Calculation of acoustical scattering from a cluster of scatterers

Abstract

The problem of determining the field scattered by a cluster of scatterers when they are insonified by a known acoustical field is addressed. The problem is formulated by using the T-matrix method and the resulting system of linear equations is solved by using the multilevel fast multipole algorithm (MLFMA) and the fast multipole method–fast Fourier transform (FMMFFT) method, and the efficiency of the two methods is compared. It was observed that, in general, the MLFMA performs better than the FMMFFT algorithm. However, when the scatterers are distributed uniformly on a rectangular grid, the FMMFFT algorithm performs as good as the MLFMA. The accuracy of the methods is evaluated by modeling a spherical scatterer as composed of many small spheres.

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

“…[14][15][16][17][18][19][20] In this approach, reflection coefficients are computed at the boundary of each sphere as quotients relating the coefficients for incident and scattered spherical harmonics of the same degree. To make use of these reflection coefficients, the spherical harmonic expansions for the scattered fields must be translated from center to center.…”

Computation of scattering from N spheres using multipole reexpansion

“…For example, the use of fast multipole methods could lead to accelerated schemes to solve these equations iteratively (Koc and Chew, 1998). Further, the expressions used to select the truncation of the series could be selected in a more rigorous manner.…”

“…In the present paper we refer to this as the 'coaxial' case. A general three-dimensional case of acoustical scattering by N objects using the T-matrix method was considered by Koc and Chew (1998). They proposed using a numerical evaluation of integral forms of the translation operators (Rokhlin, 1993) and the fast multipole method (FMM) applied to iterative solution of a large system of equations that appear in the T-matrix method.…”

“…Another approach to solve this problem is a semi-analytical method such as the T-matrix method (Waterman and Truell (1961), Peterson and Strom (1974), Varadan and Varadan (1980), Mischenko et al (1996), Koc and Chew (1998)). In this method, the scattering properties of a scatterer, and of the collection are characterized in terms of the so-called T-matrices that act on the coefficients of the local expansion of the incoming wave, centered at the scatterer, and transform them into the coefficients of an outgoing wave from the scatterer.…”

Iterative simulation of elastic wave scattering in arbitrary dispersions of spherical particles

“…Additionally, multipole-based acoustic models for particulate systems have been limited to either longitudinal wave propagation or periodic lattices of particles. [7][8][9] Little work has been reported on the modeling of full elastic wave scattering in random particulate systems, with longitudinal and shear waves in both particles and matrix.…”