A posteriori error estimation and adaptivity in non-intrusive couplings between concurrent models

Tirvaudey, Marie; Chamoin, Ludovic; Bouclier, Robin; Passieux, Jean‐Charles

doi:10.1016/j.cma.2020.113104

Cited by 7 publications

(2 citation statements)

References 85 publications

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“…In many cases, the GOEE approach has been used to represent the uncertainty in a physically relevant quantity that may be turned into an error on a failure criterion 24‐27 . In the multiscale setting, a posteriori error estimates have been applied to Type A problems in the work of Tirvaudey et al, 28 wherein a weighted residual based GOEE is applied in non‐intrusive sub‐modeling problems. A posteriori error estimates for MsFEM problems have been developed in the work of Chung and Chamoin 29,30 .…”

Section: Introductionmentioning

confidence: 99%

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

Rouse

Kerfriden

Hamadi

2022

Numerical Meth Engineering

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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.

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Section: Introductionmentioning

confidence: 99%

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

Rouse

Kerfriden

Hamadi

2022

Numerical Meth Engineering

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“…However, the issue of certification and optimal driving of such a coupling method has been addressed in very few works until now [2]. In the present work, we tackle this subject using the concept of constitutive relation error (CRE) [3] which is a generic tool able to certify the quality of a numerical solution.…”

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confidence: 99%

Certification, Adaptivity, and Reduction in Non-Intrusive Model Couplings

Verwee¹,

Chamoin²

2021

10th International Conference on Adaptative Modeling and Simulation

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The non-intrusive coupling method [1] is a local analysis method that aims to separate the macroscopic and local scales both from mesh, operator, and loading viewpoints. This method has demonstrated that it can be used for a large set of problems such as those with local plasticity, and it has been implemented in an industrial code. In order to reduce the complexity of a given problem, a coarse model is defined on the total domain with its properties (geometry, connectivity, operator, solver) and a separated fine model is set locally with its different properties. The solution is obtained iteratively by exchanging data on the interface between the global and local models.

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References

2022

IGA: Non‐conforming Coupling and Shape Optimization of Complex Multipatch Structures

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A posteriori error estimation and adaptivity in non-intrusive couplings between concurrent models

Cited by 7 publications

References 85 publications

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

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

Certification, Adaptivity, and Reduction in Non-Intrusive Model Couplings

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