A Reduced Basis Framework: Application to large scale non-linear multi-physics problems

Cécile Daversin (1) , Stéphane Veys (2) , Christophe Trophime (1) , Christophe Prud'Homme (3)

1 LNCMI-G - Laboratoire national des champs magnétiques intenses - Grenoble
2 EDP - Equations aux Dérivées Partielles
3 IRMA - Institut de Recherche Mathématique Avancée

In this paper we present applications of the reduced basis method (RBM) to large-scale non-linear multi-physics problems. We first describe the mathematical framework in place and in particular the Empirical Interpolation Method (EIM) to recover an affine decomposition and then we propose an implementation using the open-source library Feel++ which provides both the reduced basis and finite element layers. Large scale numerical examples are shown and are connected to real industrial applications arising from the High Field Resistive Magnets development at the Laboratoire National des Champs Magnétiques Intenses.

Keywords: Reduced Basis Method; Non-linear multi-physics simulations; high performance computing

Domains: Analysis of PDEs [math.AP]

Cécile Daversin, Stéphane Veys, Christophe Trophime, Christophe Prud'Homme. A Reduced Basis Framework: Application to large scale non-linear multi-physics problems. ESAIM: Proceedings, 2013, 43, pp.225-254. ⟨10.1051/proc/201343015⟩. ⟨hal-00786557⟩