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.

中文翻译：

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具有参数和隐式频率相关性的结构声学系统贪婪约简基算法

在本文中，针对具有参数和隐式频率相关性的结构声学系统的求解，提出了一种贪婪约简基算法。线性时谐弹性动力学和声学的基本方程分别使用有限元和边界元方法离散化。参数域内的解由简化的基向量的线性组合确定。这个基础是迭代生成的，并由结构声学系统在某些参数样本下的响应给出。遵循贪婪方法是在当前近似最差的参数样本处评估下一个基向量。该算法在一个小型训练集上运行，该集限制了内存要求，并允许应用程序解决具有高维参数域的大规模问题。