112
Views
1
CrossRef citations to date
0
Altmetric
Section B

A minimal communication approach to parallel time integration

Pages 601-615 | Received 03 Oct 2012, Accepted 22 Apr 2013, Published online: 24 May 2013

References

  • K. E. Atkinson, An Introduction to Numerical Analysis, Wiley, New York, 1989.
  • A. J. Christlieb, C. D. MacDonald, and B. W. Ong, Parallel high-order integrators, SIAM J. Sci. Comput. 2 (2010), pp. 818–835. doi: 10.1137/09075740X
  • M. Duarte, M. Massot, and S. Descombes, Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies, Math. Model. Numer. Anal. 2 (2011), pp. 825–852. doi: 10.1051/m2an/2010104
  • C. Farhat and M. Chandesris, Time-decomposed parallel time-integrators: Theory and feasibility studies for fluid, structure, and fluid–structure applications, Int. J. Numer. Methods Eng. 2 (2003), pp. 1397–1434. doi: 10.1002/nme.860
  • C. Farhat, J. Cortial, C. Dastillung, and H. Bavestrello, Time-parallel implicit integrators for the near-real-time prediction of linear structural dynamic responses, Int. J. Numer. Methods Eng. 2 (2006), pp. 697–724. doi: 10.1002/nme.1653
  • P. F. Fischer, F. Hecht, and Y. Maday, A parareal in time semi-implicit approximation of the Navier–Stokes equations, in Domain Decomposition Methods in Science and Enginnering, T. J. Barth, M. Griebel, D. E. Keyes, R. M. Nieminen, D. Roose, T. Schlick, R. Kornhuber, R. Hoppe, J. Priaux, O. Pironneau, O. Widlund, and J. Xu, eds., Lecture Notes in Computational Science and Engineering, Vol. 40, Springer, Berlin, 2005, pp. 443–440.
  • E. Gallopoulos and Y. Saad, Efficient solution of parabolic equations by Krylov approximation methods, SIAM J. Sci. Stat. Comput. 2 (1992), pp. 1236–1264. doi: 10.1137/0913071
  • M. Gander and M. Petcu, Analysis of a modified parareal algorithm for second-order ordinary differential equations, AIP Conf. Proc. 2 (2007), pp. 233–236. doi: 10.1063/1.2790116
  • M. Gander and M. Petcu, Analysis of a Krylov subspace enhanced parareal algorithm for linear problems, ESAIM Proc. 2 (2008), pp. 114–129. doi: 10.1051/proc:082508
  • M. J. Gander, Analysis of the parareal algorithm applied to hyperbolic problems using characteristics, Bol. Soc. Esp. Mat. Apl. 2 (2008), pp. 5–19.
  • M. J. Gander and S. Güttel, Paraexp: A parallel integrator for linear initial-value problems, SIAM J. Sci. Comput. 2 (2013), pp. C123–C142. doi: 10.1137/110856137
  • M. J. Gander and S. Vandewalle, Analysis of the parareal time-parallel time-integration method, SIAM J. Sci. Comput. 2 (2007), pp. 556–678. doi: 10.1137/05064607X
  • I. P. Gavrilyuk and L. Makarov, Exponentially convergent algorithms for the operator exponential with applications to inhomogeneous problems in Banach spaces, SIAM J. Numer. Anal. 2 (2005), pp. 2144–2177. doi: 10.1137/040611045
  • P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York, 1961.
  • M. Hochbruck and A. Ostermann, Exponential Runge–Kutta methods for parabolic problems, Appl. Numer. Math. 2 (2005), pp. 323–339. doi: 10.1016/j.apnum.2004.08.005
  • J. L. Lions, Y. Maday, and G. Turinici, Résolution d'EDP par un schéma en temps pararéel, C.R. Acad. Sci. Paris 3322001661–668. doi: 10.1016/S0764-4442(00)01793-6
  • Y. Liu and J. Hu, Modified propagators of parareal in time algorithm and application to Princeton Ocean model, Int. J. Numer. Methods Fluids 5720081793–1804. doi: 10.1002/fld.1703
  • Y. Maday and G. Turinici, The parareal in time iterative solver: A further direction to parallel implementation, in Domain Decomposition Methods in Science and Engineering, T. J. Barth, M. Griebel, D. E. Keyes, R. M. Nieminen, D. Roose, T. Schlick, R. Kornhuber, R. Hoppe, J. Priaux, O. Pironneau, O. Widlund, and J. Xu, eds., Lecture Notes in Computational Science and Engineering, Vol. 40, Springer, Berlin, 2005, pp. 441–448.
  • M. L. Minion, A hybrid parareal spectral deferred corrections method, Commun. Appl. Math. Comput. Sci. 2 (2010), pp. 265–301. doi: 10.2140/camcos.2010.5.265
  • J. Nievergelt, Parallel methods for integrating ordinary differential equations, Commun. ACM 71964731–733. doi: 10.1145/355588.365137
  • D. Sheen, I. H. Sloan, and V. Thomée, A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature, IMA J. Numer. Anal. 2 (2003), pp. 269–299. doi: 10.1093/imanum/23.2.269
  • L. N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, PA, 2000.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.