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- Publisher Website: 10.1016/j.jcp.2016.07.031
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Article: A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation
Title | A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation |
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Authors | |
Keywords | Multigrid method Block lower triangular Toeplitz matrix Block ϵ-circulant approximation Fractional sub-diffusion equations |
Issue Date | 2016 |
Citation | Journal of Computational Physics, 2016, v. 323, p. 204-218 How to Cite? |
Abstract | © 2016 Elsevier Inc. 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. |
Persistent Identifier | http://hdl.handle.net/10722/276764 |
ISSN | 2023 Impact Factor: 3.8 2023 SCImago Journal Rankings: 1.679 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Lin, Xue lei | - |
dc.contributor.author | Lu, Xin | - |
dc.contributor.author | Ng, Micheal K. | - |
dc.contributor.author | Sun, Hai Wei | - |
dc.date.accessioned | 2019-09-18T08:34:35Z | - |
dc.date.available | 2019-09-18T08:34:35Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Journal of Computational Physics, 2016, v. 323, p. 204-218 | - |
dc.identifier.issn | 0021-9991 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276764 | - |
dc.description.abstract | © 2016 Elsevier Inc. 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. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Computational Physics | - |
dc.subject | Multigrid method | - |
dc.subject | Block lower triangular Toeplitz matrix | - |
dc.subject | Block ϵ-circulant approximation | - |
dc.subject | Fractional sub-diffusion equations | - |
dc.title | A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.jcp.2016.07.031 | - |
dc.identifier.scopus | eid_2-s2.0-84982732808 | - |
dc.identifier.volume | 323 | - |
dc.identifier.spage | 204 | - |
dc.identifier.epage | 218 | - |
dc.identifier.eissn | 1090-2716 | - |
dc.identifier.isi | WOS:000381585500011 | - |
dc.identifier.issnl | 0021-9991 | - |