A preconditioned fast finite volume scheme for a fractional differential equation discretized on a locally refined composite mesh

JOURNAL OF COMPUTATIONAL PHYSICS

卷:299

Article

Jia, Jinhong¹  Wang, Hong² 

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

[2] Univ S Carolina, Dept Math, Columbia, SC 29208 USA

关键词: Circulant matrix;    Fast solution method;    Finite volume method;    Fractional differential equation;    Locally refined mesh;    Toeplitz matrix;   

DOI  :  10.1016/j.jcp.2015.06.028

来源: Elsevier

【 摘 要 】

Numerical methods for fractional differential equations generate full stiffness matrices, which were traditionally solved via Gaussian type direct solvers that require O(N-3) of computational work and O(N-2) of memory to store where N is the number of spatial grid points in the discretization. We develop a preconditioned fast Krylov subspace iterative method for the efficient and faithful solution of finite volume schemes defined on a locally refined composite mesh for fractional differential equations to resolve boundary layers of the solutions. Numerical results are presented to show the utility of the method. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free