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- Publisher Website: 10.1016/j.camwa.2016.11.023
- Scopus: eid_2-s2.0-85009250133
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Article: A divide-and-conquer fast finite difference method for space–time fractional partial differential equation
Title | A divide-and-conquer fast finite difference method for space–time fractional partial differential equation |
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Authors | |
Keywords | Anomalous diffusion Space–time fractional partial differential equation Krylov subspace iterative solver Finite difference method Divide-and-conquer method |
Issue Date | 2017 |
Citation | Computers and Mathematics with Applications, 2017, v. 73, n. 6, p. 1233-1242 How to Cite? |
Abstract | © 2016 Elsevier Ltd Fractional partial differential equations (FPDEs) provide better modeling capabilities for challenging phenomena with long-range time memory and spatial interaction than integer-order PDEs do. A conventional numerical discretization of space–time FPDEs requires O(N2+MN) memory and O(MN3+M2N) computational work, where N is the number of spatial freedoms per time step and M is the number of time steps. We develop a fast finite difference method (FDM) for space–time FPDE: (i) We utilize the Toeplitz-like structure of the coefficient matrix to develop a matrix-free preconditioned fast Krylov subspace iterative solver to invert the coefficient matrix at each time step. (ii) We utilize a divide-and-conquer strategy, a recursive direct solver, to handle the temporal coupling of the numerical scheme. The fast method has an optimal memory requirement of O(MN) and an approximately linear computational complexity of O(NM(logN+log2M)), without resorting to any lossy compression. Numerical experiments show the utility of the method. |
Persistent Identifier | http://hdl.handle.net/10722/277053 |
ISSN | 2023 Impact Factor: 2.9 2023 SCImago Journal Rankings: 0.949 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Fu, Hongfei | - |
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Wang, Hong | - |
dc.date.accessioned | 2019-09-18T08:35:28Z | - |
dc.date.available | 2019-09-18T08:35:28Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Computers and Mathematics with Applications, 2017, v. 73, n. 6, p. 1233-1242 | - |
dc.identifier.issn | 0898-1221 | - |
dc.identifier.uri | http://hdl.handle.net/10722/277053 | - |
dc.description.abstract | © 2016 Elsevier Ltd Fractional partial differential equations (FPDEs) provide better modeling capabilities for challenging phenomena with long-range time memory and spatial interaction than integer-order PDEs do. A conventional numerical discretization of space–time FPDEs requires O(N2+MN) memory and O(MN3+M2N) computational work, where N is the number of spatial freedoms per time step and M is the number of time steps. We develop a fast finite difference method (FDM) for space–time FPDE: (i) We utilize the Toeplitz-like structure of the coefficient matrix to develop a matrix-free preconditioned fast Krylov subspace iterative solver to invert the coefficient matrix at each time step. (ii) We utilize a divide-and-conquer strategy, a recursive direct solver, to handle the temporal coupling of the numerical scheme. The fast method has an optimal memory requirement of O(MN) and an approximately linear computational complexity of O(NM(logN+log2M)), without resorting to any lossy compression. Numerical experiments show the utility of the method. | - |
dc.language | eng | - |
dc.relation.ispartof | Computers and Mathematics with Applications | - |
dc.subject | Anomalous diffusion | - |
dc.subject | Space–time fractional partial differential equation | - |
dc.subject | Krylov subspace iterative solver | - |
dc.subject | Finite difference method | - |
dc.subject | Divide-and-conquer method | - |
dc.title | A divide-and-conquer fast finite difference method for space–time fractional partial differential equation | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.camwa.2016.11.023 | - |
dc.identifier.scopus | eid_2-s2.0-85009250133 | - |
dc.identifier.volume | 73 | - |
dc.identifier.issue | 6 | - |
dc.identifier.spage | 1233 | - |
dc.identifier.epage | 1242 | - |
dc.identifier.isi | WOS:000398875300028 | - |
dc.identifier.issnl | 0898-1221 | - |