Abstract The classical boundary element method (BEM) is widely used to obtain detailed information on the acoustic performance of large-scale dynamical systems due to the nature of semi-analytical characteristic. Its use, however, results in asymmetric and dense system matrix, which makes original full-order model evaluation very time consuming and memory demanding. Moreover, the frequency sweep analysis which is indispensable for the assessment of noise emission levels and the design of high-quality products requires the repetitive assembly and solution of system of equations, which further increases the computational complexity. In order to alleviate these problems, an adaptive structure-preserving model order reduction method is presented, which is based on an offline–online solution framework. In the offline phase, we first factor out the frequency term as a scalar function from the BE integral kernels of the Burton–Miller formulation, followed by integration to set up the system matrices. A global frequency-independent orthonormal basis is then constructed via the second-order Arnoldi (SOAR) method to span a projection subspace, onto which the frequency-decoupled system matrices are projected column by column to solve the memory problem arising from the frequency-related decomposition. In addition, the number of iterations required for convergence can be automatically determined by exploiting the condition number of an upper Hessenberg matrix in SOAR. In the online stage, a reliable reduced-order model can be quickly recovered by the sum of those offline stored reduced matrices multiplied by frequency-dependent coefficients, which is favored in many-query applications. Two academic benchmarks and a more realistic problem are investigated in order to demonstrate the potentials of the proposed approach.

中文翻译：

---

基于边界元的多频声波问题自适应模型降阶方法

摘要 由于半解析特性，经典边界元法(BEM)被广泛用于获取大型动力系统声学性能的详细信息。然而，它的使用会导致不对称和密集的系统矩阵，这使得原始全阶模型评估非常耗时且需要内存。此外，对于噪声发射水平的评估和高质量产品的设计必不可少的扫频分析需要方程组的重复组装和求解，这进一步增加了计算复杂度。为了缓解这些问题，提出了一种基于离线-在线求解框架的自适应结构保持模型降阶方法。在离线阶段，我们首先从 Burton-Miller 公式的 BE 积分核中将频率项分解为标量函数，然后进行积分以建立系统矩阵。然后通过二阶 Arnoldi (SOAR) 方法构建全局频率无关的正交基以跨越投影子空间，将频率解耦的系统矩阵逐列投影到该子空间上，以解决频率相关的内存问题。分解。此外，收敛所需的迭代次数可以通过利用 SOAR 中上 Hessenberg 矩阵的条件数自动确定。在在线阶段，通过将那些离线存储的降阶矩阵乘以频率相关系数的总和，可以快速恢复可靠的降阶模型，这在多查询应用程序中受到青睐。研究了两个学术基准和一个更现实的问题，以证明所提出方法的潜力。