@article {Schwarz-Röhr:2006:1610-1928:521,
title = "Scattering of Sound by a Hollow, Hard Sphere with an Opening",
journal = "Acta Acustica united with Acustica",
parent_itemid = "infobike://dav/aaua",
publishercode ="dav",
year = "2006",
volume = "92",
number = "4",
publication date ="2006-07-01T00:00:00",
pages = "521-529",
itemtype = "ARTICLE",
issn = "1610-1928",
url = "https://www.ingentaconnect.com/content/dav/aaua/2006/00000092/00000004/art00003",
author = "Schwarz-R{\"o}hr, Bernhard",
abstract = "In this paper the scattering on a hollow sphere with infinitely thin, hard walls and an opening is calculated in order to provide benchmark solutions for BEM and FEM methods. The calculations are based on an expansion into products of Bessel or Neumann functions and Legendre Polynomials.
Solutions are obtained by minimizing the residual errors on the surface and in the opening of the sphere. This leads to infinite sets of linear equations which include certain Wigner 3j symbols. An implementation of the recursion for these symbols is presented. Criteria for the truncation
of the infinite set of equations are discussed, good results are obtained for 2 kr
0 k and r
0 denoting the wavenumber and the radius of the sphere respectively. The results are in agreement with the asymptotic calculations of Morse and
Feshbach regarding the position of the first resonance, some difference found at low wave numbers for the surface velocity field is discussed.",
}