A Numerical Comparison Between Quasi-Monte Carlo and Sparse Grid Stochastic Collocation Methods (Communications in Computational Physics, 2012)
Quasi-Monte Carlo methods and stochastic collocation methods based onsparse 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 whichmethod is best, specially on random models of physical phenomena. We numericallystudy the error of quasi-Monte Carlo and sparse grid methods in the context of ground-water flow in heterogeneous media. In particular, we consider the dependence of thevariance error on the stochastic dimension and the number of samples/collocationpoints for steady flow problems in which the hydraulic conductivity is a lognormalprocess. The suitability of each technique is identified in terms of computational costand error tolerance.