Analytical and Numerical Methods in Acoustics

Numerous analytical and numerical methods are displayed in this book together with the solutions for special tasks. This chapter contains analytical and numerical methods to be applied in acoustics, going beyond the scope of single examples. The description of a method unavoidably needs more textual explanations than the representation of just the resulting formulas. Section O.1 describes a procedure for optimisation of the parameters of a sound absorber; the Section O.2 outlines a method for the evaluation of many concatenated transfer matrices. The Section O.3 will present five standard problems of numerical acoustics which frequently occur in practical applications. In Sects. O.4–O.6 three important methods for the numerical solution of these problems will be described. The source simulation technique and the boundary element method are mainly used for exterior problems such as the radiation or the scattering problem (see Sects. O.4 and O.5). The finite element method is especially suited for computing sound fields in interior spaces (see Sect. O.6). The fluid-structure interaction problem can be treated by a combined finite element and boundary element approach, for example with the method of Sect. O.6. The transmission problem can be formulated in terms of boundary integral equations (see Sect. O.5). Analytical field solutions for benchmark models are given in Sects. O.7, O.8.

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