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Title: Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble when applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.
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  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
Publication Date:
Report Number(s):
Journal ID: ISSN 2166-2525; 656365
Grant/Contract Number:
Accepted Manuscript
Journal Name:
SIAM/ASA Journal on Uncertainty Quantification
Additional Journal Information:
Journal Volume: 6; Journal Issue: 1; Journal ID: ISSN 2166-2525
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; sampling methods; stochastic collocation methods; stochastic partial differential equations; anisotropic diffusion models; forward uncertainty propagation; embedded ensemble propagation
OSTI Identifier: