  In gradient-based time domain topology optimization, design sensitivity
analysis (DSA) of the dynamic response is essential, and requires high
computational cost to directly differentiate, especially for high-order dynamic
system. To address this issue, this study develops an efficient reduced basis
method (RBM)-based discrete adjoint sensitivity analysis method, which on the
one hand significantly improves the efficiency of sensitivity analysis and on
the other hand avoids the consistency errors caused by the continuum method. In
this algorithm, the basis functions of the adjoint problem are constructed in
the offline phase based on the greedy-POD method, and a novel model-based
estimation is developed to facilitate the acceleration of this process. Based
on these basis functions, a fast and reasonably accurate model is then built by
Galerkin projection for sensitivity analysis in each dynamic topology
optimization iteration. Finally, the effectiveness of the error measures, the
efficiency and the accuracy of the presented reduced-order method are verified
by 2D and 3D dynamic structure studies.
