Error Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertainty

Handle URI:
http://hdl.handle.net/10754/597966
Title:
Error Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertainty
Authors:
Bryant, C. M.; Prudhomme, S.; Wildey, T.
Abstract:
In this work, we investigate adaptive approaches to control errors in response surface approximations computed from numerical approximations of differential equations with uncertain or random data and coefficients. The adaptivity of the response surface approximation is based on a posteriori error estimation, and the approach relies on the ability to decompose the a posteriori error estimate into contributions from the physical discretization and the approximation in parameter space. Errors are evaluated in terms of linear quantities of interest using adjoint-based methodologies. We demonstrate that a significant reduction in the computational cost required to reach a given error tolerance can be achieved by refining the dominant error contributions rather than uniformly refining both the physical and stochastic discretization. Error decomposition is demonstrated for a two-dimensional flow problem, and adaptive procedures are tested on a convection-diffusion problem with discontinuous parameter dependence and a diffusion problem, where the diffusion coefficient is characterized by a 10-dimensional parameter space.
Citation:
Bryant CM, Prudhomme S, Wildey T (2015) Error Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertainty. SIAM/ASA J Uncertainty Quantification 3: 1020–1045. Available: http://dx.doi.org/10.1137/140962632.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM/ASA Journal on Uncertainty Quantification
Issue Date:
Jan-2015
DOI:
10.1137/140962632
Type:
Article
ISSN:
2166-2525
Sponsors:
This material is based on work supported by the Department of Energy [National Nuclear Security Administration] under award DE-FC52-08NA28615.This author participated in the Visitors’ Program of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.This author is a participant of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBryant, C. M.en
dc.contributor.authorPrudhomme, S.en
dc.contributor.authorWildey, T.en
dc.date.accessioned2016-02-25T13:16:57Zen
dc.date.available2016-02-25T13:16:57Zen
dc.date.issued2015-01en
dc.identifier.citationBryant CM, Prudhomme S, Wildey T (2015) Error Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertainty. SIAM/ASA J Uncertainty Quantification 3: 1020–1045. Available: http://dx.doi.org/10.1137/140962632.en
dc.identifier.issn2166-2525en
dc.identifier.doi10.1137/140962632en
dc.identifier.urihttp://hdl.handle.net/10754/597966en
dc.description.abstractIn this work, we investigate adaptive approaches to control errors in response surface approximations computed from numerical approximations of differential equations with uncertain or random data and coefficients. The adaptivity of the response surface approximation is based on a posteriori error estimation, and the approach relies on the ability to decompose the a posteriori error estimate into contributions from the physical discretization and the approximation in parameter space. Errors are evaluated in terms of linear quantities of interest using adjoint-based methodologies. We demonstrate that a significant reduction in the computational cost required to reach a given error tolerance can be achieved by refining the dominant error contributions rather than uniformly refining both the physical and stochastic discretization. Error decomposition is demonstrated for a two-dimensional flow problem, and adaptive procedures are tested on a convection-diffusion problem with discontinuous parameter dependence and a diffusion problem, where the diffusion coefficient is characterized by a 10-dimensional parameter space.en
dc.description.sponsorshipThis material is based on work supported by the Department of Energy [National Nuclear Security Administration] under award DE-FC52-08NA28615.This author participated in the Visitors’ Program of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.This author is a participant of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.titleError Decomposition and Adaptivity for Response Surface Approximations from PDEs with Parametric Uncertaintyen
dc.typeArticleen
dc.identifier.journalSIAM/ASA Journal on Uncertainty Quantificationen
dc.contributor.institutionInstitute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, Austin, TX 78712en
dc.contributor.institutionDepartement de Mathematiques et de Genie Industriel, Ecole Polytechnique de Montreal, Montreal, QC H3T 1J4, Canadaen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.