Progress in parallel implementation of the multilevel plane wave time domain algorithm

The computational complexity and memory requirements of classical schemes for evaluating transient electromagnetic fields produced by N_s dipoles active for N_t time steps scale as O(N_tN_s²) and O(N_s²), respectively. The multilevel plane wave time domain (PWTD) algorithm [A.A. Ergin et al., Antennas and Propagation Magazine, IEEE, vol. 41, pp. 39-52, 1999], viz. the extension of the frequency domain fast multipole method (FMM) to the time domain, reduces the above costs to O(N_tN_slog²N_s) and O(N_s^α) with α = 1.5 for surface current distributions and α = 4/3 for volumetric ones. Its favorable computational and memory costs notwithstanding, serial implementations of the PWTD scheme unfortunately remain somewhat limited in scope and ill-suited to tackle complex real-world scattering problems, and parallel implementations are called for.