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Computational Acoustics pp 69–158Cite as

Boundary Element Method for Time-Harmonic Acoustic Problems

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Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 579))

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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  1. Vibroacoustics of Vehicles and Machines, Technical University of Munich, Boltzmannstraße 15, 85748, Garching Bei München, Germany

    Steffen Marburg

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  1. Steffen Marburg
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Correspondence to Steffen Marburg .

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  1. Institute of Mechanics and Mechatronics, Vienna University of Technology Institute of Mechanics and Mechatronics, Vienna, Wien, Austria

    Manfred Kaltenbacher

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Marburg, S. (2018). Boundary Element Method for Time-Harmonic Acoustic Problems. In: Kaltenbacher, M. (eds) Computational Acoustics. CISM International Centre for Mechanical Sciences, vol 579. Springer, Cham. https://doi.org/10.1007/978-3-319-59038-7_3

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

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