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A probabilistic data assimilation framework to reconstruct finite element error fields from sparse error estimates: Application to sub-modeling

Rouse, James Paul; Kerfriden, Pierre; Hamadi, Maxime

Authors

JAMES ROUSE JAMES.ROUSE@NOTTINGHAM.AC.UK
Assistant Professor

Pierre Kerfriden

Maxime Hamadi



Abstract

The present work proposes a computational approach that recovers full finite element error fields from a small number of estimates of errors in scalar quantities of interest. The approach is weakly intrusive and is motivated by large scale industrial applications wherein modifying the finite element models is undesirable and multiple regions of interest may exist in a single model. Error estimates are developed using a Zhu-Zienkiewicz estimator coupled with the adjoint methodology to deliver goal-oriented results. A Bayesian probabilistic estimation framework is deployed for full field estimation. An adaptive, radial basis function based reduced order modeling strategy is implemented to reduce the cost of calculating the posterior. The Bayesian reconstruction approach, accelerated by the proposed model reduction technology, is shown to yield good probabilistic estimates of full error fields, with a computational complexity that is acceptable compared to the evaluation of the goal-oriented error estimates. The novelty of the work is that a set of computed error estimates are considered as partial observations of an underlying error field, which is to be recovered. Future improvements of the method include the optimal selection of goal-oriented error measures to be acquired prior to the error field reconstruction.

Citation

Rouse, J. P., Kerfriden, P., & Hamadi, M. (2022). A probabilistic data assimilation framework to reconstruct finite element error fields from sparse error estimates: Application to sub-modeling. International Journal for Numerical Methods in Engineering, 123(23), 5826-5853. https://doi.org/10.1002/nme.7090

Journal Article Type Article
Acceptance Date Jul 26, 2022
Online Publication Date Aug 23, 2022
Publication Date Dec 15, 2022
Deposit Date Apr 19, 2023
Publicly Available Date May 4, 2023
Journal International Journal for Numerical Methods in Engineering
Print ISSN 0029-5981
Electronic ISSN 1097-0207
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 123
Issue 23
Pages 5826-5853
DOI https://doi.org/10.1002/nme.7090
Keywords Applied Mathematics; General Engineering; Numerical Analysis
Public URL https://nottingham-repository.worktribe.com/output/9589016
Publisher URL https://onlinelibrary.wiley.com/doi/10.1002/nme.7090

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