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A local multiple proper generalized decomposition based on the partition of unity
Author(s) -
Ibáñez Rubén,
AbissetChavanne Emmanuelle,
Chinesta Francisco,
Huerta Antonio,
Cueto Elías
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6128
Subject(s) - partition of unity , partition (number theory) , subspace topology , mathematics , nonlinear system , model order reduction , dimensionality reduction , mathematical optimization , reduction (mathematics) , algorithm , computer science , mathematical analysis , artificial intelligence , geometry , combinatorics , engineering , finite element method , projection (relational algebra) , physics , structural engineering , quantum mechanics
Summary 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 nonlinear manifold. To overcome these difficulties (notably, an undesirable increase in the number of required modes in the solution), several solutions have been suggested. Among them, we can cite the use of nonlinear dimensionality reduction techniques or, alternatively, the employ of linear local reduced order approaches. These last approaches usually present the difficulty of ensuring continuity between these local models. Here, a new method is presented, which ensures this continuity by resorting to the paradigm of the partition of unity while employing proper generalized decompositions at each local patch.