Geodesic
Reduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA)
Denis Devaud1 ; Gianluigi Rozza2
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;
ESAIM. Proceedings, Tome 48 (2015), pp. 98-115.

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In many engineering applications, the investigation of the vibro-acoustic response of structures 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.
DOI : 10.1051/proc/201448004

Denis Devaud 1 ; Gianluigi Rozza 2

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; 
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     author = {Denis Devaud and Gianluigi Rozza},
     title = {Reduced {Basis} {Approximation} for the {Structural-Acoustic} {Design} based on {Energy} {Finite} {Element} {Analysis} {(RB-EFEA)}},
     journal = {ESAIM. Proceedings},
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Denis Devaud; Gianluigi Rozza. Reduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA). ESAIM. Proceedings, Tome 48 (2015), pp. 98-115. doi : 10.1051/proc/201448004. http://geodesic.mathdoc.fr/articles/10.1051/proc/201448004/

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