Application of the multiple sphere superposition solution to large–scale systems of spheres via an accelerated algorithm

Abstract

The application of an algorithm, based upon an FFT–enabled discrete Fourier convolution, to the multiple sphere superposition solution is presented. As opposed to the NS2 operation count scaling for the standard superposition solution algorithm, where NS is the number of spheres, the accelerated algorithm results in closer to NSlnNS scaling. The new algorithm has been adopted into the Multiple Sphere T Matrix (MSTM) fortran-90 code, and the code has been optimized to allow for rapid calculation of configuration– and/or orientation–averaged radiative properties of large–scale systems of randomly–positioned spheres. Improvement in computational times by more than two orders of magnitude are possible for systems containing in excess of 1000 spheres. Illustrative examples of the application of the updated code are presented.