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Sine transform based preconditioners for solving constant-coefficient first-order PDEs
Jin X.-Q.1; Lei S.-L.2
2003-06-01
Source PublicationLinear Algebra and Its Applications
ISSN00243795
Volume366Issue:SPEC. ISS.Pages:283-294
Abstract

In this paper, we study nonsymmetric and highly nondiagonally dominant linear systems that arise from discretizations of constant-coefficient first-order partial differential equations (PDEs). We apply the generalized minimal residual method [Y. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston] for solving the system with a preconditioner based on the fast sine transform. An analytic formula for the eigenvalues of the preconditioned matrix is derived and it is shown that the eigenvalues are clustered around 1 except some outliers. The outlier eigenvalues are bounded and well separated from the origin when the size of system increases. In numerical experiments, we compare our preconditioner with the semi-Toeplitz preconditioner proposed in [SIAM J. Sci. Comput. 17 (1996) 47]. We refer to [J. Numer. Linear Algebra Appl. 1 (1992) 77, Numer. Math. J. Chinese Univ. 2 (1993) 116, BIT 32 (1992) 650, Linear Algebra Appl. 293 (1999) 85] for the early works on preconditioning techniques for PDEs.

KeywordClustered Spectrum Constant-coefficient First-order Pdes Gmres Method Preconditioner Sine Transform
DOIhttps://doi.org/10.1016/S0024-3795(02)00467-6
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000182667200016
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Cited Times [WOS]:0   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Personal research not belonging to the institution
Corresponding AuthorJin X.-Q.
Affiliation1.Faculty of Science and Technology, University of Macau, Macau
2.Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong
First Author AffilicationFaculty of Science and Technology
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Jin X.-Q.,Lei S.-L.. Sine transform based preconditioners for solving constant-coefficient first-order PDEs[J]. Linear Algebra and Its Applications,2003,366(SPEC. ISS.):283-294.
APA Jin X.-Q.,&Lei S.-L..(2003).Sine transform based preconditioners for solving constant-coefficient first-order PDEs.Linear Algebra and Its Applications,366(SPEC. ISS.),283-294.
MLA Jin X.-Q.,et al."Sine transform based preconditioners for solving constant-coefficient first-order PDEs".Linear Algebra and Its Applications 366.SPEC. ISS.(2003):283-294.
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