High Performance Computing for the Reduced Basis Method. Application to Natural Convection

¹ Laboratoire Jacques Louis Lions, UPMC, 4 Place Jussieu, 75005 Paris, France
² Inria Paris-Rocquencourt, Domaine de Voluceau B.P. 105, 78153 Le Chesnay Cedex, France
elisa.schenone@inria.fr
³ Laboratoire Jean Kuntzmann, Université Joseph Fourier Grenoble 1, BP53 38041 Grenoble Cedex 9, France
stephane.veys@imag.fr
⁴ Université de Strasbourg, IRMA UMR 7501, 7 rue René-Descartes, 67084 Strasbourg Cedex, France
prudhomme@unistra.fr

Abstract

In this paper, we are interested in applying the reduced basis methodology (RBM) to steady-state natural convection problems. The latter has applications in many engineering domains and being able to apply the RBM would allow to gain huge computation savings when querying the model for many parameter evaluations. In this work, we focus on the order reduction of the model — in particular the handling of the non-linear terms, — as well as the design of the RBM computational framework and the requirements on high performance computing to treat 3D models using Feel++, a C++ open source library to solve partial differential equations. Numerical experiments are presented on 2D and 3D models.