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Article: On preconditioned iterative methods for certain time-dependent partial differential equations
Title | On preconditioned iterative methods for certain time-dependent partial differential equations |
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Authors | |
Keywords | GMRES method Time-dependent partial differential equation Sinc-Galerkin discretization Preconditioning Eigenvalue bound Toeplitzlike matrix |
Issue Date | 2009 |
Citation | SIAM Journal on Numerical Analysis, 2009, v. 47, n. 2, p. 1019-1037 How to Cite? |
Abstract | When the Newton method or the fixed-poin t method is employed to solve the systems of nonlinear equations arising in the sinc-Galerkin discretization of certain time-dependent partial differential equations, in each iteration step we need to solve a structured subsystem of linear equations iteratively by, for example, a Krylov subspace method such as the preconditioned GMRES. In this paper, based on the tensor and the Toeplitz structures of the linear subsystems we construct structured preconditioners for their coefficient matrices and estimate the eigenvalue bounds of the preconditioned matrices under certain assumptions. Numerical examples are given to illustrate the effectiveness of the proposed preconditioning methods. It has been shown that a combination of the Newton/fixed-point iteration with the preconditioned GMRES method is efficient and robust for solving the systems of nonlinear equations arising from the sinc-Galerkin discretization of the time-dependent partial differential equations. © 2009 Society for Industrial and Applied Mathematics. |
Persistent Identifier | http://hdl.handle.net/10722/276895 |
ISSN | 2023 Impact Factor: 2.8 2023 SCImago Journal Rankings: 2.163 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bah, Zhong Zhi | - |
dc.contributor.author | Huang, Yu Mei | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:58Z | - |
dc.date.available | 2019-09-18T08:34:58Z | - |
dc.date.issued | 2009 | - |
dc.identifier.citation | SIAM Journal on Numerical Analysis, 2009, v. 47, n. 2, p. 1019-1037 | - |
dc.identifier.issn | 0036-1429 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276895 | - |
dc.description.abstract | When the Newton method or the fixed-poin t method is employed to solve the systems of nonlinear equations arising in the sinc-Galerkin discretization of certain time-dependent partial differential equations, in each iteration step we need to solve a structured subsystem of linear equations iteratively by, for example, a Krylov subspace method such as the preconditioned GMRES. In this paper, based on the tensor and the Toeplitz structures of the linear subsystems we construct structured preconditioners for their coefficient matrices and estimate the eigenvalue bounds of the preconditioned matrices under certain assumptions. Numerical examples are given to illustrate the effectiveness of the proposed preconditioning methods. It has been shown that a combination of the Newton/fixed-point iteration with the preconditioned GMRES method is efficient and robust for solving the systems of nonlinear equations arising from the sinc-Galerkin discretization of the time-dependent partial differential equations. © 2009 Society for Industrial and Applied Mathematics. | - |
dc.language | eng | - |
dc.relation.ispartof | SIAM Journal on Numerical Analysis | - |
dc.subject | GMRES method | - |
dc.subject | Time-dependent partial differential equation | - |
dc.subject | Sinc-Galerkin discretization | - |
dc.subject | Preconditioning | - |
dc.subject | Eigenvalue bound | - |
dc.subject | Toeplitzlike matrix | - |
dc.title | On preconditioned iterative methods for certain time-dependent partial differential equations | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/080718176 | - |
dc.identifier.scopus | eid_2-s2.0-79954499023 | - |
dc.identifier.volume | 47 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 1019 | - |
dc.identifier.epage | 1037 | - |
dc.identifier.isi | WOS:000265778900011 | - |
dc.identifier.issnl | 0036-1429 | - |