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Article: A separable preconditioner for time-space fractional Caputo-Riesz diffusion equations
Title | A separable preconditioner for time-space fractional Caputo-Riesz diffusion equations |
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Authors | |
Keywords | Diagonalization Block lower triangular Time-space fractional diffusion equations Separable Block ε-circulant preconditioner Toeplitz-like matrix |
Issue Date | 2018 |
Citation | Numerical Mathematics, 2018, v. 11, n. 4, p. 827-853 How to Cite? |
Abstract | © 2018 Global-Science Press. In this paper, we study linear systems arising from time-space fractional Caputo-Riesz diffusion equations with time-dependent diffusion coefficients. The coefficient matrix is a summation of a block-lower-triangular-Toeplitz matrix (temporal component) and a block-diagonal-with-diagonal-times-Toeplitz-block matrix (spatial component). The main aim of this paper is to propose separable preconditioners for solving these linear systems, where a block ε-circulant preconditioner is used for the temporal component, while a block diagonal approximation is used for the spatial variable. The resulting preconditioner can be block-diagonalized in the temporal domain. Furthermore, the fast solvers can be employed to solve smaller linear systems in the spatial domain. Theoretically, we show that if the diffusion coefficient (temporal-dependent or spatial-dependent only) function is smooth enough, the singular values of the preconditioned matrix are bounded independent of discretization parameters. Numerical examples are tested to show the performance of proposed preconditioner. |
Persistent Identifier | http://hdl.handle.net/10722/276632 |
ISSN | 2023 Impact Factor: 1.9 2023 SCImago Journal Rankings: 0.670 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Lin, Xuelei | - |
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Sun, Haiwei | - |
dc.date.accessioned | 2019-09-18T08:34:11Z | - |
dc.date.available | 2019-09-18T08:34:11Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Numerical Mathematics, 2018, v. 11, n. 4, p. 827-853 | - |
dc.identifier.issn | 1004-8979 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276632 | - |
dc.description.abstract | © 2018 Global-Science Press. In this paper, we study linear systems arising from time-space fractional Caputo-Riesz diffusion equations with time-dependent diffusion coefficients. The coefficient matrix is a summation of a block-lower-triangular-Toeplitz matrix (temporal component) and a block-diagonal-with-diagonal-times-Toeplitz-block matrix (spatial component). The main aim of this paper is to propose separable preconditioners for solving these linear systems, where a block ε-circulant preconditioner is used for the temporal component, while a block diagonal approximation is used for the spatial variable. The resulting preconditioner can be block-diagonalized in the temporal domain. Furthermore, the fast solvers can be employed to solve smaller linear systems in the spatial domain. Theoretically, we show that if the diffusion coefficient (temporal-dependent or spatial-dependent only) function is smooth enough, the singular values of the preconditioned matrix are bounded independent of discretization parameters. Numerical examples are tested to show the performance of proposed preconditioner. | - |
dc.language | eng | - |
dc.relation.ispartof | Numerical Mathematics | - |
dc.subject | Diagonalization | - |
dc.subject | Block lower triangular | - |
dc.subject | Time-space fractional diffusion equations | - |
dc.subject | Separable | - |
dc.subject | Block ε-circulant preconditioner | - |
dc.subject | Toeplitz-like matrix | - |
dc.title | A separable preconditioner for time-space fractional Caputo-Riesz diffusion equations | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.4208/nmtma.2018.s09 | - |
dc.identifier.scopus | eid_2-s2.0-85061877683 | - |
dc.identifier.volume | 11 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 827 | - |
dc.identifier.epage | 853 | - |
dc.identifier.eissn | 2079-7338 | - |
dc.identifier.isi | WOS:000438884900010 | - |
dc.identifier.issnl | 1004-8979 | - |