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Distributed-memory parallelization of the Wigner Monte Carlo method using spatial domain decomposition

Abstract

The Wigner Monte Carlo method, based on the generation and annihilation of particles, has emerged as a promising approach to treat transient problems of quantum electron transport in nanostructures. Tackling these simulations in multiple spatial dimensions demands a parallelized approach to facilitate a practical application of the method in order to investigate realistic problems, due to the otherwise exorbitant execution-times and memory requirements. Because of the annihilation step, a straight-forward parallelization of the Wigner Monte Carlo code is not possible, since sub-ensembles of particles can not be treated independently. Moreover, the large memory requirements of the annihilation procedure presents challenges when working in a distributed-memory setting. A solution to this problem is presented here with a parallelization approach using a spatial domain decomposition, implemented using the message passing interface. The presented benchmark results, based on standard one-dimensional examples, exhibit a good efficiency in the scalability of not only speed, but also memory consumption, which is paramount for the simulation of realistic devices.

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Notes

  1. If a sub-ensemble is big enough to yield a statistically representative solution to the simulation task, the ’parallelization’ simply amounts to a simultaneous repetition of the same experiment on different computational units, the results of which are averaged.

  2. In this context a node refers to a computer, which is part of a larger cluster.

  3. For the remainder of this work, the term process refers to an MPI process.

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Acknowledgments

The research leading to these results has received funding from: the Austrian Science Fund (FWF) through the grant P23296, the European Commission under FP7 project AComIn (FP7 REGPOT-2012-2013-1), as well as by the Bulgarian National Science Fund (NSF) under Grant DCVP 02/1. The computational results presented have been achieved in part using the Vienna Scientific Cluster (VSC).

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Ellinghaus, P., Weinbub, J., Nedjalkov, M. et al. Distributed-memory parallelization of the Wigner Monte Carlo method using spatial domain decomposition. J Comput Electron 14, 151–162 (2015). https://doi.org/10.1007/s10825-014-0635-3

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  • DOI: https://doi.org/10.1007/s10825-014-0635-3

Keywords

  • Wigner
  • Monte Carlo
  • Message passing interface
  • Domain decomposition
  • Parallel
  • Memory-distributed