Numerical performance of a sweep parallel algorithm on distributed memory multiprocessors

An efficient sweep parallel algorithm used when solving the nonlinear Schrödinger equation by the implicit Crank-Nicolson scheme with a spatial and time mesh refinement mechanism is considered. Its performance on distributed-memory multiprocessors is analyzed. It is shown on the basis of computational experiments and the well-known theoretical model (Amdahl's law) that the proposed algorithm scales well and achieves efficiency and speedup over the sequential algorithm up to $0.7$ and $30$, respectively. The effect of the numerical mesh size (range, $10^4 - 10^6$) and the network communication delays (CPU number range, $6$–$128$) on the performance of computing is discussed.