An adaptive model order reduction method for boundary element-based multi-frequency acoustic wave problems

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.