Variance-Based Global Sensitivity Analysis via Sparse-Grid Interpolation and Cubature

作     者：Gregery T.Buzzard Dongbin Xiu 

作者机构：Department of MathematicsPurdue UniversityWest LafayetteIN 47907USA 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2011年第9卷第3期

页      面：542-567页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

主　　题：Stochastic collocation sparse grids sensitivity analysis Smolyak Sobol’ 

摘      要：The stochastic collocation method using sparse grids has become a popular choice for performing stochastic computations in high dimensional(random)parameter *** addition to providing highly accurate stochastic solutions,the sparse grid collocation results naturally contain sensitivity information with respect to the input random *** this paper,we use the sparse grid interpolation and cubature methods of Smolyak together with combinatorial analysis to give a computationally efficient method for computing the global sensitivity values of Sobol’.This method allows for approximation of all main effect and total effect values from evaluation of f on a single set of sparse *** discuss convergence of this method,apply it to several test cases and compare to existing *** a result which may be of independent interest,we recover an explicit formula for evaluating a Lagrange basis interpolating polynomial associated with the Chebyshev *** allows one to manipulate the sparse grid collocation results in a highly efficient manner.