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