Multigrid method for fractional diffusion equations

Authors:
Hong-Kui Pang;Hai-Wei Sun
Affiliations:
School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, 221116 Jiangsu, China;Department of Mathematics, University of Macau, Macao, China
Venue:
Journal of Computational Physics
Year:
2012

Citing 19
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Abstract

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(NlogN) complexity, where N is the number of the grid points. Numerical experiments are given to demonstrate the efficiency of the method.