Comparison of model order reduction techniques with one-shot procedure for topology optimization for thermal applications
For engineers performing topology optimization with large-scale simulations, this work offers a practical acceleration method, though it is incremental as it combines existing MOR and one-shot techniques.
The paper investigates model order reduction (MOR) techniques to accelerate density-based topology optimization for thermal applications, achieving up to 16x speedup over high-fidelity simulations when combined with the one-shot method.
Density-based topology optimization has become a powerful method for automatically generating optimized designs in a wide variety of applications. However, it comes with a large computational cost when solving the physical model requires large-scale simulations. Here, we investigate the use of model order reduction (MOR) techniques to accelerate the simulations in the context of thermal design applications. We project the governing and the adjoint equations onto a low-dimensional subspace by constructing two distinct reduced bases -- one for the forward state and one for the adjoint system -- using solution snapshots from previous design iterations. These snapshots are generated using either the high-fidelity solver or inaccurate fast solvers, such as the one-shot method \citep{amir2024one}. Additionally, we demonstrate that properly selecting the stopping criterion for the iterative linear solver is crucial for the effective use of reduced models. In our 3D example, the proposed framework reduces the overall total simulation time relative to the high-fidelity workflow by a factor up to $3$ when combined with high-fidelity solves and a factor up to $16$ when combined with the one-shot method. Moreover, we find that the reduced order model approach is able to achieve a speed up of $1.54$ with respect to the one-shot method.