A local multiple proper generalized decomposition based on the partition of unity. (18th June 2019)

• Record Type: Journal Article
• Authors: Ibáñez, Rubén; Abisset‐Chavanne, Emmanuelle; Chinesta, Francisco; Huerta, Antonio; Cueto, Elías
• Is Part Of: International journal for numerical methods in engineering. Volume 120:Number 2(2019)
• Page Start: 139
• Page End: 152
• Publication Date: 2019-06-18
• Subjects: local reduced order modeling -- model order reduction -- partition of unity -- proper generalized decomposition; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6128
• Languages: English
• ISSNs: 0029-5981

Abstract

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.