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Article: On preconditioned iterative methods for Burgers equations
Title | On preconditioned iterative methods for Burgers equations |
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Authors | |
Keywords | Sinc-Galerkin discretization GMRES method Toeplitz-like matrices Preconditioners Burgers equation |
Issue Date | 2007 |
Citation | SIAM Journal on Scientific Computing, 2007, v. 29, n. 1, p. 415-439 How to Cite? |
Abstract | We study the Newton method and a fixed-point method for solving the system of nonlinear equations arising from the Sinc-Galerkin discretization of the Burgers equations. In each step of the Newton method or the fixed-point method, a structured subsystem of linear equations is obtained and needs to be solved numerically. In this paper, preconditioning techniques are applied to solve such linear subsystems. The bounds for eigenvalues of the preconditioned matrices are derived and numerical examples are given to illustrate the effectiveness of the proposed methods. We also find that a combination of the Newton/fixed-point iteration with the preconditioned GMRES method is quite efficient for the Sinc-Galerkin discretization of the Burgers equations. © 2007 Society for Industrial and Applied Mathematics. |
Persistent Identifier | http://hdl.handle.net/10722/276826 |
ISSN | 2023 Impact Factor: 3.0 2023 SCImago Journal Rankings: 1.803 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bai, Zhong Zhi | - |
dc.contributor.author | Huang, Yu Mei | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:46Z | - |
dc.date.available | 2019-09-18T08:34:46Z | - |
dc.date.issued | 2007 | - |
dc.identifier.citation | SIAM Journal on Scientific Computing, 2007, v. 29, n. 1, p. 415-439 | - |
dc.identifier.issn | 1064-8275 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276826 | - |
dc.description.abstract | We study the Newton method and a fixed-point method for solving the system of nonlinear equations arising from the Sinc-Galerkin discretization of the Burgers equations. In each step of the Newton method or the fixed-point method, a structured subsystem of linear equations is obtained and needs to be solved numerically. In this paper, preconditioning techniques are applied to solve such linear subsystems. The bounds for eigenvalues of the preconditioned matrices are derived and numerical examples are given to illustrate the effectiveness of the proposed methods. We also find that a combination of the Newton/fixed-point iteration with the preconditioned GMRES method is quite efficient for the Sinc-Galerkin discretization of the Burgers equations. © 2007 Society for Industrial and Applied Mathematics. | - |
dc.language | eng | - |
dc.relation.ispartof | SIAM Journal on Scientific Computing | - |
dc.subject | Sinc-Galerkin discretization | - |
dc.subject | GMRES method | - |
dc.subject | Toeplitz-like matrices | - |
dc.subject | Preconditioners | - |
dc.subject | Burgers equation | - |
dc.title | On preconditioned iterative methods for Burgers equations | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/060649124 | - |
dc.identifier.scopus | eid_2-s2.0-39449110451 | - |
dc.identifier.volume | 29 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 415 | - |
dc.identifier.epage | 439 | - |
dc.identifier.isi | WOS:000245031900019 | - |
dc.identifier.issnl | 1064-8275 | - |