Numerical approach and parallel implementation for computer simulation of stacked long Josephson Junctions

 pdf (219K)  / List of references

We consider a model of stacked long Josephson junctions (LJJ), which consists of alternating superconducting and dielectric layers. The model takes into account the inductive and capacitive coupling between the neighbor junctions. The model is described by a system of nonlinear partial differential equations with respect to the phase differences and the voltage of LJJ, with appropriate initial and boundary conditions. The numerical solution of this system of equations is based on the use of standard three-point finite-difference formulae for discrete approximations in the space coordinate, and the applying the four-step Runge-Kutta method for solving the Cauchy problem obtained. Designed parallel algorithm is implemented by means of the MPI technology (Message Passing Interface). In the paper, the mathematical formulation of the problem is given, numerical scheme and a method of calculation of the current-voltage characteristics of the LJJ system are described. Two variants of parallel implementation are presented. The influence of inductive and capacitive coupling between junctions on the structure of the current-voltage characteristics is demonstrated. The results of methodical calculations with various parameters of length and number of Josephson junctions in the LJJ stack depending on the number of parallel computing nodes, are presented. The calculations have been performed on multiprocessor clusters HybriLIT and CICC of Multi-Functional Information and Computing Complex (Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna). The numerical results are discussed from the viewpoint of the effectiveness of presented approaches of the LJJ system numerical simulation in parallel. It has been shown that one of parallel algorithms provides the 9 times speedup of calculations.

Keywords: Josephson junctions, finite difference approximation, parallel computing
Citation in English: Bashashin M.V., Zemlyanay E.V., Rahmonov I.R., Shukrinov J.M., Atanasova P.C., Volokhova A.V. Numerical approach and parallel implementation for computer simulation of stacked long Josephson Junctions // Computer Research and Modeling, 2016, vol. 8, no. 4, pp. 593-604
Citation in English: Bashashin M.V., Zemlyanay E.V., Rahmonov I.R., Shukrinov J.M., Atanasova P.C., Volokhova A.V. Numerical approach and parallel implementation for computer simulation of stacked long Josephson Junctions // Computer Research and Modeling, 2016, vol. 8, no. 4, pp. 593-604
DOI: 10.20537/2076-7633-2016-8-4-593-604
According to Crossref, this article is cited by:
  • Nikolay A. Kutovskiy, Andrey V. Nechaevskiy, Gennady Alekseevich Ososkov, Darya I. Pryahina, Vladimir V. Trofimov. Simulation of interprocessor interactions for MPI-applications in the cloud infrastructure. // Computer Research and Modeling. 2017. — V. 9, no. 6. — P. 955. DOI: 10.20537/2076-7633-2017-9-6-955-963
  • Nikita Balashov, Maxim Bashashin, Pavel Goncharov, Ruslan Kuchumov, Nikolay Kutovskiy, Kiril Kulikov, Mikhail Matveev, Andrey Nechaevskiy, Gennady Ososkov, Ilkhom Rahmonov, Rahmonov Ilkhom, Rahmonov Ilkhom, Shukrinov Yuri, Sokolov Ivan, Shukrinov Yuri, Streltsova Oksana, Zemlyanaya Elena. Service for parallel applications based on JINR cloud and HybriLIT resources. // EPJ Web of Conferences. 2019. — V. 214. — P. 07012. DOI: 10.1051/epjconf/201921407012
Please note that citation information may be incomplete as it includes data from Crossref cited-by program partners only.
Views (last year): 7. Citations: 6 (RSCI).

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the List of Russian peer-reviewed journals publishing the main research results of PhD and doctoral dissertations.

International Interdisciplinary Conference "Mathematics. Computing. Education"

The journal is included in the RSCI

Indexed in Scopus