Skip to main content
SpringerLink
Log in

Parallel algorithms and domain decomposition techniques for solving three-dimensional boundary value problems on quasi-structured grids

  • Published:
Numerical Analysis and Applications Aims and scope Submit manuscript

Abstract

A new approach to the decomposition of a three-dimensional computational domain into subdomains matched without overlapping is proposed. It is based on direct approximation of the Poincare–Steklov equation at the interface. Parallel algorithms and techniques for solving threedimensional boundary value problems on quasi-structured grids are presented. Experimental evaluation of parallel efficiency is done by solving a model problem with quasi-structured parallelepipedal matching and non-matching grids as an example.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Agoshkov, V. and Ovtchinnikov, E., Projection Decomposition Method, Math.Mod. Met. Appl. Sci., 1994, vol. 4, pp. 773–794.

    Article  MathSciNet  MATH  Google Scholar 

  2. Gervasio, P., Ovtchinnikov, E., and Quarteroni, A., The Spectral Projection DecompositionMethod for Elliptic Equations in Two Dimensions, SIAM J. Numer. An., 1997, vol. 34, no. 4, pp. 1616–1639.

    Article  MathSciNet  MATH  Google Scholar 

  3. Sveshnikov, V.M., Construction of Direct and Iterative Decomposition Methods, Sib. Zh. Vych. Mat., 2009, vol. 12, no. 3, pp. 99–109.

    MathSciNet  MATH  Google Scholar 

  4. Sveshnikov, V.M. and Belyaev, D.O., Construction of Quasi-Structured Locally Modified Grids to Solve Problems of High-Current Electronics, Vestnik YuUrGU, Ser. MMP, 2012, no. 40(299), iss. 14, pp. 130–140.

    MATH  Google Scholar 

  5. Sveshnikov, V.M. and Rybdylov, B.D., Parallel Solving of Boundary Value Problems on Quasi-Structured Grids, Vestnik YuUrGU, Ser. VMI, 2013, vol. 2, no. 3, pp. 63–72.

    Google Scholar 

  6. Il’in, V.P., Metody konechnykh raznostei i konechnykh ob″emov dlya ellipticheskikh uravnenii (Finite Difference and Finite Volume Methods for Elliptic Equations), Novosibirsk: Publ. House of ICM&MG SB RAS, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    V. D. Korneev & V. M. Sveshnikov

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    V. D. Korneev & V. M. Sveshnikov

Authors
  1. V. D. Korneev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. M. Sveshnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. D. Korneev.

Additional information

Original Russian Text © V.D. Korneev, V.M. Sveshnikov, 2016, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2016, Vol. 19, No. 2, pp. 183–194.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Korneev, V.D., Sveshnikov, V.M. Parallel algorithms and domain decomposition techniques for solving three-dimensional boundary value problems on quasi-structured grids. Numer. Analys. Appl. 9, 141–149 (2016). https://doi.org/10.1134/S1995423916020051

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995423916020051

Keywords

Search

Navigation