頁籤選單縮合
題 名 | A Model Reduction Method for Elliptic PDEs with Random Input Using the Heterogeneous Stochastic FEM Framework |
---|---|
作 者 | Hou, Thomas Y.; Liu, Pengfei; Zhang, Zhiwen; | 書刊名 | Bulletin of the Institute of Mathematics, Academia Sinica New Series |
卷 期 | 11:1 2016.03[民105.03] |
頁 次 | 頁179-216 |
分類號 | 314.223 |
關鍵詞 | Model reduction; Local stochastic basis; Hilbert-Karhunen-Loève expansion; |
語 文 | 英文(English) |
英文摘要 | We introduce a model reduction method for elliptic PDEs with random input, which follows the heterogeneous stochastic finite element method framework and exploits the compactness of the solution operator in the stochastic direction on local regions of the spatial domain. This method consists of two stages and suits the multi-query setting. In the offline stage, we adaptively construct local stochastic basis functions that can capture the stochastic structure of the solution space in local regions of the domain. This is achieved through local Hilbert-Karhunen-Lo`eve expansions of sampled stochastic solutions with randomly chosen forcing functions. In the online stage, for given forcing functions, we discretize the equation using the heterogeneous coupling of spatial basis with the constructed local stochastic basis, and obtain the numerical solutions through Galerkin projection. Convergence of the online numerical solutions is proved based on the thresholding in the offline stage. Numerical results are presented to demonstrate the effectiveness of this model reduction method. |
本系統中英文摘要資訊取自各篇刊載內容。