A Numerical Algorithm of the Multiple Scattering from an Ensemble of Arbitrary Scatterers

Abstract

Sound scattering by a finite number of arbitrary scatterers has remained a complicatedproblems. For this reason, only limited numerical results have been documented in the liter-ature. The main difficulty perhaps has been associated with the lack of efficient numericalalgorithmsandthelimitedcomputingcapability.Amongmanyusefulformalismssuggestedfor describing sound scattering by a finite group of arbitrary scatterers, three approachesappear to be particularly useful, that is, the self-consistent approach [1, 2], theT-matrixmethod [3, 4], and the method of moments [5].The recent expanding capability of digital computers has in principle made it possibleto compute the more complicated problem of multiple scattering from a finite numberof scatterers. Following the self-consistent scheme in Foldy [1], the multiple scatteringprocesses can be represented by a set of coupled linear equations. The solution to theseequations can be obtained by a matrix inversion. Such a procedure has been used previouslyto investigate multiple scattering by isotropic scatterers, especially the acoustic localizationin bubbly liquids in which air-filled bubbles are isotropic scatterers [6]. The purpose ofthis paper is to generalize the numerical matrix method in Ye and Alvarez [6] to morecomplicated cases involving many anisotropic scatterers. It will be clear from the derivationthat the present approach can be used for scattering from many scatterers with arbitraryconfigurations for a wide range of situations.