  A transient Mie-like solution for acoustic scattering from a spherical object
is derived within a mesh-free and singularity-free Time Domain Integral
Equation (TDIE) framework for the sound-soft, sound-rigid and penetrable cases.
The method is based on an expansion of the time domain Green's function that
allows independent evaluation of spatial and temporal convolutions. Solution of
the TDIE system may be effected by descretizing the integral equations in space
and time, forming a matrix system via the Method of Moments, and solving the
system with the Marching on in Time algorithm. Spatial discretization using
tesseral harmonics leads to closed form expressions for spatial integrals, and
use of a strictly band limited temporal interpolant permits efficient, accurate
computation of temporal convolutions utilizing numerical quadrature. The
accuracy of these integrations ensures late time stability and accuracy of the
deconvolution data. Results presented demonstrate the accuracy and convergence
of the approach for broadband simulations against Fourier transformed
analytical data.
