On Pixel-swap Sensitivities in Acoustic Material-distribution Topology Optimization

Sammanfattning

This thesis studies finite-variation sensitivity analysis for binary acoustic topology optimization. The model problem is a two-dimensional transition section between waveguides of different widths, where each design element is either fluid or sound-hard material. The objective is to minimize the reflected planar-wave amplitude at the inlet. Because a binary pixel swap is a finite material change, conventional adjoint sensitivities do not necessarily reproduce the exact objective variation caused by switching an element. The thesis therefore compares direct pixel-swap sensitivities with an efficient Sherman--Morrison--Woodbury (SMW) formulation, which treats the local material change as a low-rank perturbation of the Helmholtz system. The numerical results show that the SMW sensitivity agrees with the direct pixel-swap calculation to numerical precision while significantly reducing the computational cost. Optimization examples demonstrate strong reflection reduction for both single-frequency and sampled multi-frequency cases. The work shows that SMW-based finite-variation sensitivities provide an accurate and efficient tool for binary acoustic topology optimization.