Original Articles: A parareal algorithm based on waveform relaxation
作者： Jun Liu , Yao-Lin Jiang
DOI: 10.1016/J.MATCOM.2012.05.017
关键词: Relaxation (iterative method) 、 Waveform 、 Parareal 、 Algorithm 、 Iterative method 、 Speedup 、 Parareal algorithm 、 Computer science 、 Differential equation
摘要: We report a new parallel iterative algorithm for time-dependent differential equations by combining the known waveform relaxation (WR) technique with classical parareal algorithm. The parallelism can be simultaneously exploited in both sub-systems WR and time parareal. also provide sharp estimation on errors iterations of are balanced to optimize performance Furthermore, speedup efficiency approach analyzed comparing technique, respectively. Numerical experiments carried out verify effectiveness theoretic work.
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sci-hub.se 参考文章(22)
David Guibert, Damien Tromeur-Dervout, Adaptive Parareal for Systems of ODEs Lecture Notes in Computational Science and Engineering. pp. 587- 594 ,(2007) , 10.1007/978-3-540-34469-8_73
Paul F. Fischer, Frédéric Hecht, Yvon Maday, A Parareal in Time Semi-implicit Approximation of the Navier-Stokes Equations Springer, Berlin, Heidelberg. pp. 433- 440 ,(2005) , 10.1007/3-540-26825-1_44
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
Guillaume Bal, Yvon Maday, A “Parareal” Time Discretization for Non-Linear PDE’s with Application to the Pricing of an American Put Springer, Berlin, Heidelberg. pp. 189- 202 ,(2002) , 10.1007/978-3-642-56118-4_12
Yvon Maday, Gabriel Turinici, The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation Springer, Berlin, Heidelberg. pp. 441- 448 ,(2005) , 10.1007/3-540-26825-1_45
Guillaume Bal, On the Convergence and the Stability of the Parareal Algorithm to Solve Partial Differential Equations Springer, Berlin, Heidelberg. pp. 425- 432 ,(2005) , 10.1007/3-540-26825-1_43
Michael L. Minion, Sarah A. Williams, Parareal and Spectral Deferred Corrections Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics 2008. ,vol. 1048, pp. 388- 391 ,(2008) , 10.1063/1.2990941
Yao-Lin Jiang, On Time-Domain Simulation of Lossless Transmission Lines with Nonlinear Terminations SIAM Journal on Numerical Analysis. ,vol. 42, pp. 1018- 1031 ,(2004) , 10.1137/S0036142902418886
Jun Liu, Yao-Lin Jiang, Waveform relaxation for reaction–diffusion equations Journal of Computational and Applied Mathematics. ,vol. 235, pp. 5040- 5055 ,(2011) , 10.1016/J.CAM.2011.04.035
Yvon Maday, Julien Salomon, Gabriel Turinici, Monotonic Parareal Control for Quantum Systems SIAM Journal on Numerical Analysis. ,vol. 45, pp. 2468- 2482 ,(2007) , 10.1137/050647086