The synthesis of electrically large, highly performing reflectarray antennas can be computationally very demanding both from the analysis and from the optimization points of view. It therefore requires the combined usage of numerical and hardware strategies to control the computational complexity and provide the needed acceleration. Recently, we have set up a multi-stage approach in which the first stage employs global optimization with a rough, computationally convenient modeling of the radiation, while the subsequent stages employ local optimization on gradually refined radiation models. The purpose of this paper is to show how reflectarray antenna synthesis can take profit from parallel computing on Graphics Processing Units (GPUs) using...