A Convergent Algorithm for Time Parallelization Applied to Reservoir Simulation

  • Izaskun Garrido
  • Magne S. Espedal
  • Gunnar E. Fladmark
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)


Parallel methods are not usually applied to the time domain because the sequential nature of time is considered to be a handicap for the development of competitive algorithms. However, this sequential nature can also play to our advantage by ensuring convergence within a given number of iterations. The novel parallel algorithm presented in this paper acts as a predictor corrector improving both speed and accuracy with respect to the sequential solvers. Experiments using our in house fluid flow simulator in porous media, Athena, show that our parallel implementation exhibit an optimal speed up relative to the method.


Domain Decomposition Newton Iteration Sequential Nature Wall Clock Time Initial Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. L. Baffico, S. Bernard, Y. Maday, G. Turinici, and G. Zérah. Parallel in time molecular dynamics simulations. Phys. Rev. E., 66, 2002.Google Scholar
  2. G. Bal and Y. Maday. A parareal time discretization for non-linear pde's with application to the pricing of an american put. In Proceedings of a Workshop on Domain Decomposition, LNCSE. Springer Verlag Zurich, 2002.Google Scholar
  3. P. E. Bjørstad, M. Dryja, and T. Rahman. Additive schwarz methods for elliptic mortar finite element problems. Submitted to Numerische Mathematik, 2002.\(\tilde p\)etter/reports/ Scholar
  4. S. C. Brenner and L.-Y. Sung. Lower bounds for non-overlapping domain decomposition preconditioners in two dimensions. Math. Comput., 69(232):1319–1339, 2000.MathSciNetCrossRefGoogle Scholar
  5. W. L. Briggs, V. E. Henson, and S. F. McCormick. A Multigrid Tutorial. SIAM, 1990.Google Scholar
  6. X.-C. Cai, D. E. Keyes, and L. Marcinkowski. Non-linear additive schwarz preconditioners and application in computational fluid dynamics. Int. J. Numer. Meth. Fluids, pages 1463–1470, 2002.Google Scholar
  7. G. E. Fladmark. Secondary oil migration. mathematical and numerical modeling in som simulator. Technical Report R-077857, Norsk Hydro, Bergen, 1997.Google Scholar
  8. I. Garrido, E. Øian, M. Chaib, G. E. Fladmark, and M. S. Espedal. Implicit treatment of compositional flow. Computational Geosciences, 2003. To appear.Google Scholar
  9. D. E. Keyes. Domain decomposition in the mainstream of computational science. In Proceedings of the 14 international conference on Domain Decomposition Methods, 2002.Google Scholar
  10. Z. Lan, V. E. Taylor, and G. Bryan. A novel dynamic load balancing scheme for parallel systems. J. Parallel Distrib. Comput., 62(12):1763–1781, 2002.CrossRefGoogle Scholar
  11. J.-L. Lions, Y. Maday, and G. Turinici. Rèsolution d'edp par un schéma en temps pararéel. C. R. Acad. Sci. Paris, 332(1):1–6, 2001.MathSciNetGoogle Scholar
  12. G. Å. Øye and H. Reme. Parallelization of a compositional simulator with a galerkin coarse/fine method. In P. Amestoy et al., editors, Euro-Par'99, volume 1685. Springer-Verlag, Berlin, 1999.Google Scholar
  13. J. Xu and L. Zikatanov. The method of alternating projections and the method of subspace corrections in Hilbert space. J. of AMS, 15, 2002. Technical report, PennState, November 2000a.Google Scholar
  14. J. Xu and L. Zikatanov. Some observations on Babuska and Brezzi theories. Num. Math., 94, 2003. Technical report, PennState, September 2000b.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Izaskun Garrido
    • 1
  • Magne S. Espedal
    • 1
  • Gunnar E. Fladmark
    • 1
  1. 1.LIM/CIPRUniversity of BergenBergen

Personalised recommendations