A rational strategy for the resolution of parametrized problems in the PGD framework

Christophe Heyberger (1) , Pierre-Alain Boucard (1) , David Néron (1)

1 LMT - Laboratoire de Mécanique et Technologie

This paper deals with the recurring question of the resolution of a problem for many different configurations, which can lead to highly expensive computations when using a direct treatment. The technique which is presented here is based on the use of Proper Generalized Decomposition (PGD) in the framework of the LATIN method. In our previous works, the feasibility of this model reduction technique approach has been demonstrated to compute the solution of a parametrized problem for a given space of parameters. For that purpose, a Reduced-Order Basis (ROB) was generated, reused and eventually enriched, by treating, one-by-one, all the various parameter sets. The novelty of the current paper is to develop a strategy, inspired by the Reduced Basis method, to explore rationally the space of parameters. The objective is to build, with the minimum of resolutions, a “complete” ROB that enables to solve all the other problems without enriching the basis.

Mots clés: Proper generalized decomposition; Parametrized problem; Model reduction; LATIN

Domaines: Mécanique des structures [physics.class-ph]

Christophe Heyberger, Pierre-Alain Boucard, David Néron. A rational strategy for the resolution of parametrized problems in the PGD framework. Computer Methods in Applied Mechanics and Engineering, 2013, 259, pp.40-49. ⟨10.1016/j.cma.2013.03.002⟩. ⟨hal-01567043⟩