A local multiple proper generalized decomposition based on the partition of unity
PublisherJohn Wiley & sons
Rights accessOpen Access
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ProjectAdMoRe - Empowered decision-making in simulation-based engineering: Advanced Model Reduction for real-time, inverse and optimization in industrial problems (EC-H2020-675919)
It is well known that model order reduction techniques that project the solution of the problem at hand onto alow-dimensional subspace present difficulties when this solution lies on a non-linear manifold. To overcomethese difficulties—notably, an undesirable augment in the number of requiredmodesin the solution—severalsolutions have been suggested. Among them we can cite the use of non-linear dimensionality reductiontechniques or, alternatively, the employ of local linear reduced order approaches. These last approachesusually present the difficulty of ensuring continuity between these local models. Here, a new method ispresented that ensures this continuity by resorting to the paradigm of the partition of unity, while employingProper Generalized Decompositions at each local patch.
This is the peer reviewed version of the following article: Ibáñez, R. [et al.]. A local multiple proper generalized decomposition based on the partition of unity. "International journal for numerical methods in engineering", 12 Octubre 2019, vol. 120, núm. 2, p. 139-152, which has been published in final form at DOI:10.1002/nme.6128. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
CitationIbáñez, R. [et al.]. A local multiple proper generalized decomposition based on the partition of unity. "International journal for numerical methods in engineering", 12 Octubre 2019, vol. 120, núm. 2, p. 139-152.