
Brancati, A., Aliabadi, M., & Milazzo, A. (2011). An improved hierarchical ACA technique for sound absorbent materials. Computer Modeling in Engineering and Sciences, 78, 1–24.MathSciNetMATH
Brebbia, C. A., Telles, J. F. C., & Wrobel, L. C. (1984). Boundary element techniques. Berlin: Springer.CrossRefMATH
Brunner, D., Junge, M., Rapp, P., Bebendorf, M., & Gaul, L. (2010). Comparison of the fast multipole method with hierarchical matrices for the Helmholtz-BEM. Computer Modeling in Engineering and Sciences, 58, 131–160.MathSciNetMATH
Burton, A. J., & Miller, G. F. (1971). The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proceedings of the Royal Society of London, 323, 201–220.MathSciNetCrossRefMATH
Chen, P. T., & Ginsberg, J. H. (1995). Complex power, reciprocity, and radiation modes for submerged bodies. Journal of the Acoustical Society of America, 98, 3343–3351.CrossRef
Chen, Z. S., Hofstetter, G., & Mang, H. A. (1993). A 3D boundary element method for determination of acoustic eigenfrequencies considering admittance boundary conditions. Journal of Computational Acoustics, 1, 455–468.CrossRefMATH
Chen, Z. S., Hofstetter, G., & Mang, H. A. (1997). A symmetric Galerkin formulation of the boundary element method for acoustic radiation and scattering. Journal of Computational Acoustics, 5, 219–241.CrossRefMATH
Chen, Z. S., Hofstetter, G., & Mang, H. A. (1998). A Galerkin-type BE-FE formulation for elasto-acoustic coupling. Computer Methods in Applied Mechanics and Engineering, 152, 147–155.CrossRefMATH
Chen, Z. S., Hofstetter, G., & Mang, H. (2008). A Galerkin-type be-formulation for acoustic radiation and scattering of structures with arbitrary shape. In S. Marburg & B. Nolte (Eds.), Computational acoustics of noise propagation in fluids. Finite and boundary element methods (pp. 435–458). Berlin: Springer.
Chen, S., Liu, Y., & Dou, X. (2000). A unified boundary element method for the analysis of sound and shell-like structure interactions. II. Efficient solution techniques. Journal of the Acoustical Society of America, 108, 2738–2745.CrossRef
Chen, L., Chen, H., Zheng, C., & Marburg, S. (2016). Structural-acoustic sensitivity analysis of radiated sound power using a finite element/ discontinuous fast multipole boundary element scheme. International Journal for Numerical Methods in Fluids, 82, 858–878.MathSciNetCrossRef
Chen, L., Marburg, S., Chen, H., Zhang, H., & Gao, H. (2017). An adjoint operator approach for sensitivity analysis of radiated sound power in fully coupled structural-acoustic systems. Journal of Computational Acoustics, 25, 1750003 (24 p.).
Ciskowski, R. D., & Brebbia, C. A. (Eds.). (1991). Boundary elements in acoustics. Southampton, Boston: Computational Mechanics Publications and Elsevier Applied Science.
Coyette, J.-P., Wynendaele, H., & Chargin, M. K. (1993). A global acoustic sensitivity tool for improving structural design. Proceedings- SPIE The International Society for Optical Engineering, 1923, 1389–1394.
Coyette, J.-P., Lecomte, C., Migeot, J.-L., Blanche, J., Rochette, M., & Mirkovic, G. (1999). Calculation of vibro-acoustic frequency response functions using a single frequency boundary element solution and a Padé expansion. Acustica, 85, 371–377.
Cremers, L., Guisset, P., Meulewaeter, L., & Tournour, M. (2000). A computer–aided engineering method for predicting the acoustic signature of vibrating structures using discrete models. Great Britain Patent No. GB 2000–16259.
Croaker, P., Kessissoglou, N., & Marburg, S. (2015). Strongly singular and hypersingular volume integrals for near-field aeroacoustics. International Journal for Numerical Methods in Fluids, 77, 274–318.MathSciNetCrossRef
Croaker, P., Kessissoglou, N. J., & Marburg, S. (2016). Aeroacoustic scattering using a particle accelerated computational fluid dynamics/boundary element technique. AIAA Journal, 54, 2116–2133.CrossRef
Croaker, P., Marburg, S., Kinns, R., & Kessissoglou, N. J. (2013). A fast low-storage method for evaluating Lighthill’s volume quadrupoles. AIAA Journal, 51, 867–884.CrossRef
do Rego Silva, J. J. (1993). Acoustic and elastic wave scattering using boundary elements Topics in engineering (Vol. 18). Southampton, Boston: Computational Mechanics Publications.
