Multi-level Adjoint-Based Aeroshape Optimization Using Active Subspace

Adjoint evaluations are increasingly used in gradient-based aerodynamic shape optimization due to their cost-effectiveness. However, high-dimensional gradient based optimizations face the curse of dimensionality, leading to higher computational costs and slower convergence rates. This paper introduces a novel multi-level strategy to accelerate convergence. The approach structures the optimization into hierarchical levels, where each level corresponds to a sub-optimization within a reduced-dimensional active subspace. The subspace’s dimension gradually increases as the optimization progresses, with the final level addressing the full-dimensional space. This aims to guide the optimizer toward the correct optimum during early iterations while minimizing errors from dimension reduction in the later stages. The method was validated on a 13-dimensional analytical geometry parametrization problem, achieving a 19