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A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation
Lin,Xue lei1; Lu,Xin1; Ng,Micheal K.2; Sun,Hai Wei1
2016-12-09
Source PublicationJournal of Computational Physics
ISSN10902716 00219991
Volume323Pages:204-218
Abstract

A fast accurate approximation method with multigrid solver is proposed to solve a two-dimensional fractional sub-diffusion equation. Using the finite difference discretization of fractional time derivative, a block lower triangular Toeplitz matrix is obtained where each main diagonal block contains a two-dimensional matrix for the Laplacian operator. Our idea is to make use of the block ϵ-circulant approximation via fast Fourier transforms, so that the resulting task is to solve a block diagonal system, where each diagonal block matrix is the sum of a complex scalar times the identity matrix and a Laplacian matrix. We show that the accuracy of the approximation scheme is of O(ϵ). Because of the special diagonal block structure, we employ the multigrid method to solve the resulting linear systems. The convergence of the multigrid method is studied. Numerical examples are presented to illustrate the accuracy of the proposed approximation scheme and the efficiency of the proposed solver.

KeywordBlock Lower Triangular Toeplitz Matrix Block Ε-circulant Approximation Fractional Sub-diffusion Equations Multigrid Method
DOI10.1016/j.jcp.2016.07.031
URLView the original
Indexed BySCI
Language英语
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000381585500011
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被引频次[WOS]:4   [WOS记录]     [WOS相关记录]
Document TypeJournal article
专题Faculty of Science and Technology
Personal research not belonging to the institution
Affiliation1.Department of MathematicsUniversity of Macau,Macao
2.Department of MathematicsHong Kong Baptist University,Hong Kong
First Author AffilicationUniversity of Macau
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Lin,Xue lei,Lu,Xin,Ng,Micheal K.,et al. A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation[J]. Journal of Computational Physics,2016,323:204-218.
APA Lin,Xue lei,Lu,Xin,Ng,Micheal K.,&Sun,Hai Wei.(2016).A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation.Journal of Computational Physics,323,204-218.
MLA Lin,Xue lei,et al."A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation".Journal of Computational Physics 323(2016):204-218.
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