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 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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@Article{CiCP-12-1051, author = {}, 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 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.260111.230911a}, url = {http://global-sci.org/intro/article_detail/cicp/7324.html} }
TY - JOUR T1 - A Numerical Comparison Between Quasi-Monte Carlo and Sparse Grid Stochastic Collocation Methods JO - Communications in Computational Physics VL - 4 SP - 1051 EP - 1069 PY - 2012 DA - 2012/12 SN - 12 DO - http://dor.org/10.4208/cicp.260111.230911a UR - https://global-sci.org/intro/article_detail/cicp/7324.html KW - AB -

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.

Juarez dos Santos Azevedo & Saulo Pomponet Oliveira. (2020). A Numerical Comparison Between Quasi-Monte Carlo and Sparse Grid Stochastic Collocation Methods. Communications in Computational Physics. 12 (4). 1051-1069. doi:10.4208/cicp.260111.230911a
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