Second-order Arnoldi accelerated boundary element method for two-dimensional broadband acoustic shape sensitivity analysis

This paper proposes a novel approach for broadband acoustic shape sensitivity analysis based on the direct differentiation approach. Since the system matrices of the boundary element method (BEM) for the analysis of acoustic state and acoustic sensitivity have frequency dependence, repeated calculations are needed at different frequencies. This is very time-consuming, especially for sensitivity calculations used in shape optimization design. The Taylor series expansion of the Hankel function is carried out to separate the frequency-dependent and frequency-independent terms in the acoustic shape sensitivity boundary integral equation to construct a frequency-independent system matrix. In addition, due to the formation of asymmetric full-coefficient matrices in acoustic shape sensitivity equations based on the BEM, repeatedly solving system equations is also extremely time-consuming at broadband frequencies for large scale issues. The second-order Arnoldi approach was employed to create a reduced-order model that maintains the key features of the initial full-order model. The strong singular and supersingular integrals within the sensitivity equations can be calculated directly utilizing the singularity elimination technique. Finally, several numerical examples confirm the accuracy and efficiency of the proposed algorithm.