Dong, J., Choi, K. K., & Kim, N.-H. (2004). Design optimization of structural-acoustic problems using FEA-BEA with adjoint variable method. ASME Journal of Mechanical Design, 126, 527–533.CrossRef
Fard, S. M. B., Peters, H., Kessissoglou, N., & Marburg, S. (2015). Three dimensional analysis of a noise barrier using a quasi-periodic boundary element method. Journal of the Acoustical Society of America, 137, 3107–3114.CrossRef
Fard, S. M. B., Peters, H., Marburg, S., & Kessissoglou, N. (2017). Acoustic performance of a barrier embedded with Helmholtz resonators using a quasi-periodic boundary element technique. Acta Acustica united with Acustica, 103, 444–450.
Fernandez-Grande, E., Jacobsen, F., & Leclére, Q. (2012). Direct formulation of the supersonic acoustic intensity in space domain. Journal of the Acoustical Society of America, 131, 186–193.CrossRef
Flemisch, B., Kaltenbacher, M., & Wohlmuth, B. I. (2006). Elasto-acoustic and acoustic-acoustic coupling on nonmatching grids. International Journal for Numerical Methods in Engineering, 67, 1791–1810.MathSciNetCrossRefMATH
Fritze, D., Marburg, S., & Hardtke, H.-J. (2005). FEM-BEM-coupling and structural-acoustic sensitivity analysis for shell geometries. Computers and Structures, 83, 143–154.CrossRef
Fritze, D., Marburg, S., & Hardtke, H.-J. (2009). Estimation of radiated sound power: A case study on common approximation methods. Acta Acustica united with Acustica, 95, 833–842.CrossRef
Fuß, S., Hawkins, S. C., & Marburg, S. (2011). An eigenvalue search algorithm for modal analysis of a resonator in free space. Journal of Computational Acoustics, 19, 95–109.MathSciNetCrossRefMATH
Galkowski, J., Müller, E. H., & Spence, E. A. (2016). Wavenumber–explicit analysis for the Helmholtz h–BEM: error estimates and iteration counts for the Dirichlet problem. Preprint in numerical analysis, Cornell University. https://​arxiv.​org/​abs/​1608.​01035.
Gaul, L., Brunner, D., & Junge, M. (2008). Coupling a fast boundary element method with a finite element formulation for fluid-structure interaction. In S. Marburg & B. Nolte (Eds.), Computational acoustics of noise propagation in fluids. Finite and boundary element methods (pp. 519–546). Berlin: Springer.
Gumerov, N. A., & Duraiswami, R. (2004). Fast multipole methods for the Helmholtz equation in three dimensions. Oxford: Elsevier Science & Technology.MATH
Gumerov, N. A., & Duraiswami, R. (2009). A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation. Journal of the Acoustical Society of America, 125, 191–205.CrossRef
Harari, I., & Hughes, T. J. R. (1992). A cost comparison of boundary element and finite element methods for problems of time-harmonic acoustics. Computer Methods in Applied Mechanics and Engineering, 97, 77–102.MathSciNetCrossRefMATH
Hornikx, M., Kaltenbacher, M., & Marburg, S. (2015). A platform for benchmark cases in computational acoustics. Acta Acustica united with Acustica, 101, 811–820.CrossRef
Ihlenburg, F. (1998). Finite element analysis of acoustic scattering (Vol. 132). Applied mathematical sciences. Berlin: Springer.
Ishiyama, S.-I., Imai, M., Maruyama, S.-I., Ido, H., Sugiura, N., & Suzuki, S. (1988). The application of ACOUST/BOOM - a noise level prediction and reduction code. SAE-Paper, 880910, 195–205.
Jean, P., & Defrance, J. (2015). Sound propagation in rows of cylinders of infinite extent: Application to sonic crystals and thickets along roads. Acta Acustica united with Acustica, 101, 474–483.CrossRef
Karimi, M., Croaker, P., & Kessissoglou, N. (2016). Boundary element solution for periodic acoustic problems. Journal of Sound and Vibration, 360, 129–139.CrossRef
Karimi, M., Croaker, P., & Kessissoglou, N. (2017). Acoustic scattering for 3D multi-directional periodic structures using the boundary element method. Journal of the Acoustical Society of America, 141, 313–323.CrossRef
Kirkup, S. M. (1998). The boundary element method in acoustics. Heptonstall: Integrated Sound Software.MATH
Koopmann, G. H., & Fahnline, J. B. (1997). Designing quiet structures: A sound power minimization approach. San Diego: Academic Press.
