ESAIM: PROCEEDINGS AND SURVEYS, January 2015, Vol. 48, p. 98-115 N. Champagnat, T. Leli` evre, A. Nouy, Editors REDUCED BASIS APPROXIMATION FOR THE STRUCTURAL-ACOUSTIC DESIGN BASED ON ENERGY FINITE ELEMENT ANALYSIS (RB-EFEA) Denis Devaud 1 and Gianluigi Rozza 2 Abstract. In many engineering applications, the investigation of the vibro-acoustic response of struc- tures is of great interest. Hence, great effort has been dedicated to improve methods in this field in the last twenty years. Classical techniques have the main drawback that they become unaffordable when high frequency impact waves are considered. In that sense, the Energy Finite Element Analysis (EFEA) is a good alternative to those methods. Based on an approximate model, EFEA gives time and locally space-averaged energy densities and has been proven to yield accurate results. However, when dealing with structural-acoustic design, it is necessary to obtain the energy density varying a large number of parameters. It is computationally unaffordable and too expensive to compute such solutions for each set of parameters. To prevent this drawback, we introduce a reduced order model which allows to drastically decrease those computational costs, while yielding a reliable and accurate approximation. In this paper, we present an approximation of the EFEA solution considering the Reduced Basis (RB) method. The RB method has already been applied successfully to many different problems. A complete development of this procedure in the context of EFEA is introduced here. Numerical tests and examples are provided for both geometrical and physical parameters. 1. Introduction and Motivation In many engineering applications, it is important to be able to compute the acoustic response of built-up structures. This is of particular interest in structural-acoustic design where noise control is desirable. At high frequency, wavelenghts are small compared to the size of the domain, which yields prohibitively large computational costs using standard techniques. Moreover, the response is highly dependent on the space location and frequency. This phenomenon may prevent from catching the general behavior of the structure. For these reasons, it is necessary to develop methods that are able to predict average results. The most widely used method is the Statistical Energy Analysis (SEA) [6, 13]. In SEA, the first step is to divide the whole system in subsystems consisting of similar resonant modes. Then, the different subsystems are coupled assuming that the difference in their modal energies is proportional to the power flow. The propor- tionality constants are related to the coupling loss factors. However, the assumptions considered to derive such method does not allow to capture spatial variation within a subsystem. Moreover, the input data are usually not consistent with the geometry data bases. Two other exact methods, the General Energetic Method (GEM) and the Simplified Energy Method (SEM) [11], can be used to predict the energy behaviour of structures. 1 EPFL SMA, CH-1015, Lausanne, Switzerland. This work has been carried out during a pre-doc visiting period of the first author at SISSA Mathlab, International School for Advanced Studies, Trieste, Italy. 2 SISSA, International School for Advanced Studies, Mathlab, Via Bonomea 265, 34136 Trieste, Italy; gianluigi.rozza@sissa.it. SISSA NOFYSAS Excellent grant and INdAM GNCS are kindly acknowledged. © EDP Sciences, SMAI 2015 Article published online by EDP Sciences and available at http://www.esaim-proc.org or http://dx.doi.org/10.1051/proc/201448004