This paper presents a novel computational scheme for sensitivity analysis of the velocity field in the level set method using the discrete adjoint method. The velocity field is represented in B-spline space, and the adjoint equations are constructed based on the discretized governing equations. The key contribution of this work is the demonstration that the velocity field in the level set method can be entirely obtained from the discrete adjoint method. This eliminates the need for shape sensitivity analysis, which is commonly used in standard level set methods. The results demonstrate the effectiveness of the approach in producing optimized results for stress and linearized buckling problems. Overall, the proposed method has the potential to simplify the way in which topology optimization problems using level set methods are solved, and has significant implications for the design of a broad range of engineering applications.

翻译：本文提出了一种利用离散伴随方法对水平集方法中速度场进行灵敏度分析的新型计算方案。速度场在B样条空间中进行表示，伴随方程基于离散化的控制方程构建。本研究的关键贡献在于证明了水平集方法中的速度场可以完全通过离散伴随方法获得，从而消除了标准水平集方法中常用的形状灵敏度分析需求。数值结果表明，该方法在应力及线性屈曲问题的优化求解中具有有效性。总体而言，所提方法有望简化基于水平集法的拓扑优化问题的求解方式，并对广泛工程应用的设计具有重要影响。