Skip to main content

C(p, q, j) Scheme with Adaptive time step and Asynchronous Communications

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 67))

Abstract

We address the challenge of speeding-up the solving of ODE/DAE/EDP nonlinear systems in term of elapsed time with using parallel computer. As modern time integrators use adaptive time steps to pass the stiffness of the solution, we propose to extend the C(p, q, j) introduced in Garbey and all. (J. Comput. Phys. Vol. 161 No. 2 401-427 ) in order to use adaptive time step between the coupled subsytems of equations and to perform asynchronous communications to send the data needed for extrapolation. The details of implementation will be given as well as numerical and efficiency performances.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G.D. Byrne and A.C. Hindmarsh, A Polyalgorithms for the numerical Solution of Ordinary Differential Equations, ACM Transactions on Mathematical software, V. 1 No. 1 71–96 (1975).

    Article  MathSciNet  Google Scholar 

  2. M. Garbey and D. Tromeur-Dervout, A parallel adaptive coupling algorithm for systems of differential equations, J. Comput. Phys., V. 161 No. 2 401 427 (2000)

    Article  MathSciNet  Google Scholar 

  3. S. Skelboe, Accuracy of Decoupled Implicit Integration Formulae, SIAM J. Sci. Comput., V. 21 2206 2224 (2000)

    Article  MathSciNet  Google Scholar 

  4. S. Skelboe and J. Sand, Stability of Backward Euler Multirate Methods and Convergence of Waveform Relaxation, BIT, V. 32 350 366 (1992)

    Google Scholar 

  5. S. Skelboe, Methods for Parallel Integration of Stiff Systems of ODEs, BIT, V.32 689 701 (1992)

    Article  MathSciNet  Google Scholar 

  6. E. Hairer and G. Wanner, Solving Ordinary Differential equations II - Stiff and DAE problems, Springer No. 14 (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

PHAM, T., OUDIN-DARDUN, F. (2009). C(p, q, j) Scheme with Adaptive time step and Asynchronous Communications. In: Parallel Computational Fluid Dynamics 2007. Lecture Notes in Computational Science and Engineering, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92744-0_41

Download citation

Publish with us

Policies and ethics