A parareal method for time-fractional differential equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:293

Article

Xu, Qinwu^1,2  Hesthaven, Jan S.³  Chen, Feng⁴ 

[1] Peking Univ, Sch Math Sci, Beijing, Peoples R China

[2] Cent South Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China

[3] Ecole Polytech Fed Lausanne, Math Sect MATHICSE, CH-1015 Lausanne, Switzerland

[4] CUNY Bernard M Baruch Coll, Dept Math, New York, NY 10010 USA

关键词: Fractional calculus;    Time-fractional;    Parareal;    Parallel-in-time;    Multi-domain spectral;   

DOI  :  10.1016/j.jcp.2014.11.034

来源: Elsevier

【 摘 要 】

In this paper, a parareal method is proposed for the parallel-in-time integration of time-fractional differential equations (TFDEs). It is a generalization of the original parareal method, proposed for classic differential equations. To match the global feature of fractional derivatives, the new method has in the correction step embraced the history part of the solution. We provide a convergence analysis under the assumption of Lipschitz stability conditions. We use a multi-domain spectral integrator to build the serial solvers and numerical results demonstrate the feasibility of the new approach and confirm the convergence analysis. Studies also show that both the coarse resolution and the nature of the differential operators can affect the performance. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free