In 1998, HEMCUVE was born as a response to the commission given by the company NAVANTIA to the COM group to conduct a study of electromagnetic compatibility and interference in radiant systems on board of ships. Since then, the group’s efforts have focused on evolving this software tool to achieve rigorous and accurate analysis of arbitrary electromagnetic problems. Currently, HEMCUVE++, the Hybrid ElectroMagnetic Code University of Vigo and Extremadura, is a complex tool based on the Moment Method, which uses spectral acceleration techniques (FMM and FMM-FFT) and exploits the resources available in the current supercomputers to solve electromagnetic simulation problems unsolvable by any other method.