Circulant-based approximate inverse preconditioners for a class of fractional diffusion equations
| Autor: | Hai-Wei Sun, Hai-Hua Qin, Hong-Kui Pang, Ting-Ting Ma |
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| Rok vydání: | 2021 |
| Předmět: |
Preconditioner
Linear system Spectrum (functional analysis) Inverse 010103 numerical & computational mathematics 01 natural sciences Fractional calculus 010101 applied mathematics Computational Mathematics Matrix (mathematics) Computational Theory and Mathematics Modeling and Simulation Applied mathematics 0101 mathematics Coefficient matrix Circulant matrix Mathematics |
| Zdroj: | Computers & Mathematics with Applications. 85:18-29 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2021.01.007 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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