Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis

JOURNAL OF COMPUTATIONAL PHYSICS

卷:371

Article

Bhaduri, Anindya¹  He, Yanyan²  Shields, Michael D.¹  Graham-Brady, Lori¹  Kirby, Robert M.³ 

[1] Johns Hopkins Univ, Dept Civil Engn, Baltimore, MD 21218 USA

[2] New Mexico Inst Min & Technol, Dept Math, Socorro, NM 87801 USA

[3] Univ Utah, Sch Comp, Salt Lake City, UT USA

关键词: Generalized polynomial chaos;    Stochastic collocation;    Adaptive mesh refinement;    Interaction check;   

DOI  :  10.1016/j.jcp.2018.06.003

来源: Elsevier

【 摘 要 】

The presence of a high-dimensional stochastic input domain with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic collocation method with adaptive mesh refinement (SCAMR) to deal with high dimensional stochastic systems with discontinuities. Specifically, the proposed approach uses generalized polynomial chaos (gPC) expansion with Legendre polynomial basis and solves for the gPC coefficients using the least squares method. It also implements an adaptive mesh (element) refinement strategy which checks for abrupt variations in the output based on a low-order gPC approximation error to track discontinuities or non-smoothness. In addition, the proposed method involves a criterion for checking possible dimensionality reduction and consequently, the decomposition of the original high-dimensional problem to a number of lower-dimensional subproblems. Specifically, this criterion checks all the existing interactions between input parameters of a specific problem based on the high-dimensional model representation (HDMR) method, and therefore automatically provides the subproblems which only involve interacting input parameters. The efficiency of the approach is demonstrated using examples of both smooth and non-smooth problems with number of input parameters up to 500, and the approach is compared against other existing algorithms. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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