Parallel simulation of drift–diffusion–recombination by cellular automata and global random walk algorithm

Anastasiya Kireeva, Karl K. Sabelfeld, Sergey Kireev

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)6889-6903
Number of pages15
JournalJournal of Supercomputing
Issue number7
Early online date4 Jan 2021
Publication statusPublished - Jul 2021


  • Drift–diffusion–recombination
  • Global random walk
  • Monte Carlo
  • Multi-particle cellular automaton
  • Parallel computing
  • diffusion&#8211
  • recombination
  • Drift&#8211


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