Time-parallel computational strategy for FDTD solution of Maxwell´s equations

A major emphasis within the computational electromagnetics (CEM) community concerns the solution of Maxwell´s differential equations using finite-difference time-domain (FDTD) techniques. Because of the computational time and memory requirements associated with these time-stepping algorithms, their application to very large problems has been somewhat limited. To alleviate these computational obstacles, some efforts have previously been aimed at the implementation of space-parallelism-the concurrent computation of unknowns at different points in the spatial mesh using multiple processors-in the FDTD algorithms. For these schemes, however, communication and synchronization requirements have limited the amount of computational speed-up provided by the use of additional processors. This limited potential for enhanced computational efficiency implies that if full exploitation of the capabilities of emerging multiple instruction multiple data (MIMD) architectures is to be realized, approaches must be developed which represent a drastic departure from traditional FDTD techniques. The aim of the paper is to present such a computational strategy. Unlike traditional approaches which use space-parallelism this methodology exploits the decoupling mechanism of an eigenvalue-eigenvector (EE) decomposition of the FDTD matrix to allow the efficient implementation of time-parallelism-the simultaneous computation of field values at multiple time steps. The resulting algorithm is highly coarse grain and has minimum communication and synchronization requirements.<>