Journal of Scientific Computing

, Volume 78, Issue 3, pp 1724–1743 | Cite as

A Preconditioned Fast Parareal Finite Difference Method for Space-Time Fractional Partial Differential Equation

  • Hongfei Fu
  • Hong WangEmail author


We develop a fast parareal finite difference method for space-time fractional partial differential equation. The method properly handles the heavy tail behavior in the numerical discretization, while retaining the numerical advantages of conventional parareal algorithm. At each time step, we explore the structure of the stiffness matrix to develop a matrix-free preconditioned fast Krylov subspace iterative solver for the finite difference method without resorting to any lossy compression. Consequently, the method has significantly reduced computational complexity and memory requirement. Numerical experiments show the strong potential of the method.


Space-time fractional partial differential equation Parareal method Fast finite difference method Bi-CGSTAB 

Mathematics Subject Classification

35R11 65F08 65F10 65M06 65M12 65T50 



The authors would like to express their sincere thanks to the referees for their very helpful comments and suggestions, which greatly improved the quality of this paper.


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Authors and Affiliations

  1. 1.College of ScienceChina University of PetroleumQingdaoChina
  2. 2.Department of MathematicsUniversity of South CarolinaColumbiaUSA

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