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NUMERICAL APPROXIMATION OF ELLIPTIC PROBLEMS WITH LOG-NORMAL RANDOM COEFFICIENTS
Wan, Xiaoliang1; Yu, Haijun2,3,4
2019
Source PublicationINTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION
ISSN2152-5080
Volume9Issue:2Pages:161-186
AbstractIn 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.
KeywordWiener chaos expansion Wick product stochastic elliptic PDE uncertainty quantification log-normal random coefficient
DOI10.1615/Int.J.UncertaintyQuantification.2019029046
Language英语
Funding ProjectNSF[DMS-1620026] ; China National Program on Key Basic Research Project[2015CB856003] ; NNSFC[11771439] ; China Science Challenge Project[TZ2018001]
WOS Research AreaEngineering ; Mathematics
WOS SubjectEngineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000473286900005
PublisherBEGELL HOUSE INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35098
Collection中国科学院数学与系统科学研究院
Corresponding AuthorYu, Haijun
Affiliation1.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
Recommended Citation
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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.
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