Parallel FMM-FFT solver for the analysis of hundreds of millions of unknowns

An efficient parallel implementation of the fast multipole method (FMM) combined with the fast fourier transform (FFT) is presented. The good scaling properties of the FMM-FFT, combined with a careful parallelization strategy, has shown to be very effective when using large parallel high performance supercomputers. For the case of very large problems, with hundreds of millions of unknowns, a nested scheme has been derived that further reduces the memory consumption. A challenging problem with more than 0.5 billion unknowns has been solved using this implementation, which demonstrates the ability of the algorithm to take advantage of the availability of supercomputers for the analysis of large, leading-edge electromagnetic problems.