The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation
This paper is the basic one of the series resulting from the minisymposium entitled “Recent Advances for the Parareal in Time Algorithm” that was held at DD15. The parareal in time algorithm is presented in its current version (predictor-corrector) and the combination of this new algorithm with other more classical iterative solvers for parallelization which makes it possible to really consider the time direction as fertile ground to reduce the time integration costs.
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- Leonardo Baffico, Stephane Bernard, Yvon Maday, Gabriel Turinici, and Gilles Zérah. Parallel in time molecular dynamics simulations. Phys. Rev. E., 66, 2002.Google Scholar
- Guillaume Bal. On the convergence and the stability of the parareal algorithm to solve partial differential equations. In Fifteen International Conference on Domain Decomposition Methods, Berlin, 2003a. Springer, Lecture Notes in Computational Science and Engineering (LNCSE).Google Scholar
- Guillaume Bal. Parallelization in time of (stochastic) ordinary differential equations. Math. Meth. Anal. Num. (submitted), 2003b.Google Scholar
- Guillaume Bal and Yvon Maday. A “parareal” time discretization for nonlinear PDE's with application to the pricing of an American put. In Recent developments in domain decomposition methods (Zürich, 2001), volume 23 of Lect. Notes Comput. Sci. Eng, pages 189–202. Springer, Berlin, 2002.Google Scholar
- Jean-François Bourgat, Roland Glowinski, Patrick Le Tallec, and Marina Vidrascu. Variational formulation and algorithm for trace operator in domain decomposition calculations. In Tony Chan, Roland Glowinski, Jacques Périaux, and Olof Widlund, editors, Domain Decomposition Methods, pages 3–16, Philadelphia, PA, 1989. SIAM.Google Scholar
- Paul Fischer, Frédéric Hecht, and Yvon Maday. A parareal in time semi implicit approximation of the Navier Stokes equations. In Fifteen International Conference on Domain Decomposition Methods, Berlin, 2003. Springer, Lecture Notes in Computational Science and Engineering (LNCSE).Google Scholar
- Gunnar Andreas Staff and Einar M. Rønquist. Stability of the parareal algorithm. In Fifteen International Conference on Domain Decomposition Methods, Berlin, 2003. Springer, Lecture Notes in Computational Science and Engineering (LNCSE).Google Scholar