Comparison of model order reduction techniques with one-shot procedure for topology optimization for thermal applications

TL;DR

This paper explores the use of model order reduction techniques to significantly accelerate thermal topology optimization simulations, achieving up to 16-fold speedups in 3D cases.

Contribution

It introduces a framework combining MOR with one-shot procedures and highlights the importance of solver stopping criteria for efficient reduced models.

Findings

Reduced simulation time by up to 16 times in 3D examples.

Achieved a 1.54 times speedup over the one-shot method.

Effective MOR depends on proper solver stopping criteria.

Abstract

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.