Quasi-Monte Carlo methods and stochastic collocation methods based on sparse grids have become popular with solving stochastic partial differential equations.These methods use deterministic points for multi-dimensiona...Quasi-Monte Carlo methods and stochastic collocation methods based on sparse grids have become popular with solving stochastic partial differential equations.These methods use deterministic points for multi-dimensional integration or interpolation without suffering from the curse of dimensionality.It is not evident which method is best,specially on random models of physical phenomena.We numerically study the error of quasi-Monte Carlo and sparse gridmethods in the context of groundwater flow in heterogeneous media.In 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 process.The suitability of each technique is identified in terms of computational cost and error tolerance.展开更多
文摘Quasi-Monte Carlo methods and stochastic collocation methods based on sparse grids have become popular with solving stochastic partial differential equations.These methods use deterministic points for multi-dimensional integration or interpolation without suffering from the curse of dimensionality.It is not evident which method is best,specially on random models of physical phenomena.We numerically study the error of quasi-Monte Carlo and sparse gridmethods in the context of groundwater flow in heterogeneous media.In 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 process.The suitability of each technique is identified in terms of computational cost and error tolerance.
