Supercomputer solutions of extremely large problems in electromagnetics: From ten million to one billion unknowns

In this work, an efficient hybrid MPI/OpenMP parallel implementation of the Multilevel Fast Multipole Algorithm - Fast Fourier Transform (MLFMA-FFT) algorithm has been successfully applied to the solution of a challenging electromagnetic problem involving more than one billion unknowns. The MLFMA-FFT was shown to be optimal from the point of view of modern mixed-memory supercomputers, combining the low computational cost of the MLFMA in shared memory computations with the high scalability properties of the FMM-FFT algorithm for the distributed computations.