Advertisement

Journal of Mechanical Science and Technology

, Volume 32, Issue 11, pp 5315–5323 | Cite as

Performance comparison of various parallel incomplete LU factorization preconditioners for domain decomposition method

  • Sungwoo Kang
  • Hyounggwon Choi
  • Wanjin Chung
  • Yo-Han Yoo
  • Jung Yul Yoo
Article

Abstract

A finite element code is parallelized by vertex-oriented domain decomposition method which utilizes one- or multi-dimensional partitioning in structured mesh and METIS Library in unstructured mesh. For obtaining the domain-decomposed solution, iterative solvers like conjugate gradient method are used. To accelerate the convergence of iterative solvers, parallel incomplete LU factorization preconditioners are employed, and their performances are compared. For the communication between processors, Message Passing Interface Library is used. The speedups of parallel preconditioned iterative solvers are estimated through computing 2- and 3-dimensional Laplace equations. The effects of mesh and partitioning method on the speedup of parallel preconditioners are also examined.

Keywords

Finite element method Domain decomposition method Preconditioned conjugate gradient Parallel ILU preconditioner 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Basermann, B. Reichel and C. Schelthoff, Preconditioned CG methods for sparse matrices on massively parallel machines, Parallel Computing, 23 (3) (1997) 381–398.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    M. Magolu monga Made and H. A. van der Vorst, A generalized domain decomposition paradigm for parallel incomplete LU factorization preconditionings, Future Generation Computer Systems, 17 (8) (2001) 925–932.CrossRefzbMATHGoogle Scholar
  3. [3]
    M. Magolu monga Made and H. A. van der Vorst, Parallel incomplete factorizations with pseudo–overlapped subdo–mains, Parallel Computing, 27 (8) (2001) 989–1008.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Y. Saad and M. Sosonkina, Distributed Schur complement techniques for general sparse linear systems, SIAM Journal on Scientific Computing, 21 (4) (1999) 1337–1356.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    M. Manguoglu, A domain–decomposing parallel sparse linear system solver, Journal of Computational and Applied Mathematics, 236 (3) (2011) 319–325.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    A. Lemmer and R. Hilfer, Parallel domain decomposition method with non–blocking communication for flow through porous media, Journal of Computational Physics, 281 (2015) 970–981.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    S. Loisel and H. Nguyen, An optimal Schwarz preconditioner for a class of parallel adaptive finite elements, Journal of Computational and Applied Mathematics, 321 (2017) 90–107.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    G. Radicati di Brozolo and Y. Robert, Parallel conjugate gradient–like algorithms for solving sparse nonsymmetric linear systems on a vector multiprocessor, Parallel Computing, 11 (2) (1989) 223–239.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Y. Saad, Iterative methods for sparse linear systems, PWS Publishing Company: Boston (1996).zbMATHGoogle Scholar
  10. [10]
    H. A. Van der Vorst, Bi–CGSTAB: A fast and smoothly converging variant of Bi–CG for the solution of nonsymmetric linear systems, SIAM Journal on Scientific and Statistical Computing, 13 (2) (1992) 631–644.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    M. Snir, S. W. Otto, S. Huss–Lederman, D. Walker and J. Dongarra, MPI: The complete reference, The MIT Press: London, England (1996).Google Scholar
  12. [12]
    http://www–users.cs.umn.edu/~karypis/metis.Google Scholar
  13. [13]
    G. F. Carey, Y. Shen and R. T. McLay, Parallel conjugate gradient performance for least–squares finite elements and transport problems, International Journal for Numerical Methods in Fluids, 28 (10) (1998) 1421–1440.CrossRefzbMATHGoogle Scholar
  14. [14]
    D. S. Kershaw, The incomplete Cholesky–conjugate gradient method for the iterative solution of systems of linear equations, Journal of Computational Physics, 26 (1) (1978) 43–65.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    K. A. Hoffmann and S. T. Chiang, Computational fluid dynamics for engineers, A Publication of Engineering Education System: Wichita, Kansas, USA, 1 (1993).Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Sungwoo Kang
    • 1
  • Hyounggwon Choi
    • 2
  • Wanjin Chung
    • 3
  • Yo-Han Yoo
    • 4
  • Jung Yul Yoo
    • 5
  1. 1.Powertrain NVH Development Team 1Hyundai Motor GroupHwaseong-si, Gyeonggi-doKorea
  2. 2.Department of Mechanical & Automotive EnggSeoul National University of Science and TechnologySeoulKorea
  3. 3.Department of Mechanical System Design EnggSeoul National University of Science and TechnologySeoulKorea
  4. 4.Agency for Defence DevelopmentYuseongDaejeonKorea
  5. 5.School of Mechanical and Aerospace EnggSeoul National UniversitySeoulKorea

Personalised recommendations