A parallel optimization method for numerical solving the system of polaron equations using the partitioning algorithm

Authors

  • A.V. Volokhova Joint Institute for Nuclear Research
  • E.V. Zemlyanaya Joint Institute for Nuclear Research
  • V.S. Rikhvitskiy Joint Institute for Nuclear Research

DOI:

https://doi.org/10.26089/NumMet.v16r227

Keywords:

hydrated electron, polaron model, finite-difference schemes, parallel algorithms, parallel computing, multiprocessor computer systems

Abstract

The previously developed method for the numerical simulation of the formation of polaron states in condensed media is modified using the partitioning algorithm, which provides a significant speedup in the parallel computations on multiprocessor systems. The software implementation is based on the MPI technology. Numerical results obtained on the multiprocessor cluster installed at the Laboratory of Information Technologies (Joint Institute for Nuclear Research, Dubna) with various numbers of processors and with various computational parameters show that the proposed approach is efficient for the numerical solution of the system of nonlinear differential equations describing the polaron dynamical model.

Author Biographies

A.V. Volokhova

E.V. Zemlyanaya

V.S. Rikhvitskiy

References

  1. V. D. Lakhno, “Dynamical Polaron Theory of the Hydrated Electron,” Chem. Phys. Lett. 437 (4-6), 198-202 (2007).
  2. F. H. Long, H. Lu, and K. B. Eisenthal, “Femtosecond Studies of the Presolvated Electron: An Excited State of the Solvated Electron?,” Phys. Rev. Lett. 64 (12), 1469-1472 (1990).
  3. A. V. Volokhova, E. V. Zemlyanaya, V. D. Lakhno, et al., “Numerical Simulation of the Hydrated Electron Formation,” Vestn. Ross. Univ. Druzhby Narodov, Ser.: Mat. Inform. Fiz., No. 2, 244-247 (2014).
  4. A. V. Volokhova, E. V. Zemlyanaya, V. D. Lakhno, et al., “Numerical Investigation of Photoexcited Polaron States in Water,” Komp’yut. Issled. Modelir. 6 (2), 253-261 (2014).
  5. V. D. Lakhno, A. V. Volokhova, E. V. Zemlyanaya, et al., “Polaron Model of the Formation of Hydrated Electron States,” Poverkhnost No. 1, 82-87 (2015) [J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 9 (1), 75-80 (2015)].
  6. I. S. Berezin and N. P. Zhidkov, Computing Methods (Nauka, Moscow, 1959; Oxford, Pergamon, 1965).
  7. I. V. Amirkhanov, E. V. Zemlyanaya, V. D. Lakhno, et al., “Mathematical Modeling of the Evolution of Polaron States,” Poverkhnost No. 1, 66-70 (2011) [J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 5 (1), 60-64 (2011)].
  8. H. H. Wang, “A Parallel Method for Tridiagonal Equations,” ACM Trans. Math. Softw. 7 (2), 170-183 (1981).
  9. K. A. Barkalov, Methods of Parallel Computing (Lobachevsky Nizhny Novgorod Univ., Nizhny Novgorod, 2011) [in Russian].
  10. A. V. Starchenko, E. A. Danilkin, V. I. Laeva, and S. A. Prokhanov, Practical Course on Parallel Computing Techniques (Mosk. Gos. Univ., Moscow, 2010) [in Russian].
  11. E. A. Hayryan, J. Buša, E. E. Donets, et al., “Numerical Studies of Perturbed Static Solutions Decay in the Coupled System of Yang-Mills-Dilaton Equations with Use of MPI Technology,” Mat. Model. 17 (6), 103-121 (2005).

Published

29-05-2015

How to Cite

Волохова А.В., Земляная Е.В., Рихвицкий В.С. A Parallel Optimization Method for Numerical Solving the System of Polaron Equations Using the Partitioning Algorithm // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2015. 16. 281-289. doi 10.26089/NumMet.v16r227

Issue

Section

Section 1. Numerical methods and applications