Shape Sensitivity Analysis of Acoustic Scattering with Series Expansion Boundary Element Methods

This study explores a sensitivity analysis method based on the boundary element method (BEM) to address the computational complexity in acoustic analysis with ground reflection problems. The advantages of BEM in acoustic simulations and its high computational cost in broadband problems are examined. To improve efficiency, a Taylor series expansion is applied to decouple frequency-dependent terms in BEM. Additionally, the Second-Order Arnoldi (SOAR) model order reduction method is integrated to reduce computational costs and enhance numerical stability. Furthermore, an isogeometric sensitivity boundary integral equation is formulated using the direct differentiation method, incorporating Cauchy principal value integrals and Hadamard finite part integrals to handle singularities. The proposed method improves the computational efficiency, and the acoustic sensitivity analysis provides theoretical support for further acoustic structure optimization.