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Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media
In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random hete...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society Publishing
2017
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5579089/ https://www.ncbi.nlm.nih.gov/pubmed/28878974 http://dx.doi.org/10.1098/rsos.170203 |
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author | Crevillén-García, D. Power, H. |
author_facet | Crevillén-García, D. Power, H. |
author_sort | Crevillén-García, D. |
collection | PubMed |
description | In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random heterogeneous porous media. We apply the four methodologies to a model problem where the only input parameter, the hydraulic conductivity, is modelled as a log-Gaussian random field by using direct Karhunen–Loéve decompositions. The random terms in such expansions represent the coefficients in the equations. Numerical calculations demonstrating the effectiveness of each of the methods are presented. A comparison of the computational cost incurred by each of the methods for three different tolerances is provided. The accuracy of the approaches is quantified via the mean square error. |
format | Online Article Text |
id | pubmed-5579089 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | The Royal Society Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-55790892017-09-06 Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media Crevillén-García, D. Power, H. R Soc Open Sci Computer Science In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random heterogeneous porous media. We apply the four methodologies to a model problem where the only input parameter, the hydraulic conductivity, is modelled as a log-Gaussian random field by using direct Karhunen–Loéve decompositions. The random terms in such expansions represent the coefficients in the equations. Numerical calculations demonstrating the effectiveness of each of the methods are presented. A comparison of the computational cost incurred by each of the methods for three different tolerances is provided. The accuracy of the approaches is quantified via the mean square error. The Royal Society Publishing 2017-08-09 /pmc/articles/PMC5579089/ /pubmed/28878974 http://dx.doi.org/10.1098/rsos.170203 Text en © 2017 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Computer Science Crevillén-García, D. Power, H. Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media |
title | Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media |
title_full | Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media |
title_fullStr | Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media |
title_full_unstemmed | Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media |
title_short | Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media |
title_sort | multilevel and quasi-monte carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media |
topic | Computer Science |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5579089/ https://www.ncbi.nlm.nih.gov/pubmed/28878974 http://dx.doi.org/10.1098/rsos.170203 |
work_keys_str_mv | AT crevillengarciad multilevelandquasimontecarlomethodsforuncertaintyquantificationinparticletraveltimesthroughrandomheterogeneousporousmedia AT powerh multilevelandquasimontecarlomethodsforuncertaintyquantificationinparticletraveltimesthroughrandomheterogeneousporousmedia |