Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 122, Issue 3, Pages 752-776Publisher
WILEY
DOI: 10.1002/nme.6559
Keywords
equilibrium formulation; error bounds; error estimation; proper generalized decomposition; quantity of interest
Funding
- Education, Audiovisual and Culture Executive Agency [FPA 2013-0043]
- Generalitat de Catalunya [2017-SGR-1278]
- H2020 Marie Sklodowska-Curie Actions [777778]
- Ministerio de Economia y Competitividad [DPI2017-85139-C2-2-R]
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In this work, compatible and equilibrated PGD solutions are computed and used in a dual analysis to obtain quantities of interest and their bounds with guaranteed accuracy. Complementary solutions are also used to compute an error indicator, driving a mesh adaptivity process focused on minimizing errors in the quantity of interest. The proposed approach results in lower errors compared to uniform refinement or global error-based indicators.
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.
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