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On a Novel Algorithmic Determination of Acoustic Low Frequency Coefficients for Arbitrary Impenetrable Scatterers

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  • Foteini Kariotou

    (Applied Mathematics Laboratory, School of Science and Technology, Hellenic Open University, 263 35 Patras, Greece)

  • Dimitris E. Sinikis

    (Applied Mathematics Laboratory, School of Science and Technology, Hellenic Open University, 263 35 Patras, Greece)

  • Maria Hadjinicolaou

    (Applied Mathematics Laboratory, School of Science and Technology, Hellenic Open University, 263 35 Patras, Greece)

Abstract

The calculation of low frequency expansions for acoustic wave scattering has been under thorough investigation for many decades due to their utility in technological applications. In the present work, we revisit the acoustic Low Frequency Scattering theory, and we provide the theoretical framework of a new algorithmic procedure for deriving the scattering coefficients of the total pressure field, produced by a plane wave excitation of an arbitrary, convex impenetrable scatterer. The proposed semi-analytical procedure reduces the demands for computation time and errors significantly since it includes mainly algebraic and linear integral operators. Based on the Atkinson–Wilcox theorem, any order low frequency scattering coefficient can be calculated, in finite steps, through algebraic operators at all steps, except for the last one, where a regular Fredholm integral equation with a continuous and separable integral kernel is needed to be solved. Explicit, ready to use formulae are provided for the first three low frequency scattering coefficients, demonstrating the applicability of the algorithm. The validation of the obtained formulae is demonstrated through recovering of the well-known analytical results for the case of a radially symmetric scatterer.

Suggested Citation

  • Foteini Kariotou & Dimitris E. Sinikis & Maria Hadjinicolaou, 2022. "On a Novel Algorithmic Determination of Acoustic Low Frequency Coefficients for Arbitrary Impenetrable Scatterers," Mathematics, MDPI, vol. 10(23), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4487-:d:986629
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    References listed on IDEAS

    as
    1. Ibrahim Mahariq & Ibrahim H. Giden & Shadi Alboon & Wael Hosny Fouad Aly & Ahmed Youssef & Hamza Kurt, 2022. "Investigation and Analysis of Acoustojets by Spectral Element Method," Mathematics, MDPI, vol. 10(17), pages 1-9, September.
    2. Antonios Charalambopoulos & Leonidas Gergidis & Eleftheria Vassilopoulou, 2022. "A Conditioned Probabilistic Method for the Solution of the Inverse Acoustic Scattering Problem," Mathematics, MDPI, vol. 10(9), pages 1-39, April.
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