Skip to main content
SpringerLink
Log in
Book cover

International Conference on Parallel Computational Technologies

PCT 2017: Parallel Computational Technologies pp 73–85Cite as

On the Parallel Strategies in Mathematical Modeling

  • Conference paper
  • First Online:

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 753))

Abstract

The article considers parallel strategies and tactics at different stages of mathematical modeling. These technological steps include geometrical and functional modeling, discretization and approximation, algebraic solvers and optimization methods for inverse problems, postprocessing and visualization of numerical results, as well as decision-making systems. Scalable parallelism can be provided by combined application of MPI tools, multi-thread computing, vectorization, and the use of graphics accelerators. The general method to achieve high-performance computing consists in minimizing data communications, which are the most time and energy consuming. The construction of efficient parallel algorithms and code optimization is based on various approaches at different levels of computational schemes. The implementation of the biggest interdisciplinary direct and inverse problems in cloud computing technologies is considered. The corresponding applied software with a long life cycle is represented as integrated environment oriented to large groups of end users.

The work was supported by the RFBR grant N 16-29-15122 and the RSF grant N 15-11-10024.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. ANSYS - Simulation Driven Product Development. http://www.ansys.com

  2. Logg, F., Mardal, K.-A., Wells, G.N. (eds.): Automated Solution of Partial Differential Equations by Finite Element Method: The FEniCS Book. Springer, Heidelberg (2011)

    Google Scholar 

  3. Schoberl, J.: Netgen - an advancing front 2D/3D mesh generator based on abstract rules. Comput. Vis. Sci. 1, 41–52 (1997). doi:10.1007/s007910050004

    Article  MATH  Google Scholar 

  4. PETSc. http://www.mcs.anl.gov/petsc

  5. Open FOAM - The Open Source Computational Fluid Dynamics (CFD) Toolbox. http://www.open-foam.com

  6. DUNE Numerics. Distributed Unified Numerical Environment. http://www.dune-project.org

  7. Il’in, V.P., Skopin, I.N.: Computational programming technologies. Programm. Comput. Softw. 37(4), 210–222 (2011). doi:10.1134/s0361768811040037

    Article  Google Scholar 

  8. Ilin, V.P.: Fundamental Issues of mathematical modeling. Herald Rus. Acad. Sci. 86, 118–126 (2016). doi:10.1134/s101933161602009x

    Article  Google Scholar 

  9. AlgoWiki: Open encyclopedia of algorithm properties. http://algowiki-project.org

  10. Il’in, V.P., Skopin, I.N.: About performance and intellectuality of supercomputer modeling. Program. Comput. Softw. 42, 5–16 (2016). doi:10.1134/s0361768816010047

    Article  Google Scholar 

  11. Golubeva, L.A., Il’in, V.P., Kozyrev, A.N.: Programming technologies in geometric aspects of mathematical modeling. Vestnik NGU. Seria: Inf. Tekhnol. 10, 25–33 (2012). (in Russian)

    Google Scholar 

  12. Il’in, V.P.: DELAUNAY: A technological environment for mesh generation. Siberian Zhurnal Indus. Math. 16, 83–97 (2013). (in Russian)

    MATH  Google Scholar 

  13. Butygin, D.S., Il’in, V.P.: Chebyshev: Principles of automation of algorithm construction in an integrated environment for mesh approximations of initial boundary value problems. In: Proceedings of International Conference on Parallel Computational Technologies 2014, Izd. YuUrGU, Chelyabinsk, pp. 42–50 (2014). (in Russian)

    Google Scholar 

  14. Intel Math. Kernel Library. http://software.intel.com/en-us/intel-mkl

  15. Butyugin, D.S., Gurieva, Y.L., Il’in, V.P., et al.: Functionality and technologies of algebraic solvers in Krylov’s library. Mathematical Modeling, Programming & Computer software, pp. 76–86. Bulletin of south Ural state university, Russain Federation (2013). (in Russian)

    Google Scholar 

  16. Konshin, I.N.: Parallel Computational Models to Estimate an Actual Speedup of Analyzed Algorithm. Russian Supercomputing Days: Proceedings of the International Conference, pp. 269–280. MSU Publ. (2016) (in Russian). doi:10.1007/978-3-319-55669-7_24

  17. Dolean, V., Jolivet, P., Nataf, F.: An Introduction to Domain Decomposition Methods: algorithms, theory and parallel implementation. doi:10.1137/1.9781611974065.. https://archives-ouvertes.fr/cel-01100932

  18. Il’in, V.P.: Problems of parallel solution of large systems of linear algebraic equations. J. Math. Sci. 216, 795–804 (2016). doi:10.1007/s10958-016-2945-4

    Article  MATH  Google Scholar 

  19. Saad, Y., Sosonkina, M.: pARMS: A package for the parallel iterative solution of general large sparse linear systems user’s guide. Report UMSI 2004–8, Minnesota Supercomp. Inst., Univer. of Minnesota, MN (2004)

    Google Scholar 

  20. Gander, M.J.: 50 Years of Time Parallel Time Integration. doi:10.1007/978-3-319-23321-5_3. http://www.unige.ch/~gander/Preprints/50YearsTimeParallel.pdf

  21. Il’in, V.P.: Numeric solving of direct and inverse problems of electromagnetic prospecting. Sibirian Zhurnal of Vychislitelnoi Mathematiki 6, 381–394 (2003). (in Russian)

    Google Scholar 

  22. Il’in, V.P.: Component technologies of high-performance mathematical modeling. In: Proceedings of the International Conference on Parallel Computational Technologies - 2015 (UFU, IMM UrO RAN, Yekaterinburg), pp. 166–171 (2015). (in Russian)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics RAS, Novosibirsk State University, 6 Pr. Lavrentieva, 630090, Novosibirsk, Russia

    Valery Il’in

Authors
  1. Valery Il’in
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valery Il’in .

Editor information

Editors and Affiliations

  1. South Ural State University, Chelyabinsk, Russia

    Leonid Sokolinsky

  2. South Ural State University, Chelyabinsk, Russia

    Mikhail Zymbler

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Il’in, V. (2017). On the Parallel Strategies in Mathematical Modeling. In: Sokolinsky, L., Zymbler, M. (eds) Parallel Computational Technologies. PCT 2017. Communications in Computer and Information Science, vol 753. Springer, Cham. https://doi.org/10.1007/978-3-319-67035-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-67035-5_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67034-8

  • Online ISBN: 978-3-319-67035-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation