Efficient stochastic Galerkin methods for random diffusion equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Xiu, Dongbin¹  Shen, Jie¹ 

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

关键词: Generalized polynomial chaos;    Stochastic Galerkin;    Random diffusion;    Uncertainty quantification;   

DOI  :  10.1016/j.jcp.2008.09.008

来源: Elsevier

【 摘 要 】

We discuss in this paper efficient solvers for stochastic diffusion equations in random media. We employ generalized polynomial chaos (gPC) expansion to express the solution in a convergent series and obtain a set of deterministic equations for the expansion coefficients by Galerkin projection. Although the resulting system of diffusion equations are coupled, we show that one can construct fast numerical methods to solve them in a decoupled fashion. The methods are based on separation of the diagonal terms and off-diagonal terms in the matrix of the Galerkin system. We examine properties of this matrix and show that the proposed method is unconditionally stable for unsteady problems and convergent for steady problems with a convergent rate independent of discretization parameters. Numerical examples are provided, for both steady and unsteady random diffusions, to support the analysis. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free