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

¹ Laboratoire National des Champs Magnétiques Intenses, 25 Av des Martyrs, 38042 Grenoble Cedex, France
cecile.daversin@lncmi.cnrs.fr
² Laboratoire Jean Kuntzmann, Université Joseph Fourier Grenoble 1, BP53 38041 Grenoble Cedex 9, France
stephane.veys@imag.fr
³ Laboratoire National des Champs Magnétiques Intenses, 25 Av des Martyrs, 38042 Grenoble Cedex, France
christophe.trophime@lncmi.cnrs.fr
⁴ Université de Strasbourg, IRMA UMR 7501, 7 rue René-Descartes, 67084 Strasbourg Cedex, France
prudhomme@unistra.fr

Abstract

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.