On the Numerical Calculation of Multidimensional Integrals Appearing in the Theory of Underwater Acoustics

Multidimensional integrals appear frequently in applied sciences. In this paper we will present some integrals from the theory of underwater acoustics. Automatic adaptive integration routines may be useful tools for computing approximations to many of these integrals, and we will focus on the properties that should be implemented in such routines in order to produce software that will meet the requirements of applied scientists. We will describe how some of these properties are implemented in recently developed routines for hyperrectangular regions, triangles and tetrahedrons. The routines to be described are now being used by a number of scientists in acoustics, and the feedback acquired has given us many ideas on how to further improve the software. Based on the needs of these scientists we will discuss which features that should be implemented in the next generation of automatic adaptive multidimensional integration routines.