Massively Parallel Fast Multipole Method Solutions of Large Electromagnetic Scattering Problems

We describe a massively parallel version of the single-level fast multipole method (FMM) that employs the fast Fourier transform (FFT) for the translation stage. The proposed FMM-FFT method alleviates the communication bottleneck and has a lower complexity, O(N^4/3 log^2/3 N), as compared to the conventional single level FMM which scales as O(N^3/2), where N is the number of unknowns. Through numerical examples we demonstrate that the proposed parallel fast multipole method yields a faster solution time than its multilevel counterpart for very large problems in a distributed memory parallel setting.