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Efficient Parallel Solvers for the FireStar3D Wildfire Numerical Simulation Model

  • Oleg BessonovEmail author
  • Sofiane Meradji
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11657)

Abstract

This paper presents efficient parallel methods for solving ill-conditioned linear systems arising in fluid dynamics problems. The first method is based on the Modified LU decomposition, applied as a preconditioner to the Conjugate gradient algorithm. Parallelization of this method is based on the use of nested twisted factorization. Another method is based on a highly parallel Algebraic multigrid algorithm with a new smoother developed for anisotropic grids. Performance comparisons demonstrate superiority of new methods over commonly used variants of the Conjugate gradient method.

Keywords

Ill-conditioned linear systems Conjugate gradient Preconditioners Multigrid Smoothers Parallelization 

Notes

Acknowledgements

This work was supported by the Russian State Assignment under contract No. AAAA-A17-117021310375-7. The work was granted access to the HPC resources of Aix-Marseille Université financed by the project Equip@Meso (ANR-10-EQPX-29-01) of the program Investissements d’Avenir supervised by the Agence Nationale pour la Recherche (France).

References

  1. 1.
    Morvan, D., Accary, G., Meradji, S., Frangieh, N., Bessonov, O.: A 3D physical model to study the behavior of vegetation fires at laboratory scale. Fire Saf. J. 101, 39–53 (2018).  https://doi.org/10.1016/j.firesaf.2018.08.011CrossRefGoogle Scholar
  2. 2.
    Frangieh, N., Morvan, D., Meradji, S., Accary, G., Bessonov, O.: Numerical simulation of grassland fires behavior using an implicit physical multiphase model. Fire Saf. J. 102, 37–47 (2018).  https://doi.org/10.1016/j.firesaf.2018.06.004CrossRefGoogle Scholar
  3. 3.
    Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing, Boston (2000)Google Scholar
  4. 4.
    Shewchuk, J.R.: An Introduction to the Conjugate Gradient Method Without the Agonizing Pain. School of Computer Science, Carnegie Mellon University, Pittsburgh (1994)Google Scholar
  5. 5.
    Bessonov, O.: Parallelization properties of preconditioners for the conjugate gradient methods. In: Malyshkin, V. (ed.) PaCT 2013. LNCS, vol. 7979, pp. 26–36. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-39958-9_3CrossRefGoogle Scholar
  6. 6.
    Stüben, K.: A review of algebraic multigrid. J. Comput. Appl. Math. 128, 281–309 (2001).  https://doi.org/10.1016/S0377-0427(00)00516-1MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bessonov, O.: Highly parallel multigrid solvers for multicore and manycore processors. In: Malyshkin, V. (ed.) PaCT 2015. LNCS, vol. 9251, pp. 10–20. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-21909-7_2CrossRefGoogle Scholar
  8. 8.
    Accary, G., Bessonov, O., Fougère, D., Gavrilov, K., Meradji, S., Morvan, D.: Efficient Parallelization of the preconditioned conjugate gradient method. In: Malyshkin, V. (ed.) PaCT 2009. LNCS, vol. 5698, pp. 60–72. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-03275-2_7CrossRefGoogle Scholar
  9. 9.
    Patankar, S.V.: Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing, New York (1980)zbMATHGoogle Scholar
  10. 10.
    Versteeg, H., Malalasekera, W.: An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Prentice Hall, Harlow (2007)Google Scholar
  11. 11.
    Moukalled, F., Darwish, M.: A unified formulation of the segregated class of algorithms for fluid flow at all speed. Numer. Heat Transf. Part B 37, 103–139 (2000).  https://doi.org/10.1080/104077900275576CrossRefGoogle Scholar
  12. 12.
    van der Vorst, H.A.: Large tridiagonal and block tridiagonal linear systems on vector and parallel computers. Parallel Comput. 5, 45–54 (1987).  https://doi.org/10.1016/0167-8191(87)90005-6MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Gustafsson, I.: A class of first order factorization methods. BIT 18, 142–156 (1978).  https://doi.org/10.1007/BF01931691MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Axelsson, O.: Analysis of incomplete matrix factorizations as multigrid smoothers for vector and parallel computers. Appl. Math. Comput. 19, 3–22 (1986).  https://doi.org/10.1016/0096-3003(86)90094-9MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Llorente, I.M., Melson, N.D.: Robust multigrid smoothers for three dimensional elliptic equations with strong anisotropies. Technical report 98-37, ICASE (1998)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Ishlinsky Institute for Problems in Mechanics RASMoscowRussia
  2. 2.IMATH, EA 2134University of ToulonLa GardeFrance

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