Acoustic sensitivity analysis for 3D structure with constant cross-section using 2.5D singular boundary method

In this paper, a 2.5D singular boundary method (SBM) in conjunction with the direct differentiation method (DDM) and adjoint variable method (AVM) are formulated for the sensitivity analysis of 3D longitudinally invariant structures. The assumption of a constant cross-section in the longitude direction enables it possible to decouple the 3D system into 2D problems at every wavenumber, and thus makes it a 2.5D-problem. The 2D sensitivity problem is solved by a boundary-type method, SBM. The SBM solves a problem with a linear combination of the fundamental solutions with respect to boundary collocation points. The fundamental solution makes the SBM available for exterior problems without the artificial truncated boundary. The source singularity issue of fundamental solution is overcome by a simple analytical formula and its derivatives. Numerical experiments present the accuracy, efficiency and feasibility of the proposed methods, and indicate that the proposed methods can be considered as an effective alternative in 3D problems with a longitudinally invariant cross-section.