ON PRECONDITIONED ITERATIVE METHODS FOR CERTAIN TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS

doi:10.1137/080718176

	ON PRECONDITIONED ITERATIVE METHODS FOR CERTAIN TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS
	Bai, Zhong-Zhi1 ; Huang, Yu-Mei 2; Ng, Michael K.3
	2009
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	47 期号:2 页码:1019-1037
摘要	When the Newton method or the fixed-point 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.
关键词	time-dependent partial differential equation sinc-Galerkin discretization Toeplitz- like matrix preconditioning eigenvalue bound GMRES method
DOI	10.1137/080718176
语种	英语
资助项目	The National Basic Research Program[2005CB321702] ; The National Outstanding Young Scientist Foundation[10525102]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000265778900011
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8158
专题	计算数学与科学工程计算研究所
通讯作者	Bai, Zhong-Zhi
作者单位	1.Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Lanzhou Univ, Sch Informat Sci & Engn, Lanzhou 730000, Peoples R China 3.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Huang, Yu-Mei,Ng, Michael K.. ON PRECONDITIONED ITERATIVE METHODS FOR CERTAIN TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2009,47(2):1019-1037.
APA	Bai, Zhong-Zhi,Huang, Yu-Mei,&Ng, Michael K..(2009).ON PRECONDITIONED ITERATIVE METHODS FOR CERTAIN TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS.SIAM JOURNAL ON NUMERICAL ANALYSIS,47(2),1019-1037.
MLA	Bai, Zhong-Zhi,et al."ON PRECONDITIONED ITERATIVE METHODS FOR CERTAIN TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS".SIAM JOURNAL ON NUMERICAL ANALYSIS 47.2(2009):1019-1037.