The computational complexity and memory requirements of classically formulated marching-on-in-time (MOT)-based surface integral equation (SIE) solvers scale as O(N N) and O(N), respectively; here N and N denote the number of temporal and spatial degrees of freedom of the current density. The multilevel plane wave time domain (PWTD) algorithm, viz., the time domain counterpart of the multilevel fast multipole method, reduces these costs to O(N Nlog N) and O(N) (Ergin et al., IEEE Trans. Antennas Mag., 41, 39–52, 1999). Previously, PWTD-accelerated MOT-SIE solvers have been used to analyze transient scattering from perfect electrically conducting (PEC) and homogeneous dielectric objects discretized in terms of a million spatial unknowns (Shanker et al., IEEE Trans. Antennas Propag., 51, 628–641, 2003). More recently, an efficient parallelized solver that employs an advanced hierarchical and provably scalable spatial, angular, and temporal load partitioning strategy has been developed to analyze transient scattering problems that involve ten million spatial unknowns (Liu et. al., in URSI Digest, 2013).
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