We suggest in this paper a parallel implementation of cellular automation and global random walk algorithms for solving drift–diffusion–recombination problems which in contrast to the classical random walk on spheres (RWS) methods calculate the solution in any desired family of m prescribed points. The method uses only N trajectories in contrast to mN trajectories in the conventional RWS algorithm. The idea is based on the adjoint symmetry property of the Green function and a double randomization approach. The synchronous multi-particle cellular automaton model of drift–diffusion–recombination is based on known cellular automata. The global RWS and cellular automaton models are tested against the exact solutions of the equation. The accuracy and computer time of both algorithms is analyzed. Parallel codes for the Monte Carlo and cellular automaton algorithms are implemented. The domain decomposition method is employed for the cellular automaton parallel implementation. The global random walk algorithm is parallelized by the Monte Carlo trajectories distribution among the cluster cores. The efficiency of the parallel codes is studied.
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This work has been carried out as a follow-up of our study  where the idea and mathematics of the GRW algorithm for drift–diffusion equation have been suggested. This study and a part of the present work are supported by the Mathematical Center in Akademgorodok. The part of the work of the present paper on the development of CA and the overall implementation including the parallel versions of GRW and CA algorithms is supported by the Russian Science Foundation. Supported by the Russian Science Foundation under Grant 19-11-00019 and the Mathematical Center in Akademgorodok, the agreement with the Ministry of Science and High Education of the Russian Federation Number 075-15-2019-1675.
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Kireeva, A., Sabelfeld, K.K. & Kireev, S. Parallel simulation of drift–diffusion–recombination by cellular automata and global random walk algorithm. J Supercomput 77, 6889–6903 (2021). https://doi.org/10.1007/s11227-020-03529-y
- Multi-particle cellular automaton
- Monte Carlo
- Global random walk
- Parallel computing