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

Foteini Kariotou (), Dimitris E. Sinikis and Maria Hadjinicolaou
Additional contact information
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

Mathematics, 2022, vol. 10, issue 23, 1-20

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.

Keywords: low frequency scattering theory; impenetrable scatterer; far field expansion; scattering coefficients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/23/4487/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/23/4487/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:23:p:4487-:d:986629

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().