Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Croce, R; Ruprecht, D; Krause, R (2014)
Publisher: Springer International Publishing
Languages: English
Types: Preprint
Subjects: Computer Science - Computational Engineering, Finance, and Science, Mathematics - Numerical Analysis
In this paper we combine the Parareal parallel-in-time method together with spatial parallelization and investigate this space-time parallel scheme by means of solving the three-dimensional incompressible Navier-Stokes equations. Parallelization of time stepping provides a new direction of parallelization and allows to employ additional cores to further speed up simulations after spatial parallelization has saturated. We report on numerical experiments performed on a Cray XE6, simulating a driven cavity flow with and without obstacles. Distributed memory parallelization is used in both space and time, featuring up to 2,048 cores in total. It is confirmed that the space-time-parallel method can provide speedup beyond the saturation of the spatial parallelization.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 1. Chorin, A.J.: Numerical solution of the NavierStokes equations. Math. Comput. 22(104), 745-762 (1968)
    • 2. Croce, R., Engel, M., Griebel, M., Klitz, M.: NaSt3DGP - a Parallel 3D Flow Solver. URL http://wissrech.ins.uni-bonn.de/research/projects/NaSt3DGP/index.htm
    • 3. Emmett, M., Minion, M.L.: Toward an efficient parallel in time method for partial differential equations. Comm. App. Math. and Comp. Sci. 7, 105-132 (2012)
    • 4. Farhat, C., Chandesris, M.: Time-decomposed parallel time-integrators: Theory and feasibility studies for fluid, structure, and fluid-structure applications. Int. J. Numer. Methods Engrg. 58, 1397-1434 (2005)
    • 5. Fischer, P.F., Hecht, F., Maday, Y.: A parareal in time semi-implicit approximation of the Navier-Stokes equations. In: R. Kornhuber, et al. (eds.) Domain Decomposition Methods in Science and Engineering, Lecture Notes in Computational Science and Engineering, vol. 40, pp. 433-440. Springer, Berlin (2005)
    • 6. Gander, M.J., Vandewalle, S.: Analysis of the parareal time-parallel time-integration method. SIAM J. Sci. Comp. 29(2), 556-578 (2007)
    • 7. Gaskell, P., Lau, A.: Curvature-compensated convective transport: SMART a new boundedness-preserving transport algorithm. Int. J. Numer. Methods Fuids 8, 617-641 (1988)
    • 8. Griebel, M., Dornseifer, T., Neunhoeffer, T.: Numerical Simulation in Fluid Dynamics, a Practical Introduction. SIAM, Philadelphia (1998)
    • 9. Leonard, B.: A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19, 59-98 (1979)
    • 10. Lions, J.L., Maday, Y., Turinici, G.: A ”parareal” in time discretization of PDE's. C. R. Acad. Sci. - Ser. I - Math. 332, 661-668 (2001)
    • 11. Minion, M.L.: A hybrid parareal spectral deferred corrections method. Comm. App. Math. and Comp. Sci. 5(2), 265-301 (2010)
    • 12. Ruprecht, D., Krause, R.: Explicit parallel-in-time integration of a linear acoustic-advection system. Computers & Fluids 59, 72-83 (2012)
    • 13. Temam, R.: Sur l'approximation de la solution des equations de Navier-Stokes par la methode des pas fractionnaires II. Arch. Rational Mech. Anal. 33, 377385 (1969)
    • 14. Trindade, J.M.F., Pereira, J.C.F.: Parallel-in-time simulation of the unsteady Navier-Stokes equations for incompressible flow. Int J. Numer. Meth. Fluids 45, 1123-1136 (2004)
    • 15. Trindade, J.M.F., Pereira, J.C.F.: Parallel-in-time simulation of two-dimensional, unsteady, incompressible laminar flows. Num. Heat Trans., Part B 50, 25-40 (2006)
    • 16. van der Vorst, H.: BiCGStab: A fast and smoothly converging variant of BiCG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13, 631 (1992)
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article