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Boundary element methods in acoustics. (English) Zbl 0758.76036

Southampton: Computational Mechanics Publications. London: Elsevier Applied Sciences. xv, 290 p. (1991).
This is a monograph on boundary element method (BEM) in acoustics. The direct formulation, that of Green’s function approach is used. In this formulation the problem unknowns are the same as the physical variables, e.g., potential or fluxes. However, the indirect approach, which uses sources or dipoles concept, is also described, and the choice of the approach is discussed. The breakthrough in BEM came when it was recognized that the use of “a” Green’s function without necessarily satisfying any particular boundary condition would reduce the dimensionality of the problem. In some cases, the chosen Green’s function does not have to be the same operator as in the mathematical model. For example, in the dual reciprocity method, the fundamental solution of Laplace equation is used to obtain boundary element formulation for an internal problem in acoustics. Discretizations using various element shapes, constant, linear, quadratic and cubic elements are presented.
Solutions to the wave propagation and vibration problems are presented. Using the free space Green’s function enables the radiation condition to be satisfied automatically for the exterior problem. Nonuniqueness of the solution at certain characteristic frequencies, natural frequencies of the complementary interior problem, is addressed. Enhanced combined Helmholtz integral equation formulation (CHIEF) which uses derivatives of the CHIEF equation in addition to interior points in the complementary internal region as constraints are used to resolve nonunique problem at intermediate frequencies. For the time dependent wave equation, Kirchhoff’s theorem is used to develop the BEM.
Discussion on a wide range of applications are given by various authors: Acoustic radiation and scattering, acoustic design sensitivity analysis, probabilistic acoustic analysis, structure-acoustic coupling, automobile cabin and enginer noises, bioacoustics, and environmental noises.

MSC:

76M15 Boundary element methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
00B15 Collections of articles of miscellaneous specific interest
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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