Proper Generalized Decomposition of Time-Multiscale Models

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

1 LAMPA - Laboratoire Angevin de Mécanique, Procédés et InnovAtion
2 Matériaux, Procédés et Technologie des Composites
3 I3A - Aragón Institute of Engineering Research [Zaragoza]

Models encountered in computational mechanics could involve many time scales. When these time scales cannot be separated, one must solve the evolution model in the entire time interval by using the finest time step that the model implies. In some cases, the solution procedure becomes cumbersome because of the extremely large number of time steps needed for integrating the evolution model in the whole time interval. In this paper, we considered an alternative approach that lies in separating the time axis (one-dimensional in nature) in a multidimensional time space. Then, for circumventing the resulting curse of dimensionality, the proper generalized decomposition was applied allowing a fast solution with significant computing time savings with respect to a standard incremental integration.

Mots clés: time multiscale; proper generalized decomposition; separated representations; transient models

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

Amine Ammar, Francisco Chinesta, Elías Cueto, Manuel Doblare. Proper Generalized Decomposition of Time-Multiscale Models. International Journal for Numerical Methods in Engineering, 2011, 90 (5), pp.569-596. ⟨10.1002/nme.3331⟩. ⟨hal-01007223⟩