A full multigrid method for nonlinear eigenvalue problems

doi:10.1007/s11425-015-0234-x

	A full multigrid method for nonlinear eigenvalue problems
	Jia, ShangHui 1; Xie, HeHu2 ; Xie, ManTing 2; Xu, Fei 2
	2016-10-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	59 期号:10 页码:2037-2048
摘要	We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal, the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method.
关键词	nonlinear eigenvalue problem full multigrid method multilevel correction finite element method
DOI	10.1007/s11425-015-0234-x
语种	英语
资助项目	National Natural Science Foundation of China[91330202] ; National Natural Science Foundation of China[11371026] ; National Natural Science Foundation of China[11201501] ; National Natural Science Foundation of China[11571389] ; National Natural Science Foundation of China[11001259] ; National Natural Science Foundation of China[11031006] ; National Basic Research Program of China[2011CB309703] ; National Center for Mathematics and Interdisciplinary Science, Chinese Academy of Sciences ; President Foundation of Academy of Mathematics and Systems Science, Chinese Academy of Sciences ; Program for Innovation Research in Central University of Finance and Economics
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000384568000010
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23694
专题	计算数学与科学工程计算研究所
通讯作者	Xu, Fei
作者单位	1.Cent Univ Finance & Econ, Sch Math & Stat, Beijing 100081, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Jia, ShangHui,Xie, HeHu,Xie, ManTing,et al. A full multigrid method for nonlinear eigenvalue problems[J]. SCIENCE CHINA-MATHEMATICS,2016,59(10):2037-2048.
APA	Jia, ShangHui,Xie, HeHu,Xie, ManTing,&Xu, Fei.(2016).A full multigrid method for nonlinear eigenvalue problems.SCIENCE CHINA-MATHEMATICS,59(10),2037-2048.
MLA	Jia, ShangHui,et al."A full multigrid method for nonlinear eigenvalue problems".SCIENCE CHINA-MATHEMATICS 59.10(2016):2037-2048.