Geodesic
Numerical performance of a sweep parallel algorithm on distributed memory multiprocessors
Numerical methods and programming, Tome 9 (2008) no. 3, pp. 305-310.

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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.
Keywords: mathematical simulation, parallel algorithms, high performance computing, Schroedinger equation. 
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     author = {V. E. Vitkovskiy and M. P. Fedoruk},
     title = {Numerical performance of a sweep parallel algorithm on distributed memory multiprocessors},
     journal = {Numerical methods and programming},
     pages = {305--310},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2008_9_3_a9/}
}
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V. E. Vitkovskiy; M. P. Fedoruk. Numerical performance of a sweep parallel algorithm on distributed memory multiprocessors. Numerical methods and programming, Tome 9 (2008) no. 3, pp. 305-310. http://geodesic.mathdoc.fr/item/VMP_2008_9_3_a9/