Proper Generalized Decomposition of Multiscale Models

Francisco Chinesta (1) , Amine Ammar (2) , Elías Cueto (3)

1 GeM - Institut de Recherche en Génie Civil et Mécanique
2 LAMPA - Laboratoire Angevin de Mécanique, Procédés et InnovAtion
3 I3A - Aragón Institute of Engineering Research [Zaragoza]

In this paper the coupling of a parabolic model with a system of local kinetic equations is analyzed. A space time separated representation is proposed for the global model (this is simply the radial approximation proposed by Pierre Ladeveze in the LATIN framework (Non-linear Computational Structural Mechanics. Springer: New York, 1999)). The originality of the present work concerns the treatment of the local problem, that is first globalized (in space and time) and then fully globalized by introducing a new coordinate related to the different species involved in the kinetic model. Thanks to the non-incremental nature of both discrete descriptions (the local and the global one) the coupling is quite simple and no special difficulties are encountered by using heterogeneous time integrations.

Mots clés: Proper Generalized Decompositions; Separated representations; Finite sums decomposition; Multidimensional models; Model reduction

Domaines: Mécanique [physics.med-ph]; Matériaux

Francisco Chinesta, Amine Ammar, Elías Cueto. Proper Generalized Decomposition of Multiscale Models. International Journal for Numerical Methods in Engineering, 2010, 83 (8-9), pp.1114-1132. ⟨10.1002/nme.2794⟩. ⟨hal-01007222⟩