A numerically stable T-matrix method for acoustic scattering by nonspherical particles with large aspect ratios and size parameters

Abstract

We consider a two-part method for computing the acoustic scattering T-matrix of a three dimensional particle. The first part involves accurately computing the far fields by solving a number of particular scattering problems. The second part calculates the T-matrix from these far fields using the Fourier transform over the sphere. The two-part method was first introduced in Ganesh and Hawkins [J. Comput. Appl. Math. 234, 1702–1709]. The focus of this work is to demonstrate the numerical stability and physical correctness of the two-part method for scattering by nonspherical particles with large aspect ratios and size parameters that are at the upper limit of numerical stability for the current state-of-the-art algorithm. The numerical stability of the method is attributed to elimination of the Hankel functions by working with the far field. The numerical experiments use our recently developed open-source software package (TMATROM3) that implements the two-part method.