Error estimation for proper generalized decomposition solutions: Dual analysis and adaptivity for quantities of interest
Author (s): Reis, J.; Moitinho de Almeida, J.P.; Díez, P. and Zlotnik, S.Journal: International Journal for Numerical Methods in Engineering
Volume: 122
Pages: 752 - 776
Date: 2021
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 can be a powerful tool, as it provides solutions to parametric problems, without being a ected 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 re nement or an indicator based on the global error, as the proposed approach focuses on minimizing the error in the quantity of interest.
Bibtex:
@article{2021-IJNME-RMDZ,
Author = {Reis, Jonatha
and Moitinho de Almeida, Jose Paulo
and D{\'i}ez, Pedro
and Zlotnik, Sergio},
Title = {Error estimation for proper generalized decomposition solutions: Dual analysis and adaptivity for quantities of interest},
Fjournal = {International Journal for Numerical Methods in Engineering},
Volume = {122},
Number = {3},
Pages = {752-776 },
Year = {2021},
Doi = {10.1002/nme.6559},
} 
