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

Published online by Cambridge University Press:  20 August 2015

Juarez dos Santos Azevedo  and
Saulo Pomponet Oliveira
Juarez dos Santos Azevedo*
Affiliation:
CETEC-UFRB, Centro, 44380-000, Cruz das Almas-BA, Brazil
Saulo Pomponet Oliveira*
Affiliation:
DMAT-UFPR, Centro Politécnico, 81531-980, Curitiba-PR, Brazil
*
Corresponding author.Email:juarezsa@gmail.com
Email:saulopo@ufpr.br
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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.

Keywords

60H1565C0565C2065C20Karhunen-Loève expansionMonte Carloquasi-Monte Carlosparse grid
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 4 , October 2012 , pp. 1051 - 1069
Copyright
Copyright © Global Science Press Limited 2012

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