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

A Numerical Comparison Between Quasi-Monte Carlo and Sparse Grid Stochastic Collocation Methods
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Year:    2012

Communications in Computational Physics, Vol. 12 (2012), Iss. 4 : pp. 1051–1069

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.260111.230911a

Communications in Computational Physics, Vol. 12 (2012), Iss. 4 : pp. 1051–1069

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:   

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