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A novel algorithm to efficiently compute transient wave fields produced by known three-dimensional source constellations is proposed. The algorithm uses domain decomposition concepts and comprises two steps to be repeated for each subdomain considered. In the first step, delay- and amplitude-compensated fields, produced by sources residing inside each subdomain are computed at a sparse set of points surrounding the observation domain. In the second step, total fields in the observer domain are evaluated by interpolation, delay and amplitude restoration, and aggregation of subdomain fields. The proposed scheme is well-suited to accelerate the solution of time domain integral equations by marching on in time, to carry out time domain physical optics calculations, and to realize near- to far-field transformations of transients. Moreover, the scheme automatically adapts to, and takes advantage of, special geometrical features of the source-observer constellation studied, a key benefit when analyzing quasi-planar configurations. In addition, it realizes a seamless transition from the dynamic to the quasi-static regime, thus facilitating a unified treatment of electrically large and small problems. Last but not least, the scheme is remarkably simple to implement.