TY - JOUR
T1 - A Numerical Comparison Between Quasi-Monte Carlo and Sparse Grid Stochastic Collocation Methods
AU - Juarez dos Santos Azevedo & Saulo Pomponet Oliveira
JO - Communications in Computational Physics
VL - 4
SP - 1051
EP - 1069
PY - 2012
DA - 2012/12
SN - 12
DO - http://doi.org/10.4208/cicp.260111.230911a
UR - https://global-sci.org/intro/article_detail/cicp/7324.html
KW - 
AB - <p style="text-align: justify;">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 grid methods in the context of ground-water 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.</p>