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- Publisher Website: 10.1016/j.jcp.2017.02.008
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Article: A multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations
Title | A multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations |
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Authors | |
Keywords | Multigrid method Non-rectangular domain Fractional diffusion equation Banded-splitting smoother |
Issue Date | 2017 |
Citation | Journal of Computational Physics, 2017, v. 336, p. 69-86 How to Cite? |
Abstract | © 2017 Elsevier Inc. In this paper, we study a V-cycle multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations. The coefficient matrices of the linear systems are structured such that their matrix-vector multiplications can be computed efficiently. The main advantage using the multigrid method is to handle the space-fractional diffusion equations on non-rectangular domains, and to solve the linear systems with non-constant coefficients more effectively. The main idea of the proposed multigrid method is to employ two banded splitting iteration schemes as pre-smoother and post-smoother. The pre-smoother and the post-smoother take banded splitting of the coefficient matrix under the x-dominant ordering and the y-dominant ordering, respectively. We prove the convergence of the proposed two banded splitting iteration schemes in the sense of infinity norm. Results of numerical experiments for time-dependent two-dimensional space-fractional diffusion equations on rectangular, L-shape and U-shape domains are reported to demonstrate that both computational time and iteration number required by the proposed method are significantly smaller than those of the other tested methods. |
Persistent Identifier | http://hdl.handle.net/10722/277061 |
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 | Ng, Michael K. | - |
dc.contributor.author | Sun, Hai Wei | - |
dc.date.accessioned | 2019-09-18T08:35:29Z | - |
dc.date.available | 2019-09-18T08:35:29Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Journal of Computational Physics, 2017, v. 336, p. 69-86 | - |
dc.identifier.issn | 0021-9991 | - |
dc.identifier.uri | http://hdl.handle.net/10722/277061 | - |
dc.description.abstract | © 2017 Elsevier Inc. In this paper, we study a V-cycle multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations. The coefficient matrices of the linear systems are structured such that their matrix-vector multiplications can be computed efficiently. The main advantage using the multigrid method is to handle the space-fractional diffusion equations on non-rectangular domains, and to solve the linear systems with non-constant coefficients more effectively. The main idea of the proposed multigrid method is to employ two banded splitting iteration schemes as pre-smoother and post-smoother. The pre-smoother and the post-smoother take banded splitting of the coefficient matrix under the x-dominant ordering and the y-dominant ordering, respectively. We prove the convergence of the proposed two banded splitting iteration schemes in the sense of infinity norm. Results of numerical experiments for time-dependent two-dimensional space-fractional diffusion equations on rectangular, L-shape and U-shape domains are reported to demonstrate that both computational time and iteration number required by the proposed method are significantly smaller than those of the other tested methods. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Computational Physics | - |
dc.subject | Multigrid method | - |
dc.subject | Non-rectangular domain | - |
dc.subject | Fractional diffusion equation | - |
dc.subject | Banded-splitting smoother | - |
dc.title | A multigrid method for linear systems arising from time-dependent two-dimensional space-fractional diffusion equations | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.jcp.2017.02.008 | - |
dc.identifier.scopus | eid_2-s2.0-85012239953 | - |
dc.identifier.volume | 336 | - |
dc.identifier.spage | 69 | - |
dc.identifier.epage | 86 | - |
dc.identifier.eissn | 1090-2716 | - |
dc.identifier.isi | WOS:000397362800004 | - |
dc.identifier.issnl | 0021-9991 | - |