Kupradze, V. D. (1956). Randwertaufgaben der Schwingungstheorie und Integralgleichungen. Berlin: Deutscher Verlag der Wissenschaften. (1. Russian edition 1950).
Kussmaul, R. (1969). Ein numerisches Verfahren zur Lösung des Neumannschen Außenraumproblems für die Helmholtzsche Schwingungsgleichung. Computing, 4, 246–273.MathSciNetCrossRefMATH
Lam, Y. W. (1999). A boundary integral formulation for the prediction of acoustic scattering from periodic structures. Journal of the Acoustical Society of America, 105, 762–769.CrossRef
Liu, Y. (2009). Fast multipole boundary element method. Theory and applications in engineering. New York: Cambridge University Press.CrossRef
Liu, X., Wu, H., & Jiang, W. (2017). Hybrid approximation hierarchical boundary element methods for acoustic problem. Journal of Computational Acoustics (in print).
Liu, D., Peters, H., Marburg, S., & Kessissoglou, N. J. (2016a). Supersonic intensity and non-negative intensity for prediction of radiated sound. Journal of the Acoustical Society of America, 139, 2797–2806.CrossRef
Liu, D., Peters, H., Marburg, S., & Kessissoglou, N. J. (2016b). Surface contributions to scattered sound power using non-negative intensity. Journal of the Acoustical Society of America, 140, 1206–1217.CrossRef
Magalhaes, M. B. S., & Tenenbaum, R. A. (2006). Supersonic acoustic intensity for arbitrarily shaped sources. Acta Acustica united with Acustica, 92, 189–201.
Marburg, S. (2002a). Developments in structural–acoustic optimization for passive noise control. Archives of Computational Methods in Engineering. State of the Art Reviews, 9, 291–370.
Marburg, S. (2002b). Six boundary elements per wavelength. Is that enough? Journal of Computational Acoustics, 10, 25–51.
Marburg, S. (2005). Normal modes in external acoustics. Part I. Investigation of the one-dimensional duct problem. Acta Acustica united with Acustica, 91, 1063–1078.
Marburg, S. (2006). Normal modes in external acoustics. Part III: Sound power evaluation based on frequency-independent superposition of modes. Acta Acustica united with Acustica, 92, 296–311.
Marburg, S. (2008). Discretization requirements: How many elements per wavelength are necessary? In S. Marburg & B. Nolte (Eds.), Computational acoustics of noise propagation in fluids. Finite and boundary element methods (pp. 309–332). Berlin: Springer.
Marburg, S. (2016a). The Burton and Miller method: Unlocking another mystery of its coupling parameter. Journal of Computational Acoustics, 24, 1550016 (20 p.).
Marburg, S. (2016b). Numerical damping in the acoustic boundary element method. Acta Acustica united with Acustica, 102, 415–418.CrossRef
Marburg, S., & Amini, S. (2005). Cat’s eye radiation with boundary elements: Comparative study on treatment of irregular frequencies. Journal of Computational Acoustics, 13, 21–45.CrossRefMATH
Marburg, S., & Anderssohn, R. (2011). Fluid structure interaction and admittance boundary conditions: Setup of an analytical example. Journal of Computational Acoustics, 19, 63–74.MathSciNetCrossRefMATH
Marburg, S., & Hardtke, H.-J. (1999). A study on the acoustic boundary admittance. Determination, results and consequences. Engineering Analysis with Boundary Elements, 23, 737–744.CrossRefMATH
Marburg, S., & Hardtke, H.-J. (2003). Investigation and optimization of a spare wheel well to reduce vehicle interior noise. Journal of Computational Acoustics, 11, 425–449.CrossRefMATH
Marburg, S., & Nolte, B. (Eds.). (2008a). Computational acoustics of noise propagation in fluids. Finite and boundary element methods. Berlin: Springer.
Marburg, S., & Nolte, B. (2008b). A unified approach to finite and boundary element discretization in linear time–harmonic acoustics. In S. Marburg & B. Nolte (Eds.), Computational acoustics of noise propagation in fluids. Finite and boundary element methods (pp. 1–34). Berlin: Springer.
Marburg, S., & Schneider, S. (2003a). Performance of iterative solvers for acoustic problems. Part I. Solvers and effect of diagonal preconditioning. Engineering Analysis with Boundary Elements, 27, 727–750.CrossRefMATH
Marburg, S., & Schneider, S. (2003b). Influence of element types on numeric error for acoustic boundary elements. Journal of Computational Acoustics, 11, 363–386.
