Primal–dual on-the-fly reduced-order modeling for large-scale transient dynamic topology optimization

Managing large-scale topology optimization under dynamic loading poses significant computational and storage challenges as against static loading. In order to fill this gap in computational cost, this paper proposes a reduced order modeling strategy that involves constructing discrete basis functions (modes) in adaptive fashion for both the primal as well as dual problem in topology optimization of transient dynamic systems. The projection bases are enriched based on the residual threshold of the corresponding systems. We address the computational cost and scalability of the ROM learning and updating phases. The approach is validated using 2D and 3D benchmark problems, by comparing alternative reduced-order-sensitivity formulations and projection basis update schemes.