Fast preconditioned iterative methods for finite volume discretization of steady-state space-fractional diffusion equations

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• 作者：Jianyu Pan ; Michael Ng ; Hong Wang
• 关键词：Iterative methods ; Preconditioning ; Space ; fractional diffusion equations ; Finite volume methods
• 刊名：Numerical Algorithms
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：74
• 期：1
• 页码：153-173
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Numeric Computing; Algorithms; Algebra; Theory of Computation; Numerical Analysis;
• 出版者：Springer US
• ISSN：1572-9265
• 卷排序：74

文摘

We consider the preconditioned Krylov subspace method for linear systems arising from the finite volume discretization method of steady-state variable-coefficient conservative space-fractional diffusion equations. We propose to use a scaled-circulant preconditioner to deal with such Toeplitz-like discretization matrices. We show that the difference between the scaled-circulant preconditioner and the coefficient matrix is equal to the sum of a small-norm matrix and a low-rank matrix. Numerical tests are conducted to show the effectiveness of the proposed method for one- and two-dimensional steady-state space-fractional diffusion equations and demonstrate that the preconditioned Krylov subspace method converges very quickly.