Marburg, S., & Wu, T. W. (2008). Treating the phenomenon of irregular frequencies. In S. Marburg & B. Nolte (Eds.), Computational acoustics of noise propagation in fluids. Finite and boundary element methods (pp. 411–434). Berlin: Springer.
Marburg, S., Shepherd, M., & Hambric, S. A. (2016). Structural acoustic optimization. In S. A. Hambric, S. H. Sung, & D. J. Nefske (Eds.), Engineering vibroacoustic analysis: methods and applications (pp. 268–304). Chichester: Wiley.
Marburg, S., Hardtke, H.-J., Schmidt, R., & Pawandenat, D. (1997). An application of the concept of acoustic influence coefficients for the optimization of a vehicle roof. Engineering Analysis with Boundary Elements, 20, 305–310.CrossRef
Marburg, S., Rennert, R., Schneider, S., & Hardtke, H.-J. (2002). Resonances in external acoustics? An example of tire noise excitation. In A. Calvo-Manzano, A. Perez-Lopez, & J. S. Santiago (Eds.), Proceedings of Forum Acusticum, Special Issue of Revista de Acustica (Vol. 33, pp. 3–4). Sevilla, (CD).
Marburg, S., Schneider, S., Vorländer, M., & Romanenko, G. (2003). Boundary elements for room acoustic measures. In Proceedings of the INTERNOISE 2003, The 32nd International Congress and Exposition on Noise Control Engineering, Held in Seogwipo/Korea (pp. 3598–3604). Seoul: Covan International Corp.
Marburg, S., Dienerowitz, F., Horst, T., & Schneider, S. (2006). Normal modes in external acoustics. Part II: Eigenvalues and eigenvectors in 2D. Acta Acustica united with Acustica, 92, 97–111.
Marburg, S., Lösche, E., Peters, H., & Kessissoglou, N. J. (2013). Surface contributions to radiated sound power. Journal of the Acoustical Society of America, 133, 3700–3705.CrossRef
Messner, M., Schanz, M., & Darve, E. (2012). Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation. Journal of Computational Physics, 231, 1175–1196.MathSciNetCrossRefMATH
Meyer, W. L., Bell, W. A., Zinn, B. T., & Stallybrass, M. P. (1978). Boundary integral solutions of three dimensional acoustic radiation problems. Journal of Sound and Vibration, 59, 245–262.CrossRefMATH
Moheit, L., & Marburg, S. (2017). Infinite elements and their influence on normal and radiation modes in exterior acoustics. Journal of Computational Acoustics, 25, 1650020 (20 p.).
Ochmann, M. (2013). Exact solutions for sound radiation from a moving monopole above an impedance plane. Journal of the Acoustical Society of America, 133, 1911–1921.CrossRef
Ochmann, M., & Brick, H. (2008). Acoustical radiation and scattering above an impedance plane. In S. Marburg & B. Nolte (Eds.), Computational acoustics of noise propagation in fluids. Finite and boundary element methods (pp. 459–494). Berlin: Springer.
Panič, O. I. (1965). K voprosu o razrešimosti vnešnich kraevich zadač dlja volnovogo uravnenija i dlja sistemi uravnenij Maxwella. Uspechi Mathematiceskich Nauk, 20, 221–226.
Peters, H., Kessissoglou, N. J., & Marburg, S. (2012a). Enforcing reciprocity in numerical analysis of acoustic radiation modes and sound power evaluation. Journal of Computational Acoustics, 20, 1250005 (19 p.).
Peters, H., Marburg, S., & Kessissoglou, N. J. (2012b). Structural-acoustic coupling on non-conforming meshes with quadratic shape functions. International Journal for Numerical Methods in Engineering, 91, 27–38.MathSciNetCrossRefMATH
Peters, H., Kessissoglou, N. J., Lösche, E., & Marburg, S. (2013a). Prediction of radiated sound power from vibrating structures using the surface contribution method. In T. McMinn (Ed.), Proceedings of Acoustics 2013 Victor Harbor: Science, Technology and Amenity. Proceedings of the Annual Conference of the Australian Acoustical Society. (CD).
Peters, H., Kessissoglou, N. J., & Marburg, S. (2013b). Modal decomposition of exterior acoustic-structure interaction. Journal of the Acoustical Society of America, 133, 2668–2677.CrossRef
Peters, H., Kessissoglou, N., & Marburg, S. (2014). Modal decomposition of exterior acoustic-structure interaction problems with model order reduction. Journal of the Acoustical Society of America, 135, 2706–2717.CrossRef
Roozen-Kroon, P. J. M. (1992). Structural optimization of bells. Dissertation, Technische Universiteit Eindhoven.
