Parareal algorithms with local time-integrators for time-fractional differential equations

被引:30
|
作者
Wu, Shu-Lin [1 ]
Zhou, Tao [2 ]
机构
[1] Sichuan Univ Sci & Engn, Sch Sci, Zigong, Sichuan, Peoples R China
[2] Chinese Acad Sci, AMSS, Inst Computat Math & Sci Engn Comp, LSEC, Beijing, Peoples R China
关键词
Parareal; Time-fractional differential equations; Local time-integrators; DIFFUSION-EQUATIONS; CONVERGENCE ANALYSIS; PERIODIC PROBLEMS; PARALLEL; APPROXIMATIONS; SIMULATIONS; SYSTEMS;
D O I
10.1016/j.jcp.2017.12.029
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
It is challenge work to design parareal algorithms for time-fractional differential equations due to the historical effect of the fractional operator. A direct extension of the classical parareal methodto such equations will lead to unbalance computational time in each process. In this work, we present an efficient parareal iteration scheme to overcome this issue, by adopting two recently developed local time-integrators for time fractional operators. In both approaches, one introduces auxiliary variables to localized the fractional operator. To this end, we propose a new strategy to perform the coarse grid correction so that the auxiliary variables and the solution variable are corrected separately in a mixed pattern. It is shown that the proposed parareal algorithm admits robust rate of convergence. Numerical examples are presented to support our conclusions. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码:135 / 149
页数:15
相关论文
共 50 条
  • [1] A parareal method for time-fractional differential equations
    Xu, Qinwu
    Hesthaven, Jan S.
    Chen, Feng
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 : 173 - 183
  • [2] Exponential integrators for time-fractional partial differential equations
    Garrappa, R.
    [J]. EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2013, 222 (08): : 1915 - 1927
  • [3] On a class of time-fractional differential equations
    Cheng-Gang Li
    Marko Kostić
    Miao Li
    Sergey Piskarev
    [J]. Fractional Calculus and Applied Analysis, 2012, 15 : 639 - 668
  • [4] On a class of time-fractional differential equations
    Li, Cheng-Gang
    Kostic, Marko
    Li, Miao
    Piskarev, Sergey
    [J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2012, 15 (04) : 639 - 668
  • [5] Exact solutions to the time-fractional differential equations via local fractional derivatives
    Guner, Ozkan
    Bekir, Ahmet
    [J]. WAVES IN RANDOM AND COMPLEX MEDIA, 2018, 28 (01) : 139 - 149
  • [6] Exponential integrators for time–fractional partial differential equations
    R. Garrappa
    [J]. The European Physical Journal Special Topics, 2013, 222 : 1915 - 1927
  • [7] On the Stability of Time-Fractional Schrodinger Differential Equations
    Hicdurmaz, B.
    Ashyralyev, A.
    [J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2017, 38 (10) : 1215 - 1225
  • [8] Local symmetry structure and potential symmetries of time-fractional partial differential equations
    Zhang, Zhi-Yong
    Lin, Zhi-Xiang
    [J]. STUDIES IN APPLIED MATHEMATICS, 2021, 147 (01) : 363 - 389
  • [9] Advances in fractional differential equations (IV): Time-fractional PDEs
    Zhou, Yong
    Feckan, Michal
    Liu, Fawang
    Tenreiro Machado, J. A.
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (06) : 873 - 873
  • [10] A Parareal Finite Volume Method for Variable-Order Time-Fractional Diffusion Equations
    Liu, Huan
    Cheng, Aijie
    Wang, Hong
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2020, 85 (01)