A time-parallel algorithm for almost integrable Hamiltonian systems

作者: Jacques Laskar , Hugo Jiménez-Pérez

DOI:

关键词:

摘要: We introduce a time-parallel algorithm for solving numerically almost integrable Hamiltonian systems in action-angle coordinates. This is refinement of that introduced by Saha, Stadel and Tremaine 1997 (SST97) the same type problems. Our refined has better convergence obtained from use derivatives perturbing term not considered original SST97 algorithm. An advantage this its independence step-size parallelized procedures which can be consider as particular case parareal scheme.

参考文章(16)
Martin J. Gander, Stefan Vandewalle, On the Superlinear and Linear Convergence of the Parareal Algorithm Lecture Notes in Computational Science and Engineering. pp. 291- 298 ,(2007) , 10.1007/978-3-540-34469-8_34
Martin J. Gander, Ernst Hairer, Nonlinear Convergence Analysis for the Parareal Algorithm Lecture Notes in Computational Science and Engineering. pp. 45- 56 ,(2008) , 10.1007/978-3-540-75199-1_4
Toshio Fukushima, Parallel/Vector Integration Methods for Dynamical Astronomy Celestial Mechanics and Dynamical Astronomy. ,vol. 73, pp. 231- 241 ,(1999) , 10.1007/978-94-011-4527-5_23
Robert I. McLachlan, Composition methods in the presence of small parameters Bit Numerical Mathematics. ,vol. 35, pp. 258- 268 ,(1995) , 10.1007/BF01737165
Robert I. McLachlan, On the numerical integration of ordinary differential equations by symmetric composition methods SIAM Journal on Scientific Computing. ,vol. 16, pp. 151- 168 ,(1995) , 10.1137/0916010
Willard L. Miranker, Werner Liniger, Parallel methods for the numerical integration of ordinary differential equations Mathematics of Computation. ,vol. 21, pp. 303- 320 ,(1967) , 10.1090/S0025-5718-1967-0223106-8
E. Lelarasmee, A.E. Ruehli, A.L. Sangiovanni-Vincentelli, The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. ,vol. 1, pp. 131- 145 ,(1982) , 10.1109/TCAD.1982.1270004
Toshio Fukushima, Vector Integration of Dynamical Motions by the Picard-Chebyshev Method The Astronomical Journal. ,vol. 113, pp. 2325- ,(1997) , 10.1086/118443