High scalability multipole method for the analysis of hundreds of millions of unknowns

In this work, we present an efficient parallel implementation of the fast multipole method (FMM) combined with the fast Fourier transform (FFT). The good scaling propensity of the FMM-FFT, combined with a careful parallelization strategy, has shown to be very effective when using large parallel high performance supercomputers. A challenging problem with more than 0.5 billion unknowns has been solved. This is the largest problem analyzed in computational electromagnetics to date, which demonstrates that the proposed implementation of the FMM-FFT constitutes a real alternative to the more frequently used multilevel FMM algorithm (MLFMA).