Stability of the Parareal Algorithm
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.
KeywordsDomain Decomposition Stability Function Real Eigenvalue Complex Eigenvalue Implicit Euler Method
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- L. Baffico, S. Bernard, Y. Maday, G. Turinici, and G. Zérah. Parallel in time molecular dynamics simulations. Physical Review. E, 66, 2002.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- E. Hairer, S.N. rsett, and G. Wanner. Solving Ordinary Equations I, volume 8 of Springer Series in Computational Mathematics. Springer, 2. edition, 2000.Google Scholar
- E. Hairer and G. Wanner. Solving Ordinary Equations II, volume 14 of Springer Series in Computational Mathematics. Springer, 2. edition, 2002.Google Scholar