Saad, Y., & Schultz, M. H. (1986). GMRES: A generalized minimal residual algorithm for solving non-symmetric linear systems. SIAM Journal of Scientific and Statistical Computing, 7, 856–869.CrossRefMATH
Sakuma, T., Schneider, S., & Yasuda, Y. (2008). Fast solution methods. In S. Marburg & B. Nolte, (Eds.), Computational acoustics of noise propagation in fluids. Finite and boundary element methods (pp. 333–368). Berlin: Springer.
Schenck, H. A. (1968). Improved integral formulation for acoustic radiation problems. Journal of the Acoustical Society of America, 44, 41–58.CrossRef
Schneider, S. (2003). Application of fast methods for acoustic scattering and radiation problems. Journal of Computational Acoustics, 11, 387–401.CrossRef
Schneider, S. & Marburg, S. (2003). Performance of iterative solvers for acoustic problems. Part ii. Acceleration by ILU-type preconditioner. Engineering Analysis with Boundary Elements, 27, 751–757.
Telles, J. C. F. (1987). A self-adaptive coordinate transformation for efficient numerical evaluation of general boundary element integrals. International Journal for Numerical Methods in Engineering, 24, 959–973.CrossRefMATH
Thompson, L. L., & Pinsky, P. M. (1994). Complex wavenumber Fourier analysis of the p-version finite element method. Computational Mechanics, 13, 255–275.MathSciNetCrossRefMATH
von Estorff, O. (Ed.). (2000). Boundary elements in acoustics: advances and applications. Southampton: WIT Press.
Vorländer, M. (1989). Simulation of the transient and steady state sound propagation in rooms using a new combined sound particle-image source algorithm. Journal of the Acoustical Society of America, 86, 172–178.CrossRef
Wilkes, D. R., & Duncan, A. J. (2015). Acoustic coupled fluid-structure interactions using a unified fast multipole boundary element method. Journal of the Acoustical Society of America, 137, 2158–2167.CrossRef
Williams, E. G. (1995). Supersonic acoustic intensity. Journal of the Acoustical Society of America, 97, 121–127.CrossRef
Williams, E. G. (2013). Convolution formulations for non-negative intensity. Journal of the Acoustical Society of America, 134, 1055–1066.CrossRef
Wu, T. W. (2000a). The Helmholtz integral equation. In T. W. Wu (Ed.), Boundary element in acoustics: Fundamentals and computer codes (pp. 9–28). Southampton: WIT Press.
Wu, T. W. (Ed.). (2000b). Boundary element acoustics: fundamentals and computer codes. Southampton: WIT Press.
Wu, S. F., & Natarajan, L. K. (2013). Panel acoustic contribution analysis. Journal of the Acoustical Society of America, 133, 799–809.CrossRef
Wu, T. W., & Seybert, A. F. (1991). Acoustic radiation and scattering. In R. D. Ciskowski & C. A. Brebbia (Eds.), Boundary elements in acoustics (pp. 61–76). Southampton: Computational Mechanics Publications; London: Elsevier Applied Science.
Wu, H. J., Liu, Y. J., & Jiang, W. K. (2013). A low-frequency fast multipole boundary element method based on analytical integration of the hypersingular integral for 3D acoustic problems. Engineering Analysis with Boundary Elements, 37, 309–318.MathSciNetCrossRefMATH
Wu, S. F., Moondra, M., & Beniwal, R. (2015). Analyzing panel acoustic contributions toward the sound field inside the passenger compartment of a full-size automobile. Journal of the Acoustical Society of America, 137, 2101–2112.CrossRef
Zheng, C.-J., Chen, H.-B., Gao, H.-F., & Du, L. (2015). Is the Burton-Miller formulation really free of fictitious eigenfrequencies? Engineering Analysis with Boundary Elements, 59, 43–51.MathSciNetCrossRef
Ziegelwanger, H., Reiter, P., & Conter, M. (2017). The three-dimensional quasi-periodic boundary element method: Implementation, evaluation, and use cases. International Journal of Computational Methods and Experimental Measurements, 5, 404–414.CrossRef
Metadata
Title
Boundary Element Method for Time-Harmonic Acoustic Problems
Author
Steffen Marburg
Copyright Year
2018
Book
Computational Acoustics

Print ISBN: 978-3-319-59037-0

Electronic ISBN: 978-3-319-59038-7

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-59038-7_3

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