Time Domain Scattering of Scalar Waves by Two Spheres in Free-Space

Abstract

The importance of the T-matrix method is well known when frequency domain scattering problems are of interest. With the relatively recent and wide-spread interest in time domain scattering problems, similar applications of the T-matrix method are expected to be useful in the time domain. In this paper, the time domain spherical scalar wave functions are introduced, translational addition theorems for the time domain spherical scalar wave functions necessary for the solution of multiple scattering problems are given, and the formulation of time domain scattering of scalar waves by two scatterers of arbitrary shape is presented. The whole analysis is performed in the time domain requiring no inverse Fourier integrals to be evaluated. Scattering by two soft spheres in free-space is studied as an application to check the numerical accuracy and demonstrate the utility of the expressions.