A local multiple Proper Generalized Decomposition based on the Partition of Unity

Author (s): Ibáñez, R., Abisset-Chavanne, E., Chinesta, F., Huerta, A., and Cueto, E.
Journal: International Journal for Numerical Methods in Engineering

Volume: 120, Issue 2
Pages: 139 – 152
Date: 2019

Abstract:
It is well known that model order reduction techniques that project the solution of the problem at hand onto a low-dimensional subspace present difficulties when this solution lies on a non-linear manifold. To overcome these difficulties -notably, an undesirable augment in the number of required modes in the solution- several solutions have been suggested. Among them we can cite the use of non-linear dimensionality reduction techniques or, alternatively, the employ of local linear reduced order approaches. These last approaches usually present the difficulty of ensuring continuity between these local models. Here, a new method is presented that ensures this continuity by resorting to the paradigm of the partition of unity, while employing Proper Generalized Decompositions at each local patch.

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Bibtex:

@article {PC-IACHC:19,
        Author = {Ruben Ibanez and Emmanuelle Abisset-Chavanne and Francisco Chinesta and 
                  Antonio Huerta and Elias Cueto},
        Title = {A local multiple Proper Generalized Decomposition based on the Partition of Unity},
        Fjournal = {International Journal for Numerical Methods in Engineering},
        Journal = {Int. J. Numer. Methods Eng.},
        Volume = {120},
        Number = {2},
        Pages = {139-152},
        Year = {2019},
        Doi = {10.1002/nme.612},
        }