Variance-Based Global Sensitivity Analysis via Sparse-Grid Interpolation and Cubature
差异为基础通过稀疏网格插值和Cubature全局灵敏度分析作者机构: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.