Abstract
A domain decomposition approach for the parallelization of the Wigner Monte Carlo method allows the huge memory requirements to be distributed amongst many computational units, thereby making large multi-dimensional simulations feasible. Two domain decomposition techniques—a uniform slab and uniform block decomposition—are compared and the design and implementation of the block decomposition approach, using the message passing interface, is discussed. The parallel performance of the two approaches is evaluated by simulating a representative physical problem. Our results show that the presumably inferior slab decomposition method is in fact superior to the block decomposition approach, due to the additional overhead incurred by the block decomposition method to set up its communication layer.
Similar content being viewed by others
References
Wigner, E.: On the quantum correction for thermodynamic equilibrium. Phys. Rev. Lett. 40, 749 (1932). doi:10.1103/PhysRev.40.749
Querlioz, D., Dollfus, P.: The Wigner Monte-Carlo Method for Nanoelectronic Devices: Particle Description of Quantum Transport and Decoherence. Wiley, New York (2010). ISBN: 9781848211506
Nedjalkov, M., Kosina, H., Selberherr, S., Ringhofer, C., Ferry, D.K.: Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices. Phys. Rev. B 70, 115319 (2004). doi:10.1103/PhysRevB.70.115319
Nedjalkov, M., Schwaha, P., Selberherr, S., Sellier, J.M., Vasileska, D.: Wigner quasi-particle attributes—an asymptotic perspective. Appl. Phys. Lett. 102(16), 163113 (2013). doi:10.1063/1.4802931
Sellier, J., Dimov, I.: The Wigner–Boltzmann Monte Carlo method applied to electron transport in the presence of a single dopant. Comput. Phys. Commun. 185(10), 2427 (2014). doi:10.1016/j.cpc.2014.05.013
Sellier, J., Nedjalkov, M., Dimov, I., Selberherr, S.: Two-dimensional transient Wigner particle model. In: Proceedings of the 18th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), pp. 404–407 (2013). doi:10.1109/SISPAD.2013.6650660
Sellier, J.M., Nedjalkov, M., Dimov, I., Selberherr, S.: The role of annihilation in a Wigner Monte Carlo approach. In: Lirkov, I., Margenov, S., Wasniewski, J. (eds.) Large-Scale Scientific Computing. Springer, Berlin (2014). doi:10.1007/978-3-662-43880-0_20
Ellinghaus, P., Weinbub, J., Nedjalkov, M., Selberherr, S., Dimov, I.: Distributed-memory parallelization of the Wigner Monte Carlo method using spatial domain decomposition. J. Comput. Electron. 14(1), 151 (2015). doi:10.1007/s10825-014-0635-3
Dimov, I.: Monte Carlo Methods For Applied Scientists. World Scientific Publishing, Singapore (2005). ISBN: 9789810223298
Weinbub, J., Ellinghaus, P., Selberherr, S.: Parallelization of the two-dimensional Wigner Monte Carlo method. In: Lirkov, I., Margenov, S., Wasniewski, J. (eds.) Large-Scale Scientific Computing. Springer, Berlin (2015, in press)
Vienna, W.D.: Wigner Ensemble Monte Carlo Simulator. (2015). http://viennawd.sourceforge.net/
Hager, G., Wellein, G.: Introduction to High Performance Computing for Scientists and Engineers. CRC Press, Boca Raton, FL (2010). ISBN: 9781439811924
Vienna Scientific Cluster. VSC-3. (2015). http://vsc.ac.at/
Acknowledgments
The computational results presented have been achieved using the Vienna Scientific Cluster (VSC).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Weinbub, J., Ellinghaus, P. & Nedjalkov, M. Domain decomposition strategies for the two-dimensional Wigner Monte Carlo Method. J Comput Electron 14, 922–929 (2015). https://doi.org/10.1007/s10825-015-0730-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10825-015-0730-0