Application of adaptive ANOVA and reduced basis methods to the stochastic Stokes-Brinkman problem

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dc.contributor.authorWilliamson, Kevin
dc.contributor.authorCho, Heyrim
dc.contributor.authorSousedík, Bedřich
dc.date.accessioned2021-03-10T17:35:17Z
dc.date.available2021-03-10T17:35:17Z
dc.date.issued2021-03-17
dc.description.abstractThe Stokes-Brinkman equations model fluid flow in highly heterogeneous porous media. In this paper, we consider the numerical solution of the Stokes-Brinkman equations with stochastic permeabilities, where the permeabilities in subdomains are assumed to be independent and uniformly distributed within a known interval. We employ a truncated anchored ANOVA decomposition alongside stochastic collocation to estimate the moments of the velocity and pressure solutions. Through an adaptive procedure selecting only the most important ANOVA directions, we reduce the number of collocation points needed for accurate estimation of the statistical moments. However, for even modest stochastic dimensions, the number of collocation points remains too large to perform high-fidelity solves at each point. We use reduced basis methods to alleviate the computational burden by approximating the expensive high-fidelity solves with inexpensive approximate solutions on a low-dimensional space. We furthermore develop and analyze rigorous a posteriori error estimates for the reduced basis approximation. We apply these methods to 2D problems considering both isotropic and anisotropic permeabilities.en_US
dc.description.urihttps://link.springer.com/article/10.1007/s10596-021-10048-zen_US
dc.format.extent23 pagesen_US
dc.genrejournal articles preprintsen_US
dc.identifierdoi:10.13016/m2hywb-hcsc
dc.identifier.citationWilliamson, K., Cho, H. & Sousedík, B. Application of adaptive ANOVA and reduced basis methods to the stochastic Stokes-Brinkman problem. Comput Geosci 25, 1191–1213 (2021). https://doi.org/10.1007/s10596-021-10048-zen_US
dc.identifier.urihttp://hdl.handle.net/11603/21141
dc.identifier.urihttps://doi.org/10.1007/s10596-021-10048-z
dc.language.isoen_USen_US
dc.publisherSpringer
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Student Collection
dc.relation.ispartofUMBC Faculty Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.titleApplication of adaptive ANOVA and reduced basis methods to the stochastic Stokes-Brinkman problemen_US
dc.typeTexten_US
dcterms.creatorhttps://orcid.org/0000-0002-9630-8901
dcterms.creatorhttps://orcid.org/0000-0002-8053-8956

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