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1 results

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

  • Juarez dos Santos Azevedo, Saulo Pomponet Oliveira
  • Journal:
    Communications in Computational Physics / Volume 12 / Issue 4 / October 2012
    Published online by Cambridge University Press:
    20 August 2015, pp. 1051-1069
    Print publication:
    October 2012

  • 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.