A multilevel finite element method for Fredholm integral eigenvalue problems

doi:10.1016/j.jcp.2015.09.043

	A multilevel finite element method for Fredholm integral eigenvalue problems
	Xie, Hehu1 ; Zhou, Tao2
	2015-12-15
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	303 页码:173-184
摘要	In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loeve expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method. (C) 2015 Elsevier Inc. All rights reserved.
关键词	Uncertainty quantification Karhunen-Loeve expansion Fredholm eigenvalue problem Multigrid finite element
DOI	10.1016/j.jcp.2015.09.043
语种	英语
资助项目	National Science Foundation of China[NSFC 91330202] ; National Science Foundation of China[11371026] ; National Science Foundation of China[11001259] ; National Science Foundation of China[11201501] ; National Science Foundation of China[2011CB309703] ; National Science Foundation of China[91130003] ; National Science Foundation of China[11201461] ; National Center for Mathematics and Interdisciplinary Science (CAS) ; President Foundation of AMSS-CAS
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000364886900011
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21299
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Tao
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC,NCMIS, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Xie, Hehu,Zhou, Tao. A multilevel finite element method for Fredholm integral eigenvalue problems[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2015,303:173-184.
APA	Xie, Hehu,&Zhou, Tao.(2015).A multilevel finite element method for Fredholm integral eigenvalue problems.JOURNAL OF COMPUTATIONAL PHYSICS,303,173-184.
MLA	Xie, Hehu,et al."A multilevel finite element method for Fredholm integral eigenvalue problems".JOURNAL OF COMPUTATIONAL PHYSICS 303(2015):173-184.