FMM-Accelerated Source-Model Technique for Many-Scatterer Problems

Motivated by the lack of scalability of the source-model technique (SMT) to many-scatterer problems, a new SMT-based method for 3-D many-scatterer problems is developed. The large time complexity of the SMT is reduced by deriving an implicit compact representation of the scattering problem via a fast multipole formulation, which divides the interactions into far and near ones while grouping and approximating the far interactions. This results in significant acceleration of classical SMT, which is demonstrated in a variety of 3-D many-body scattering problems. The improvement is notable already at the minimal number of unknowns necessary, and grows with the size of the problem.