Circulant-based approximate inverse preconditioners for a class of fractional diffusion equations. (1st March 2021)

• Record Type: Journal Article
• Authors: Pang, Hong-Kui; Qin, Hai-Hua; Sun, Hai-Wei; Ma, Ting-Ting
• Is Part Of: Computers & mathematics with applications. Volume 85(2021)
• Page Start: 18
• Page End: 29
• Publication Date: 2021-03-01
• Subjects: Fractional diffusion equation -- Finite difference method -- Toeplitz-like -- Circulant-based preconditioner -- Decay property; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.01.007
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We consider fast solving a class of spatial fractional diffusion equations where the fractional differential operators are comprised of Riemann–Liouville and Caputo fractional derivatives. A circulant-based approximate inverse preconditioner is established for the discrete linear systems resulted from the finite difference discretization of this kind of fractional diffusion equations. By sufficiently exploring the Toeplitz-like structure and the rapid decay properties of the internal sub-matrices in the coefficient matrix, we show that the spectrum of the preconditioned matrix is clustered around one. Numerical experiments are performed to demonstrate the effectiveness of the proposed preconditioner.