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Deflated Krylov Iterations in Domain Decomposition Methods

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Domain Decomposition Methods in Science and Engineering XXIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 116))

Abstract

The paper is dedicated to an experimental evaluation of some coarse grid techniques in the context of additive Schwarz method and Krylov subspace methods. Some theoretical aspects are considered and a few modifications of well-known methods are presented. The choice of a correction operator is also studied. The results indicate that a coarse grid correction approach may accelerate an iterative process if employed sensibly. The paper also presents a comparison of overlapping and coarse grid correction in terms of convergence speed and performance.

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References

  • R. Bridson, C. Greif, A multipreconditioned conjugate gradient algorithm. SIAM J. Matrix Anal. Appl. 27 (4), 1056–1068 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • V. Dolean, P. Jolivet, F. Nataf, An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation, vol. 144 (Society for Industrial and Applied Mathematics, Philadelphia, 2015)

    Book  MATH  Google Scholar 

  • O. Dubois, M.J. Gander, S. Loisel, A. St-Cyr, D.B. Szyld, The optimized Schwarz method with a coarse grid correction. SIAM J. Sci. Comput. 34 (1), A421–A458 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • S.C. Eisenstat, H.C. Elman, M.H. Schultz, Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 20 (2), 345–357 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  • Y.L. Gurieva, V.P. Il’in, Parallel approaches and technologies of domain decomposition methods. J. Math. Sci. 207 (5), 724–735 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • V.P. Il’in, On exponential finite volume approximations. Russ. J. Numer. Anal. Math. Model. 18 (6), 479–506 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • V.P. Il’in, E.A. Itskovich, Semi-conjugate direction methods with dynamic preconditioning. Sibirskii Zhurnal Industrial’noi Matematiki 10 (4), 41–54 (2007)

    MATH  Google Scholar 

  • NKS-30T, http://www2.sscc.ru/ENG/Resources.htm (2017)

  • Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edn. (Society for Industrial and Applied Mathematics, Philadelphia, PA, 2003)

    Book  MATH  Google Scholar 

  • A. Toselli, O. Widlund, Domain Decomposition Methods—Algorithms and Theory. Springer Series in Computational Mathematics, vol. 34 (Springer, Berlin, 2005)

    Google Scholar 

  • J.Y. Yuan, G.H. Golub, R.J. Plemmons, W.A.G. Cecílio, Semi-conjugate direction methods for real positive definite systems. BIT Numer. Math. 44 (1), 189–207 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia

    Y. L. Gurieva, V. P. Ilin & D. V. Perevozkin

  2. Novosibirsk State University, Novosibirsk, Russia

    V. P. Ilin

Authors
  1. Y. L. Gurieva
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  2. V. P. Ilin
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  3. D. V. Perevozkin
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Corresponding author

Correspondence to D. V. Perevozkin .

Editor information

Editors and Affiliations

  1. Dept. of Mathematical Sciences, KAIST, Daejeon, Korea (Republic of)

    Chang-Ock Lee

  2. Dept. of Computer Science, University of Colorado, Boulder, Colorado, USA

    Xiao-Chuan Cai

  3. Applied Math & Computational Science, KAUST, Thuwal, Saudi Arabia

    David E. Keyes

  4. Dept. of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. Mathematisches Institut, Universität zu Köln, Köln, Germany

    Axel Klawonn

  6. Dept. of Computational Science & Engineering, Yonsei University, Seoul, Korea (Republic of)

    Eun-Jae Park

  7. Courant Institute of Mathematical Sciences, New York University, New York, New York, USA

    Olof B. Widlund

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Gurieva, Y.L., Ilin, V.P., Perevozkin, D.V. (2017). Deflated Krylov Iterations in Domain Decomposition Methods. In: Lee, CO., et al. Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-52389-7_35

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