Abstract
In this paper scattering problems with elastic obstacles that are hit by an incident acoustic wave are discussed. Underwater acoustics mainly differs from air acoustics in the fact that a strong coupling scheme between the structural part and the acoustic domain is necessary. Such a scheme is discussed, using the fast multilevel multipole boundary element method (FMBEM) to model the exterior acoustic fluid. The structural part is modeled with the finite element method (FEM). To obtain a high flexibility, an interface to a commercial FE package is established. For a high efficiency, an iterative solver with preconditioning is applied. The numerical results are compared with an analytical solution for a model problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Benzi M (2002) Preconditioning techniques for large linear systems: A survey. Journal of Computational Physics 182:418–477
Brunner D, Junge M, Gaul L (2007) Strong coupling of the fast multilevel multipole boundary element method with the finite element method for vibro-acoustic problems. In: Proceedings of the 14th International Congress on Sound and Vibration (ICSV14)
Brunner D, Junge M, Gaul L (2009) A comparison of FE–BE coupling schemes for large scale problems with fluid-structure interaction. International Journal for Numerical Methods in Engineering 77 (5): 664–688
Burton AJ, Miller GF (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
Chen ZS, Hofstetter G, Mang HA (1998) A Galerkin-type BE-FE formulation for elasto-acoustic coupling. Computer Methods in Applied Mechanics and Engineering 152:147–155
Coifman R, Rokhlin V, Wandzura S (1993) The fast multipole method for the wave equation: A pedestrian description. IEEE Antennas and Propagation Magazine 35:7–12
Estorff O von (ed) (2000) Boundary Elements in Acoustics: Advances and Applications. WIT Press, Southampton, UK
Everstine GC, Henderson FM (1990) Coupled finite element/boundary element approach for fluid-structure interaction. Journal of Sound and Vibration 87:1938–1947
Fahy F (2007) Sound and Structural Vibration. Academic Press, New York, 2nd edition
Fischer M (2004) The Fast Multipole Boundary Element Method and its Application to Structure-Acoustic Field Interaction. PhD Thesis, University of Stuttgart
Gaul L, Fischer M (2006) Large-scale simulations of acoustic-structure interaction using the fast multipole BEM. Zeitschrift für Angewandte Mathematik und Mechanik 86:4–17
Gaul L, Kögl M, Wagner M (2003) Boundary Element Methods for Engineers and Scientists. Springer Verlag, Berlin Heidelberg
Greengard L, Rokhlin V (1987) A fast algorithm for particle simulations. Journal of Computational Physics 73:325–348
Gyure MF, Stalzer MA (1998) A prescription for the multilevel Helmholtz FMM. IEEE Computational Science & Engineering 5:39–47
Hughes MD, Chen K (2004) An efficient preconditioned iterative solver for solving a coupled fluid structure interaction problem. International Journal of Computer Mathematics 81:583–594
Junge M, Fischer M, Maess M, Gaul L (July 11–14 2005) Acoustic simulation of an idealized exhaust system by coupled FEM and Fast Multipole BEM. In: Proceedings of the 12th International Congress on Sound and Vibration (ICSV12), Lisboa
Junger MC, Feit D (1986) Sound, Structures, and Their Interaction. The MIT Press, Cambridge, 2nd edition
Kinsler LE, Frey AR, Coppens A, Sanders J (1999) Fundamentals of Acoustics. John Wiley and Sons, Inc., New York
Moosrainer M (2000) Fluid-Struktur-Kopplung. PhD Thesis, Universität der Bundeswehr München
Ochmann M, Homm A, Makarov S, Semenov S (2003) An iterative GMRES-based boundary element solver for acoustic scattering. Engineering Analysis with Boundary Elements 27: 714–725
Rjasanow S, Steinbach O (2007) The Fast Solution of Boundary Integral Equations. Springer–Verlag, New York
Rokhlin V (1993) Diagonal forms of translation operators for the Helmholtz equation in three dimensions. Applied and Computational Harmonic Analysis, 1:82–93
Schneider S (2003) Efficient Usage of the Boundary Element Method for Solving the Time Harmonic Helmholtz Equation in Three Dimensions. PhD Thesis, Technische Universität Dresden
Seybert AF, Soenarko B, Rizzo FJ, Shippy DJ (1985) An advanced computational method for radiation and scattering of acoustic waves in three dimensions. Journal of the Acoustical Society of America, 77:362–368
Shen L, Liu YJ (2007) An adaptive fast multipole boundary element method for three–dimensional acoustic wave problems based on the Burton-Miller formulation. Computer Mechanical 40:461–472
van der Vorst HA (2003) Iterative Krylov Methods for Large Linear Systems. Cambridge University Press, Cambridge
Wu TW (2000) Boundary Element Acoustics: Fundamentals and Computer Codes. WIT Press, Southampton, UK
Zienkiewicz OC, Taylor RL (2000) The Finite Element Method, Vol. 1. Butterworth-Heinemann, Oxford, 5th edition
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Gaul, L., Brunner, D., Junge, M. (2009). Simulation of Elastic Scattering with a Coupled FMBE-FE Approach. In: Manolis, G.D., Polyzos, D. (eds) Recent Advances in Boundary Element Methods. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9710-2_10
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9710-2_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9709-6
Online ISBN: 978-1-4020-9710-2
eBook Packages: EngineeringEngineering (R0)