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- Publisher Website: 10.1016/j.jcp.2015.09.042
- Scopus: eid_2-s2.0-85000716656
- WOS: WOS:000364886900013
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Article: A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations
Title | A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations |
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Authors | |
Keywords | Block triangular Toeplitz-like matrix Direct methods Divide-and-conquer strategy Fractional partial differential equations Fast Fourier transform |
Issue Date | 2015 |
Citation | Journal of Computational Physics, 2015, v. 303, p. 203-211 How to Cite? |
Abstract | © 2015 Elsevier Inc. In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O(MNlog2M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method. |
Persistent Identifier | http://hdl.handle.net/10722/277044 |
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 | Ke, Rihuan | - |
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Sun, Hai Wei | - |
dc.date.accessioned | 2019-09-18T08:35:26Z | - |
dc.date.available | 2019-09-18T08:35:26Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Journal of Computational Physics, 2015, v. 303, p. 203-211 | - |
dc.identifier.issn | 0021-9991 | - |
dc.identifier.uri | http://hdl.handle.net/10722/277044 | - |
dc.description.abstract | © 2015 Elsevier Inc. In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O(MNlog2M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Computational Physics | - |
dc.subject | Block triangular Toeplitz-like matrix | - |
dc.subject | Direct methods | - |
dc.subject | Divide-and-conquer strategy | - |
dc.subject | Fractional partial differential equations | - |
dc.subject | Fast Fourier transform | - |
dc.title | A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.jcp.2015.09.042 | - |
dc.identifier.scopus | eid_2-s2.0-85000716656 | - |
dc.identifier.volume | 303 | - |
dc.identifier.spage | 203 | - |
dc.identifier.epage | 211 | - |
dc.identifier.eissn | 1090-2716 | - |
dc.identifier.isi | WOS:000364886900013 | - |
dc.identifier.issnl | 0021-9991 | - |