A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators

Abstract

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method.

Fast multi-particle scattering: A hybrid solver for the Maxwell equations in microstructured materials

“…We simply equate the tangential components of E l 0 ; H l 0 defined in (13), (14) with the tangential components of the interior representations ðE l ; H l Þ defined in (11), (12). This yields a dense linear system of dimension 4Mðp þ 1Þ 2 for the coefficients ða l n;m ; b l n;m ; c l n;m ; d l n;m Þ.…”

“…This is discussed in the context of acoustic scattering in [12,14]. Since the literature on FMMs is substantial, we omit a detailed discussion of the technique, but present results in Section 6.…”

Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres

“…14,15,25 The approach presented here uses direct application of the addition theorem in two dimensions and an efficient, diagonal approach thoroughly described in Ref. 13 for three-dimensional scattering from spheres.…”

“…However, a faster approach was developed in Ref. 13 by employing diagonal translation operators. 22 This paper presents a unification and extension of the work undertaken in Refs.…”

“…The method presented in Ref. 13 is here generalized in a form that is easily adapted to scattering problems in both two and three dimensions. A new nested iterative approach is additionally presented to decouple the solution of scattering from interior cylinders or spheres from the additional constraints imposed by an enclosing cylinder or sphere.…”