NUMERICAL APPROXIMATION OF ELLIPTIC PROBLEMS WITH LOG-NORMAL RANDOM COEFFICIENTS
文献类型：期刊论文
| 作者 | Wan, Xiaoliang4; Yu, Haijun1,2,3 |
| 刊名 | INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION
 |
| 出版日期 | 2019 |
| 卷号 | 9期号:2页码:161-186 |
| 关键词 | Wiener chaos expansion Wick product stochastic elliptic PDE uncertainty quantification log-normal random coefficient |
| ISSN号 | 2152-5080 |
| DOI | 10.1615/Int.J.UncertaintyQuantification.2019029046 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000473286900005 |
| 出版者 | BEGELL HOUSE INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/35097]  |
| 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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 3.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS, Beijing 100190, Peoples R China 4.Louisiana State Univ, Ctr Computat & Technol, Dept Math, Baton Rouge, LA 70803 USA |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。