File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach

TitleA Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach
Authors
KeywordsLocalized data-driven stochastic basis
Multiscale elliptic PDEs
Optimization method
Random partial differential equations (RPDEs)
Uncertainty quantification (UQ)
Issue Date2019
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at https://www.siam.org/Publications/Journals/Multiscale-Modeling-and-Simulation-A-SIAM-Interdisciplinary-Journal-MMS
Citation
SIAM Multiscale Modeling and Simulation, 2019, v. 17 n. 2, p. 826-853 How to Cite?
AbstractIn this paper, we propose a model reduction method for solving multiscale elliptic PDEs with random coefficients in the multiquery setting using an optimization approach. The optimization approach enables us to construct a set of localized multiscale data-driven stochastic basis functions that give an optimal approximation property of the solution operator. Our method consists of the offline and online stages. In the offline stage, we construct the localized multiscale data-driven stochastic basis functions by solving an optimization problem. In the online stage, using our basis functions, we can efficiently solve multiscale elliptic PDEs with random coefficients with relatively small computational costs. Therefore, our method is very efficient in solving target problems with many different force functions. The convergence analysis of the proposed method is also presented and has been verified by the numerical simulations. © 2019 Society for Industrial and Applied Mathematics
Persistent Identifierhttp://hdl.handle.net/10722/272214
ISSN
2019 Impact Factor: 1.855
2015 SCImago Journal Rankings: 1.062

 

DC FieldValueLanguage
dc.contributor.authorHou, T-
dc.contributor.authorMa, D-
dc.contributor.authorZhang, Z-
dc.date.accessioned2019-07-20T10:37:54Z-
dc.date.available2019-07-20T10:37:54Z-
dc.date.issued2019-
dc.identifier.citationSIAM Multiscale Modeling and Simulation, 2019, v. 17 n. 2, p. 826-853-
dc.identifier.issn1540-3459-
dc.identifier.urihttp://hdl.handle.net/10722/272214-
dc.description.abstractIn this paper, we propose a model reduction method for solving multiscale elliptic PDEs with random coefficients in the multiquery setting using an optimization approach. The optimization approach enables us to construct a set of localized multiscale data-driven stochastic basis functions that give an optimal approximation property of the solution operator. Our method consists of the offline and online stages. In the offline stage, we construct the localized multiscale data-driven stochastic basis functions by solving an optimization problem. In the online stage, using our basis functions, we can efficiently solve multiscale elliptic PDEs with random coefficients with relatively small computational costs. Therefore, our method is very efficient in solving target problems with many different force functions. The convergence analysis of the proposed method is also presented and has been verified by the numerical simulations. © 2019 Society for Industrial and Applied Mathematics-
dc.languageeng-
dc.publisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at https://www.siam.org/Publications/Journals/Multiscale-Modeling-and-Simulation-A-SIAM-Interdisciplinary-Journal-MMS-
dc.relation.ispartofSIAM Multiscale Modeling and Simulation-
dc.rightsSIAM Multiscale Modeling and Simulation. Copyright © Society for Industrial and Applied Mathematics.-
dc.rights© [year] Society for Industrial and Applied Mathematics. First Published in [Publication] in [volume and number, or year], published by the Society for Industrial and Applied Mathematics (SIAM).-
dc.subjectLocalized data-driven stochastic basis-
dc.subjectMultiscale elliptic PDEs-
dc.subjectOptimization method-
dc.subjectRandom partial differential equations (RPDEs)-
dc.subjectUncertainty quantification (UQ)-
dc.titleA Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach-
dc.typeArticle-
dc.identifier.emailZhang, Z: zhangzw@hku.hk-
dc.identifier.authorityZhang, Z=rp02087-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1137/18M1205844-
dc.identifier.scopuseid_2-s2.0-85068443448-
dc.identifier.hkuros298665-
dc.identifier.volume17-
dc.identifier.issue2-
dc.identifier.spage826-
dc.identifier.epage853-
dc.publisher.placeUnited States-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats