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Enhanced parametric shape descriptions in PGD-based space separated representations

Article dans une revue avec comité de lecture
Author
KAZEMZADEH-PARSI, Mohammad Javad
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
AMMAR, Amine
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
DUVAL, Jean-Louis
564849 ESI Group [ESI Group]
CHINESTA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]

URI
http://hdl.handle.net/10985/21175
DOI
10.1186/s40323-021-00208-2
Date
2021
Journal
Advanced Modeling and Simulation in Engineering Sciences

Abstract

Space separation within the Proper Generalized Decomposition—PGD—rationale allows solving high dimensional problems as a sequence of lower dimensional ones. In our former works, different geometrical transformations were proposed for addressing complex shapes and spatially non-separable domains. Efficient implementation of separated representations needs expressing the domain as a product of characteristic functions involving the different space coordinates. In the case of complex shapes, more sophisticated geometrical transformations are needed to map the complex physical domain into a regular one where computations are performed. This paper aims at proposing a very efficient route for accomplishing such space separation. A NURBS-based geometry representation, usual in computer aided design—CAD—, is retained and combined with a fully separated representation for allying efficiency (ensured by the fully separated representations) and generality (by addressing complex geometries). Some numerical examples are considered to prove the potential of the proposed methodology.

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