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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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CiteScore 2016: 0.70

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Source Normalized Impact per Paper (SNIP) 2016: 0.908

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Volume 18, Issue 3 (Sep 2012)


Quasi Monte Carlo methods applied to equations in transient regime on the Theis equation

Juarez S. Azevedo
Published Online: 2012-09-01 | DOI: https://doi.org/10.1515/mcma-2012-0007


In this study, we present the basic-concepts of ground-water hydraulic on stochastic media, whose the Theis equation is used in the transient movement of groundwater as a result of pumping in a confined aquifer in saturated porous media under random parameters. A special importance is given on circumstances which requires a high-dimension stochastic to obtain a certain precision in probability space. As an alternative, we introduce quasi-Monte Carlo methods considering Sobol and Halton sequences for uncertainty assessment. Accuracy and efficiency are studied here with allusion to model problem using as reference the solution obtained by Monte Carlo method and numerical experiments on two-dimensional random field identified some restrictions with the increase of realizations number. To represent the realizations of the hydraulic conductivity field based on available data was used the Karhunen–Loève expansion.

Keywords: Exponential covariance; Karhunen–Loève expansion; Monte Carlo; quasi-Monte Carlo; power-law covariance; Theis equation

About the article

Received: 2011-08-27

Accepted: 2012-05-28

Published Online: 2012-09-01

Published in Print: 2012-09-01

Citation Information: , ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma-2012-0007.

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© 2012 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

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