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The plane wave time domain (PWTD) algorithm permits the fast evaluation of transient wave fields generated by like sources and thereby constitutes the extension to the time domain of the frequency domain fast multipole method. When coupled to classical marching on in time (MOT) solvers, it drastically accelerates the solution of time domain integral equations (TDIE) pertinent to the analysis of electromagnetic scattering problems while minimizing their memory requirements. This paper describes a parallel implementation of a multilevel PWTD kernel and associated MOT scheme that solves a combined field integral equation (CFIE) pertinent to the analysis of transient scattering from three-dimensional perfect electrically conducting (PEC) objects. The described solver executes on a distributed-memory parallel cluster and uses the message passing interface (MPI) paradigm to communicate data between processors. A "space/direction partitioning" scheme is adopted to divide the computational tasks involved and achieve reasonable load balancing among the available processors. The performance of the parallel solvers is verified by a numerical example.