Proper generalized decomposition of multiscale models

Abstract: 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 [12]). The main originality of the present work concerns the treatment of the local problem, that is firstly 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.

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