A greedy reduced basis algorithm for structural acoustic systems with parameter and implicit frequency dependence

作     者：Jelich, Christopher Baydoun, Suhaib Koji Voigt, Matthias Marburg, Steffen 

作者机构：Tech Univ Munich Chair Vibroacoust Vehicles & Machines Boltzmannstr 15 D-85748 Garching Germany UniDistance Suisse Brig Switzerland 

出 版 物：《INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING》 (国际工程数值法杂志)

年 卷 期：2021年第122卷第24期

页      面：7409-7430页

核心收录：

学科分类：08[工学] 0701[理学-数学] 

基　　金：Deutsche Forschungsgemeinschaft 

主　　题：boundary element method finite element method greedy algorithm implicit parameter dependence reduced basis structural acoustic interaction 

摘      要：In this article, a greedy reduced basis algorithm is proposed for the solution of structural acoustic systems with parameter and implicit frequency dependence. The underlying equations of linear time-harmonic elastodynamics and acoustics are discretized using the finite element and boundary element method, respectively. The solution within the parameter domain is determined by a linear combination of reduced basis vectors. This basis is generated iteratively and given by the responses of the structural acoustic system at certain parameter samples. A greedy approach is followed by evaluating the next basis vector at the parameter sample which is currently approximated worst. The algorithm runs on a small training set which bounds the memory requirements and allows applications to large-scale problems with high-dimensional parameter domains. The computational efficiency of the proposed scheme is illustrated based on two numerical examples: a point-excited spherical shell submerged in water and a satellite structure subject to a diffuse sound pressure field excitation.