Abstract
This chapter presents a general survey of the main approximation methods used in acoustics. The methods discussed: (1) Kirchhoff approximation, (2) Neumann series, (3) W.K.B. method, (4) Born approximation and Rytov approximation, (5) image method, (6) ray method, (7) geometrical theory of diffraction, (8) parabolic approximation and (9) Wiener–Hopf method. These approximation methods can be used in computer programs in several ways. These can be used as input data of an iterative algorithm. Simple problems for which approximate solutions are known can be used as “benchmarks” to validate numerical algorithms. The methods used to solve acoustics problems are divided into two groups: purely numerical— such as finite element or boundary integral equation methods and the analytical and asymptotic methods, such as the method of steepest descent or geometrical theory of diffraction, which provide approximate expressions of the solution or simpler equations, which are then solved by a numerical procedure.
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