An FFT T-matrix method for scattering solutions from inhomogeneous bodies and random discrete scatterers

We propose a fast and efficient method of solving the inhomogeneous body and the random discrete scatterer problem. An inhomogeneous body can be modelled by a dense packing of discrete spherical particles whose T matrices exist in closed form. A set of linear algebraic equations is easily derived to solve for the scattering amplitudes from the spheres. When the discrete scatterers are randomly distributed, we aggregate the discrete scattering centers to scattering centers which reside on an array using the addition theorem. When the discrete scatterers reside on a regular array, no such aggregation is required. As a result, we have a block-Toeplitz matrix structure. An iterative solver such as the biconjugate gradient method can be used to solve for the matrix equation. Exploiting the block-Toeplitz structure, we can perform the matrix-vector multiplication in O(NlogN) operations by the FFT, where N is the total number of spheres involved. The method requires O(N) memory storage.