Volume 12, Issue 4
A Numerical Comparison Between Quasi-Monte Carlo and Sparse Grid Stochastic Collocation Methods

Juarez dos Santos Azevedo & Saulo Pomponet Oliveira

Commun. Comput. Phys., 12 (2012), pp. 1051-1069.

Published online: 2012-12

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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 theerrorofquasi-MonteCarloandsparsegridmethodsinthecontextofgroundwater 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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@Article{CiCP-12-1051, author = {Juarez dos Santos Azevedo and Saulo Pomponet Oliveira}, title = {A Numerical Comparison Between Quasi-Monte Carlo and Sparse Grid Stochastic Collocation Methods}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {4}, pages = {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 theerrorofquasi-MonteCarloandsparsegridmethodsinthecontextofgroundwater 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. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.260111.230911a}, url = {http://global-sci.org/intro/article_detail/cicp/7324.html} }
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