期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 194, 期 12-16, 页码 1295-1331出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2004.05.027
关键词
linear and nonlinear elliptic stochastic partial differential equations; Galerkin methods; Karhunen-Loeve expansion; Wiener's polynomial chaos; white noise analysis; sparse Smolyak quadrature; Monte Carlo methods; stochastic finite elements
Stationary systems modelled by elliptic partial differential equations-linear as well as nonlinear-with stochastic coefficients (random fields) are considered. The mathematical setting as a variational problem, existence theorems, and possible discretisations-in particular with respect to the stochastic part-are given and investigated with regard to stability. Different and increasingly sophisticated computational approaches involving both Wiener's polynomial chaos as well as the Karhunen-Loeve expansion are addressed in conjunction with stochastic Galerkin procedures, and stability within the Galerkin framework is established. New and effective algorithms to compute the mean and covariance of the solution are proposed. The similarities and differences with better known Monte Carlo methods are exhibited, as well as alternatives to integration in high-dimensional spaces. Hints are given regarding the numerical implementation and parallelisation. Numerical examples serve as illustration. (C) 2004 Elsevier B.V. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据