Subdomain Solution of Problem with Unilateral Constraints in Grid Environments

  • Ming Chau
  • Thierry Garcia
  • Abdelhamid Laouar
  • Pierre Spiteri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6864)


The present study deals with the solution of problem arising in fluid mechanics with unilateral constraints on the boundary. The problem is defined in the three-dimensional domain. An implicit scheme is used for the time dependent part of the operator and the problem is then reduced to the solution of a sequence of stationary problems. The discretization of such stationary problem by appropriate schemes leads to the solution of a large-scale algebraic system. According to the size of these systems, parallel iterative asynchronous and synchronous subdomain methods are carried out on distributed architectures. Finally the experiment studies are presented and analyzed.


parallel iterative algorithms asynchronous iterations unilateral constraints problem grid computing fluid mechanics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baudet, G.: Asynchronous iterative methods for multiprocessors. Journal Assoc. Comput. Mach. 25, 226–244 (1978)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Bolze, R., Cappello, F., Caron, E., Dayde, M., Desprez, F., Jeannot, E., Jegou, Y., Lanteri, S., Leduc, J., Melab, N., Mornet, G., Namyst, R., Primet, P., Quetier, B., Richard, O., Talbi, E.G., Touche, I.: Grid’5000: A large scale and highly reconfigurable experimental grid testbed. International Journal of High Performance Computing Applications 20(4), 481–494 (2006)CrossRefGoogle Scholar
  3. 3.
    Duvaut, G., Lions, J.L.: Les inéquations en mécanique, Dunod (1972)Google Scholar
  4. 4.
    Evans, D.J., Deren, W.: An asynchronous parallel algorithm for solving a class of nonlinear simultaneous equations. Parallel Computing 17, 165–180 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Giraud, L., Spiteri, P.: Résolution parallèle de problèmes aux limites non linéaires. M2AN 25, 579–606 (1991)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Glowinski, R., Lions, J.L., Tremolieres, R.: Analyse numérique des inéquations variationnelles. Dunod, tome, vol. 1 and 2 (1976)Google Scholar
  7. 7.
    Hoffman, K.H., Zou, J.: Parallel effciency domain decomposition methods. Parallel Computing 19, 1375–1391 (1993)CrossRefGoogle Scholar
  8. 8.
    Miellou, J.: Algorithmes de relaxation chaotique à retards. RAIRO Analyse numérique R1, 55–82 (1975)MathSciNetGoogle Scholar
  9. 9.
    Miellou, J., El Baz, D., Spiteri, P.: A new class of asynchronous iterative algorithms with order interval. Mathematics of Computation 67-221, 237–255 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Miellou, J., Spiteri, P.: Un critère de convergence pour des méthodes générales de point fixe. M2AN 19, 645–669 (1985)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, LondonGoogle Scholar
  12. 12.
    Collignon, T.P., Van Gijzen, M.B.: Solving Large Sparse Linear Systems Efficiently on Grid Computers Using an Asynchronous Iterative Method as a Preconditioner. In: Kreiss, G., Lötstedt, P., Målqvist, A., Neytcheva, M. (eds.) The 8th European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2009), pp. 261–268. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Spiteri, P., Miellou, J.C., El Baz, D.: Parallel asynchronous Schwarz and multisplitting methods for a non linear diffusion problem. Numerical Algorithm 33, 461–474 (2003)zbMATHCrossRefGoogle Scholar
  14. 14.
    El Baz, D., Frommer, A., Spiteri, P.: Asynchronous iterations with flexible communication : contracting operators. Journal of Computational and Applied Mathematics 176, 91–103 (2005)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ming Chau
    • 1
  • Thierry Garcia
    • 2
  • Abdelhamid Laouar
    • 3
  • Pierre Spiteri
    • 2
  1. 1.Advanced Solutions AcceleratorCastelnau Le LezFrance
  2. 2.IRIT-ENSEEIHTToulouseFrance
  3. 3.Faculté des Sciences, Département de MathématiquesUniversité d’Annaba, Laboratoire LANOSAnnabaAlgérie

Personalised recommendations