期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 231, 期 2, 页码 693-703出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2011.10.005
关键词
Fractional diffusion equation; Toeplitz matrices; Fast Fourier transform; Multigrid method; Damped-Jacobi method
资金
- University of Macau [MYRG140(Y1-L2)-FST11-SHW]
The fractional diffusion equation is discretized by the implicit finite difference scheme with the shifted Grunwald formula. The scheme is unconditionally stable and the coefficient matrix possesses the Toeplitz-like structure. A multigrid method is proposed to solve the resulting system. Meanwhile, the fast Toeplitz matrix-vector multiplication is utilized to lower the computational cost with only O(N log N) complexity, where N is the number of the grid points. Numerical experiments are given to demonstrate the efficiency of the method. (C) 2011 Elsevier Inc. All rights reserved.
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