A novel reduced basis method for adjoint sensitivity analysis of dynamic topology optimization

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 estimator is developed to accurately predict the true error for facilitating 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 efficiency and accuracy of the suggest method are verified by 2D and 3D dynamic structure studies.