PRECONDITIONING TECHNIQUES IN CHEBYSHEV COLLOCATION METHOD FOR ELLIPTIC EQUATIONS

UM > Faculty of Science and Technology > DEPARTMENT OF MATHEMATICS

Status	已發表Published
	PRECONDITIONING TECHNIQUES IN CHEBYSHEV COLLOCATION METHOD FOR ELLIPTIC EQUATIONS
	Fang, Z.W.; Shen, J.; Sun, H. W.
	2018
Source Publication	International Journal of Numerical Analysis & Modeling
ISSN	1705-5105
Pages	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(ℓNxNy logNx), where Nx,Ny 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.
Keyword	Chebyshev collocation method elliptic equation finite-difference preconditioner approximate inverse
URL	View the original
Language	英語English
The Source to Article	PB_Publication
PUB ID	35303
Document Type	Journal article
Collection	DEPARTMENT OF MATHEMATICS
Corresponding Author	Sun, H. W.
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 & Modeling, 2018, 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 & Modeling, 277-287.
MLA	Fang, Z.W.,et al."PRECONDITIONING TECHNIQUES IN CHEBYSHEV COLLOCATION METHOD FOR ELLIPTIC EQUATIONS".International Journal of Numerical Analysis & Modeling (2018):277-287.

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