期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 78, 期 3, 页码 1724-1743出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-018-0835-2
关键词
Space-time fractional partial differential equation; Parareal method; Fast finite difference method; Bi-CGSTAB
资金
- OSD/ARO MURI Grant [W911NF-15-1-0562]
- National Science Foundation [DMS-1216923, DMS-1620194]
- National Natural Science Foundation of China [11571367, 91130010, 11471194, 11571115]
- Shandong Provincial Natural Science Foundation [ZR2017MA006]
- Fundamental Research Funds for the Central Universities [18CX02044A]
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.
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