The proposed fast Time Domain Physical Optics (TDPO)scheme is based on a domain decomposition of the scattering surface or radiating aperture into smaller patches. The scheme exploits the fact that, asymptotically, the number of samples required to describe the scattered or radiated fields in time and angular domains, is proportional to the size of the patch. Therefore the radiation patterns are computed directly only for the smallest subdomains. Subsequently, the radiation patterns are aggregated through a two- or multi-level process comprising temporal and angular interpolations and timeshifts, and leading to reduced computational complexities