Parareal

Introduced in 2001 by Lions, Maday and Turinici and one of the most widely studied time-parallel methods [1]. See also the corresponding entry on Wikipedia.

1. LionsEtAl2001

   J.-L. Lions, Y. Maday, and G. Turinici, “A ‘parareal’ in time discretization of PDE’s,” Comptes Rendus de l’Académie des Sciences - Series I - Mathematics, vol. 332, pp. 661–668, 2001, doi: 10.1016/S0764-4442(00)01793-6. [Online]. Available at: http://dx.doi.org/10.1016/S0764-4442(00)01793-6

   BibTeX

   Abstract

   BibTeX entry LionsEtAl2001

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   @article{LionsEtAl2001,
     author = {Lions, J.-L. and Maday, Yvon and Turinici, Gabriel},
     doi = {10.1016/S0764-4442(00)01793-6},
     journal = {Comptes Rendus de l'Académie des Sciences - Series I - Mathematics},
     pages = {661--668},
     title = {{A "parareal" in time discretization of {PDE}'s}},
     url = {http://dx.doi.org/10.1016/S0764-4442(00)01793-6},
     volume = {332},
     year = {2001}
   }
   

   Abstract for BibTeX entry LionsEtAl2001

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   The purpose of this Note is to propose a time discretization of a partial differential evolution equation that allows for parallel implementations. The method, based on an Euler scheme, combines coarse resolutions and independent fine resolutions in time in the same spirit as standard spacial approximations. The resulting parallel implementation is done in the non standard time direction. Its main goal concerns real time problems, hence the proposed terminology of “parareal” algorithm.