Efficiency Estimation for the Mathematical Physics Algorithms for Distributed Memory Computers

  • Igor KonshinEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 965)


The paper presents several models of parallel program runs on computer platforms with distributed memory. The prediction of the parallel algorithm efficiency is based on algorithm arithmetic and communication complexities. For some mathematical physics algorithms for explicit schemes of the solution of the heat transfer equation the speedup estimations were obtained, as well as numerical experiments were performed to compare the actual and theoretically predicted speedups.


Mathematical physics Parallel computing Parallel efficiency estimation Speedup 



The theoretical part of this work has been supported by the Russian Science Foundation through the grant 14-11-00190. The experimental part was partially supported by RFBR grant 17-01-00886.


  1. 1.
    AlgoWiki: Open encyclopedia of algorithm properties. Accessed 15 Apr 2018
  2. 2.
    Voevodin, V.V., Voevodin, Vl.V.: Parallel Computing. BHV-Petersburg, St. Petersburg (2002, in Russian)Google Scholar
  3. 3.
    Gergel, V.P., Strongin, R.G.: Fundamentals of Parallel Computing for Multiprocessor Computer Systems. Publishing House of the Nizhny Novgorod State Univ., Nizhny Novgorod (2003, in Russian)Google Scholar
  4. 4.
    Konshin, I.N.: Parallel computational models to estimate an actual speedup of analyzed algorithm. In: Proceedings of the International Conference on Russian Supercomputing Days, 26–27 September 2016, Moscow, Russia, pp. 269–280. Moscow State University, Moscow (2016, in Russian)
  5. 5.
    Konshin, I.: Parallel computational models to estimate an actual speedup of analyzed algorithm. In: Voevodin, V., Sobolev, S. (eds.) RuSCDays 2016. CCIS, vol. 687, pp. 304–317. Springer, Cham (2016). Scholar
  6. 6.
    Konshin, I.N.: Parallelism in computational mathematics. International Summer Supercomputer Academy. Track: Parallel Algorithms of Algebra and Analysis and Experiments of Supercomputer Modeling. MSU, Moscow (2012, in Russian). Accessed 15 Apr 2018
  7. 7.
    INM RAS cluster (2018, in Russian). Accessed 15 Apr 2018
  8. 8.
    MPI: The Message Passing Interface standard. Accessed 15 Apr 2018
  9. 9.
    Bajdin, G.V.: On some stereotypes of parallel programming. Vopr. Atomn. Nauki Tekhn., Ser. Mat. Model Fiz. Prots., no. 1, pp. 67–75 (2008, in Russian)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dorodnicyn Computing Centre of FRC CSC RASMoscowRussia
  2. 2.Marchuk Institute of Numerical Mathematics of the Russian Academy of SciencesMoscowRussia

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