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

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Numerical Integration

Part of the book series: NATO ASI Series ((ASIC,volume 357))

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Abstract

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.

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Author information

Authors and Affiliations

  1. Institute of Marine Research, P.O.Box 1870, N-5024, Bergen- Nordnes, Norway

    Jarle Berntsen

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  1. Jarle Berntsen
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Terje O. Espelid

  2. School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA, USA

    Alan Genz

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© 1992 Springer Science+Business Media Dordrecht

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Berntsen, J. (1992). On the Numerical Calculation of Multidimensional Integrals Appearing in the Theory of Underwater Acoustics. In: Espelid, T.O., Genz, A. (eds) Numerical Integration. NATO ASI Series, vol 357. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2646-5_19

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  • DOI: https://doi.org/10.1007/978-94-011-2646-5_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5169-9

  • Online ISBN: 978-94-011-2646-5

  • eBook Packages: Springer Book Archive

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