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- Publisher Website: 10.1007/s11075-018-0623-y
- Scopus: eid_2-s2.0-85055992234
- WOS: WOS:000485980200016
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Article: Circulant preconditioners for a kind of spatial fractional diffusion equations
Title | Circulant preconditioners for a kind of spatial fractional diffusion equations |
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Authors | |
Keywords | Fractional diffusion equation Krylov subspace methods Fast Fourier transform Circulant preconditioner Toeplitz matrix |
Issue Date | 2019 |
Citation | Numerical Algorithms, 2019, v. 82 n. 2, p. 729-747 How to Cite? |
Abstract | © 2018, Springer Science+Business Media, LLC, part of Springer Nature. In this paper, circulant preconditioners are studied for discretized matrices arising from finite difference schemes for a kind of spatial fractional diffusion equations. The fractional differential operator is comprised of left-sided and right-sided derivatives with order in (12,1). The resulting discretized matrices preserve Toeplitz-like structure and hence their matrix-vector multiplications can be computed efficiently by the fast Fourier transform. Theoretically, the spectra of the circulant preconditioned matrices are shown to be clustered around 1 under some conditions. Numerical experiments are presented to demonstrate that the preconditioning technique is very efficient. |
Persistent Identifier | http://hdl.handle.net/10722/276614 |
ISSN | 2023 Impact Factor: 1.7 2023 SCImago Journal Rankings: 0.829 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Fang, Zhi Wei | - |
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Sun, Hai Wei | - |
dc.date.accessioned | 2019-09-18T08:34:08Z | - |
dc.date.available | 2019-09-18T08:34:08Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | Numerical Algorithms, 2019, v. 82 n. 2, p. 729-747 | - |
dc.identifier.issn | 1017-1398 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276614 | - |
dc.description.abstract | © 2018, Springer Science+Business Media, LLC, part of Springer Nature. In this paper, circulant preconditioners are studied for discretized matrices arising from finite difference schemes for a kind of spatial fractional diffusion equations. The fractional differential operator is comprised of left-sided and right-sided derivatives with order in (12,1). The resulting discretized matrices preserve Toeplitz-like structure and hence their matrix-vector multiplications can be computed efficiently by the fast Fourier transform. Theoretically, the spectra of the circulant preconditioned matrices are shown to be clustered around 1 under some conditions. Numerical experiments are presented to demonstrate that the preconditioning technique is very efficient. | - |
dc.language | eng | - |
dc.relation.ispartof | Numerical Algorithms | - |
dc.subject | Fractional diffusion equation | - |
dc.subject | Krylov subspace methods | - |
dc.subject | Fast Fourier transform | - |
dc.subject | Circulant preconditioner | - |
dc.subject | Toeplitz matrix | - |
dc.title | Circulant preconditioners for a kind of spatial fractional diffusion equations | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s11075-018-0623-y | - |
dc.identifier.scopus | eid_2-s2.0-85055992234 | - |
dc.identifier.volume | 82 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 729 | - |
dc.identifier.epage | 747 | - |
dc.identifier.eissn | 1572-9265 | - |
dc.identifier.isi | WOS:000485980200016 | - |
dc.identifier.issnl | 1017-1398 | - |