FAST EIGENPAIRS COMPUTATION WITH OPERATOR ADAPTED WAVELETS AND HIERARCHICAL SUBSPACE CORRECTION

doi:10.1137/18M1194079

CSpace

	FAST EIGENPAIRS COMPUTATION WITH OPERATOR ADAPTED WAVELETS AND HIERARCHICAL SUBSPACE CORRECTION
	Xie, Hehu 1,2; Zhang, Lei 3,4; Owhadi, Houman 5
	2019
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	57 期号:6 页码:2519-2550
摘要	We present a method for the fast computation of the eigenpairs of a bijective positive symmetric linear operator L. The method is based on a combination of operator adapted wavelets (gamblets) with hierarchical subspace correction. First, gamblets provide a raw but fast approximation of the eigensubspaces of L by block-diagonalizing L into sparse and well-conditioned blocks. Next, the hierarchical subspace correction method computes the eigenpairs associated with the Galerkin restriction of L to a coarse (low-dimensional) gamblet subspace and then corrects those eigenpairs by solving a hierarchy of linear problems in the finer gamblet subspaces (from coarse to fine, using multigrid iteration). The proposed algorithm is robust to the presence of multiple (a continuum of) scales and is shown to be of near-linear complexity when L is an (arbitrary local, e.g., differential) operator mapping H-0(s)(Omega) to H-s(Omega) (e.g., an elliptic PDE with rough coefficients).
关键词	multiscale eigenvalue problem gamblet decomposition multigrid iteration subspace correction numerical homogenization
DOI	10.1137/18M1194079
收录类别	SCI
语种	英语
资助项目	Science Challenge project[TZ2016002] ; National Natural Science Foundation of China[11871339] ; National Natural Science Foundation of China[11861131004] ; National Natural Science Foundation of China[11571314] ; National Natural Science Foundation of China[11771434] ; National Natural Science Foundation of China[91330202] ; National Center for Mathematics and Interdisciplinary Science, CAS ; Air Force Office of Scientific Research (AFOSR) DARPA EQUiPS program[FA9550-16-1-0054] ; Air Force Office of Scientific Research[FA9550-18-1-0271] ; Office of Naval Research[N00014-18-1-2363]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000546984300002
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/51769
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Lei
作者单位	1.Chinese Acad Sci, LSEC, Acad Math & Syst Sci, 55 Zhongguancun Donglu, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Shanghai Jiao Tong Univ, Sch Math Sci, Inst Nat Sci, Shanghai 200240, Peoples R China 4.Shanghai Jiao Tong Univ, Minist Educ, Key Lab Sci & Engn Comp, Shanghai 200240, Peoples R China 5.CALTECH, Comp & Math Sci, Pasadena, CA 91125 USA
推荐引用方式 GB/T 7714	Xie, Hehu,Zhang, Lei,Owhadi, Houman. FAST EIGENPAIRS COMPUTATION WITH OPERATOR ADAPTED WAVELETS AND HIERARCHICAL SUBSPACE CORRECTION[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2019,57(6):2519-2550.
APA	Xie, Hehu,Zhang, Lei,&Owhadi, Houman.(2019).FAST EIGENPAIRS COMPUTATION WITH OPERATOR ADAPTED WAVELETS AND HIERARCHICAL SUBSPACE CORRECTION.SIAM JOURNAL ON NUMERICAL ANALYSIS,57(6),2519-2550.
MLA	Xie, Hehu,et al."FAST EIGENPAIRS COMPUTATION WITH OPERATOR ADAPTED WAVELETS AND HIERARCHICAL SUBSPACE CORRECTION".SIAM JOURNAL ON NUMERICAL ANALYSIS 57.6(2019):2519-2550.