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Preconditioning techniques in chebyshev collocation method for elliptic equations
Fang Z.-W.1; Shen J.2; Sun H.-W.1
2018
Source PublicationInternational Journal of Numerical Analysis and Modeling
ISSN17055105
Volume15Issue:1Pages:277-287
Abstract

When one approximates elliptic equations by the spectral collocation method on the Chebyshev-Gauss-Lobatto (CGL) grid, the resulting coefficient matrix is dense and ill-conditioned. It is known that a good preconditioner, in the sense that the preconditioned system becomes well conditioned, can be constructed with finite difference on the CGL grid. However, there is a lack of an efficient solver for this preconditioner in multi-dimension. A modified preconditioner based on the approximate inverse technique is constructed in this paper. The computational cost of each iteration in solving the preconditioned system is O(ℓNN logN), where N,N are the grid sizes in each direction and ℓ is a small integer. Numerical examples are given to demonstrate the efficiency of the proposed preconditioner.

KeywordApproximate Inverse Chebyshev Collocation Method Elliptic Equation Finite-difference Preconditioner
URLView the original
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000428719500016
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Universidade de Macau
2.Purdue University
Recommended Citation
GB/T 7714
Fang Z.-W.,Shen J.,Sun H.-W.. Preconditioning techniques in chebyshev collocation method for elliptic equations[J]. International Journal of Numerical Analysis and Modeling,2018,15(1):277-287.
APA Fang Z.-W.,Shen J.,&Sun H.-W..(2018).Preconditioning techniques in chebyshev collocation method for elliptic equations.International Journal of Numerical Analysis and Modeling,15(1),277-287.
MLA Fang Z.-W.,et al."Preconditioning techniques in chebyshev collocation method for elliptic equations".International Journal of Numerical Analysis and Modeling 15.1(2018):277-287.
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