NUMERICAL APPROXIMATION OF ELLIPTIC PROBLEMS WITH LOG-NORMAL RANDOM COEFFICIENTS

doi:10.1615/Int.J.UncertaintyQuantification.2019029046

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	NUMERICAL APPROXIMATION OF ELLIPTIC PROBLEMS WITH LOG-NORMAL RANDOM COEFFICIENTS
	Wan, Xiaoliang 1; Yu, Haijun 2,3,4
	2019
发表期刊	INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION
ISSN	2152-5080
卷号	9 期号:2 页码:161-186
摘要	In this work, we consider a non-standard preconditioning strategy for the numerical approximation of the classical elliptic equations with log-normal random coefficients. In earlier work, a Wick-type elliptic model was proposed by modeling the random flux through the Wick product. Due to the lower-triangular structure of the uncertainty propagator, this model can be approximated efficiently using the Wiener chaos expansion in the probability space. Such a Wick-type model provides, in general, a second-order approximation of the classical one in terms of the standard deviation of the underlying Gaussian process. Furthermore, when the correlation length of the underlying Gaussian process goes to infinity, the Wick-type model yields the same solution as the classical one. These observations imply that the Wick-type elliptic equation can provide an effective preconditioner for the classical random elliptic equation under appropriate conditions. We use the Wick-type elliptic model to accelerate the Monte Carlo method and the stochastic Galerkin finite element method. Numerical results are presented and discussed.
关键词	Wiener chaos expansion Wick product stochastic elliptic PDE uncertainty quantification log-normal random coefficient
DOI	10.1615/Int.J.UncertaintyQuantification.2019029046
语种	英语
资助项目	NSF[DMS-1620026] ; China National Program on Key Basic Research Project[2015CB856003] ; NNSFC[11771439] ; China Science Challenge Project[TZ2018001]
WOS研究方向	Engineering ; Mathematics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000473286900005
出版者	BEGELL HOUSE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35098
专题	中国科学院数学与系统科学研究院
通讯作者	Yu, Haijun
作者单位	1.Louisiana State Univ, Ctr Computat & Technol, Dept Math, Baton Rouge, LA 70803 USA 2.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS, Beijing 100190, Peoples R China 3.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Wan, Xiaoliang,Yu, Haijun. NUMERICAL APPROXIMATION OF ELLIPTIC PROBLEMS WITH LOG-NORMAL RANDOM COEFFICIENTS[J]. INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION,2019,9(2):161-186.
APA	Wan, Xiaoliang,&Yu, Haijun.(2019).NUMERICAL APPROXIMATION OF ELLIPTIC PROBLEMS WITH LOG-NORMAL RANDOM COEFFICIENTS.INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION,9(2),161-186.
MLA	Wan, Xiaoliang,et al."NUMERICAL APPROXIMATION OF ELLIPTIC PROBLEMS WITH LOG-NORMAL RANDOM COEFFICIENTS".INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION 9.2(2019):161-186.