A reduced-order boundary element method for two-dimensional acoustic scattering

Abstract

This study presents a novel method for wideband acoustic analysis using the Boundary Element Method (BEM), addressing significant computational challenges. Traditional BEM requires repetitive computations across different frequencies due to the frequency-dependent system matrix, resulting in high computational costs. To overcome this, the Hankel function is expanded into a Taylor series, enabling the separation of frequency-dependent and frequency-independent components in the boundary integral equations. This results in a frequency-independent system matrix, improving computational efficiency. Additionally, the method addresses the issue of full-rank, asymmetric coefficient matrices in BEM, which complicate the solution of system equations over wide frequency ranges, particularly for large-scale problems. A Reduced-Order Model (ROM) is developed using the Second-Order Arnoldi (SOAR) method, which retains the key characteristics of the original Full-Order Model (FOM). The singularity elimination technique is employed to directly compute the strong singular and super-singular integrals in the acoustic equations. Numerical examples demonstrate the accuracy and efficiency of the proposed approach, showing its potential for large-scale applications in noise control and acoustic design, where fast and precise analysis is crucial.