Modern applied engineering problems often call for the solution of partial differential equations. Unfortunately most real-life problems cannot be easily solved with analytic methods and numerical techniques must be used. In this work, the numerical solution to problems of electrodynamics is considered, using the finite-difference time-domain (FDTD) algorithm. This algorithm simulates the evolution of electromagnetic fields in space and time.; One drawback to FDTD is that large solution regions containing electrically-small objects often require colossal simulation grids. Simulation scenarios involving resonators, high frequencies, and others often require a lengthy evolution in time. To reduce the simulation time, the research community has developed methods to distribute the computations among multiple processors. Recently, techniques broadly called model order reduction (MOR) have begun to compete with the distributed processing in FDTD. One way the MOR techniques work is by examining the FDTD evolution engine in the frequency domain and removing unessential components. This dissertation highlights our work in distributed computation and MOR.; In distributed computation the author's contribution is based on relaxing the synchronization of parallel FDTD partitions. In addition he has examined the overlap of partitions and how it will affect the synchronization. Ten to twenty percent improvement in computation time has been obtained.; For MOR techniques a novel recursive convolution approach based on an eigenmodal decomposition of the FDTD engine has been used. In this work, techniques are proposed to reduce the overall FDTD simulation burden by showing how the recursive convolution approach can lead to a system with reduced multiplications per time step. The envisioned system consists of one or many modules whose response is realized through a compact MOR form. This approach has resulted in at least a factor of four improvement in the computation time.; Multivariate system identification, an alternative MOR algorithm, based on the linear prediction theory is also proposed and discussed. Finally a new paradigm for distributed computation is proposed which is based on the MOR treated in this work. An evaluation of the recursive convolution and the system ID approaches shows that both result in algorithms with improved performance metrics for distributed computation.
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