COUPLING FINITE ELEMENTS AND PROPER GENERALIZED DECOMPOSITIONS

摘要

Numerous models encountered in science and engineering exist, despite the impressive recent progresses attained in computational simulation techniques, intractable when the usual and experienced discretization techniques are applied for their numerical simulation. Thus, different challenging issues remain for the proposal of new alternative advanced simulation techniques. Separated representations offer the possibility to address some challenging models with CPU time savings of some orders of magnitude. In other cases, they allowed models to be addressed which until now, have never been solved. The number of published works concerning this kind of approximation remains quite reduced, and then numerous difficulties that were successfully circumvented in the context of more experienced discretization techniques, as is the case of the finite element method, must be considered again within the separated representation framework. One of these issues in the one that concerns the treatment of localized behavior of model solutions. This work focuses on this topic and proposes an efficient finite element (or extended finite element) enrichment of usual separated representation.