A Numerical Comparison Between Quasi-Monte Carlo and Sparse Grid Stochastic Collocation Methods

作     者：Juarez dos Santos Azevedo Saulo Pomponet Oliveira 

作者机构：CETEC-UFRBCentro44380-000Cruz das Almas-BABrazil.2 DMAT-UFPRCentro Politecnico81531-980Curitiba-PRBrazil 

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

年 卷 期：2012年第12卷第9期

页      面：1051-1069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：Karhunen-Loève expansion Monte Carlo quasi-Monte Carlo sparse grid 

摘      要：Quasi-Monte Carlo methods and stochastic collocation methods based on sparse grids have become popular with solving stochastic partial differential *** methods use deterministic points for multi-dimensional integration or interpolation without suffering from the curse of *** is not evident which method is best,specially on random models of physical *** numerically study the error of quasi-Monte Carlo and sparse gridmethods in the context of groundwater flow in heterogeneous *** particular,we consider the dependence of the variance error on the stochastic dimension and the number of samples/collocation points for steady flow problems in which the hydraulic conductivity is a lognormal *** suitability of each technique is identified in terms of computational cost and error tolerance.