Summary: Large electromagnetic simulations are needed for improvement of design in industry. Up to now, the previous limits in the scalability of the available codes were an important barrier. In this work, an efficient parallel implementation of the fast multipole method (FMM) combined with the fast Fourier transform (FFT) is presented. The good scalability of the parallel FMM-FFT, combined with some performance improvements, 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 in the Finis Terrae Supercomputer recently. This is the largest problem analyzed in computational electromagnetics to date, which confirms that the proposed implementation of the FMM-FFT constitutes a very interesting alternative to the more frequently used multilevel FMM algorithm (MLFMA).