A non-adapted sparse approximation of PDEs with stochastic inputs

JOURNAL OF COMPUTATIONAL PHYSICS

卷:230

Article

Doostan, Alireza¹  Owhadi, Houman² 

[1] Univ Colorado, Dept Aerosp Engn Sci, Boulder, CO 80309 USA

[2] CALTECH, Appl & Computat Math Dept, Pasadena, CA 91125 USA

关键词: Polynomial chaos;    Uncertainty quantification;    Stochastic PDE;    Compressive sampling;    Sparse approximation;   

DOI  :  10.1016/j.jcp.2011.01.002

来源: Elsevier

【 摘 要 】

We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples. We show that the method is well suited for truly high-dimensional problems. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free