Diagonal translation operators for transient wave fields

The scientific community has expressed a renewed interest in the analysis of short-pulse radiation and transient scattering phenomena. This paper presents diagonal translation operators for transient wave fields which permit the fast evaluation of fields produced by transient surface bound sources. These operators act as the time domain counterparts of the frequency domain diagonal translation operators, which are the essence of the fast multipole method (FMM). In a similar vein, the proposed diagonal translation operators for transient wave fields form the basis of plane wave time domain (PWTD) algorithms which augment classical marching-on-in-time schemes for efficiently solving time domain integral equations that arise in the analysis of transient surface scattering phenomena.