Summary
We discuss the stability of the Parareal algorithm for an autonomous set of differential equations. The stability function for the algorithm is derived, and stability conditions for the case of real eigenvalues are given. The general case of complex eigenvalues has been investigated by computing the stability regions numerically.
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References
L. Baffico, S. Bernard, Y. Maday, G. Turinici, and G. Zérah. Parallel in time molecular dynamics simulations. Physical Review. E, 66, 2002.
G. Bal and Y. Maday. A “parareal” time discretization for non-linear pde's with application to the pricing of an american put. In L. F. Pavarino and A. Toselli, editors, Recent Developments in domain Decomposition Methods, volume 23 of Lecture Notes in Computational Science and Engineering, pages 189–202. Springer, 2002.
C. Farhat and M. Chandesris. Time-decomposed parallel time-integrators: theory and feasibility studies for fluid, structure, and fluid-structure applications. to appear in International Journal for Numerical Methods in Engineering, 2003.
E. Hairer, S.N. rsett, and G. Wanner. Solving Ordinary Equations I, volume 8 of Springer Series in Computational Mathematics. Springer, 2. edition, 2000.
E. Hairer and G. Wanner. Solving Ordinary Equations II, volume 14 of Springer Series in Computational Mathematics. Springer, 2. edition, 2002.
J.-L. Lions, Y. Maday, and G. Turinici. Résolution d'edp par un schéma en temps pararéel. C.R.Acad Sci. Paris Sér. I Math, 332:661–668, 2001.
Y. Maday and G. Turinici. A parareal in time procedure for the control of partial differential equations. C.R.Acad Sci. Paris Sér. I Math, 335:387–392, 2002.
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Staff, G.A., Rønquist, E.M. (2005). Stability of the Parareal Algorithm. In: Barth, T.J., et al. Domain Decomposition Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26825-1_46
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DOI: https://doi.org/10.1007/3-540-26825-1_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22523-2
Online ISBN: 978-3-540-26825-3
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