Error estimation for proper generalized decomposition solutions: dual analysis and adaptivity for quantities of interest
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hdl:2117/336847
Tipus de documentArticle
Data publicació2021-02-15
Condicions d'accésAccés obert
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ProjecteMATHROCKS - Multiscale Inversion of Porous Rock Physics using High-Performance Simulators: Bridging the Gap between Mathematics and Geophysics (EC-H2020-777778)
ASIMILACION DE DATOS PARA UNA SIMULACION INGENIERIL CREIBLE (AEI-DPI2017-85139-C2-2-R)
ASIMILACION DE DATOS PARA UNA SIMULACION INGENIERIL CREIBLE (AEI-DPI2017-85139-C2-2-R)
Abstract
When designing a structure or engineering a component, it is crucial to use methods that provide fast and reliable solutions, so that a large number of design options can be assessed. In this context, the proper generalized decomposition (PGD) can be a powerful tool, as it provides solutions to parametric problems, without being affected by the “curse of dimensionality.” Assessing the accuracy of the solutions obtained with the PGD is still a relevant challenge, particularly when seeking quantities of interest with guaranteed bounds. In this work, we compute compatible and equilibrated PGD solutions and use them in a dual analysis to obtain quantities of interest and their bounds, which are guaranteed. We also use these complementary solutions to compute an error indicator, which is used to drive a mesh adaptivity process, oriented for a quantity of interest. The corresponding solutions have errors that are much lower than those obtained using a uniform refinement or an indicator based on the global error, as the proposed approach focuses on minimizing the error in the quantity of interest.
Descripció
This is the peer reviewed version of the following article: Reis, J. [et al.]. Error estimation for proper generalized decomposition solutions: dual analysis and adaptivity for quantities of interest. "International journal for numerical methods in engineering", 15 Febrer 2021, vol. 122, núm. 3, p. 752-776, which has been published in final form at https://onlinelibrary.wiley.com/doi/10.1002/nme.6559. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
CitacióReis, J. [et al.]. Error estimation for proper generalized decomposition solutions: dual analysis and adaptivity for quantities of interest. "International journal for numerical methods in engineering", 15 Febrer 2021, vol. 122, núm. 3, p. 752-776.
ISSN1097-0207
Versió de l'editorhttps://onlinelibrary.wiley.com/doi/10.1002/nme.6559
Fitxers | Descripció | Mida | Format | Visualitza |
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QoI.pdf | Postprint https://doi.org/10.1002/nme.6559 | 7,344Mb | Visualitza/Obre |