In this paper, several accelerating strategies for the numerical methods of topology optimization are proposed. In our implementation, the finite element method is used for discretization, and the novelty of this research lies in two aspects. Two different meshes with variable element sizes are used to discretize the state equation and the level-set evolution equation. On the other hand, GPU-based accelerating schemes are implemented both for finite element assembler and sparse linear solver. Such combination is shown numerically to be effective to reduce the computational costs. Numerical illustrations are presented on several benchmark problems for topology optimization, such as the Cantilever and MBB problems. Compared with the traditional finite element calculations, our GPU-based two-grid schemes run up to 20 times faster without losing numerical accuracy.

针对拓扑优化的数值方法，提出了几种加速策略。在我们的实现中，有限元方法被用于离散化，并且这项研究的新颖性在于两个方面。使用两个具有可变元素大小的不同网格来离散状态方程和水平集演化方程。另一方面，基于GPU的加速方案既适用于有限元汇编程序，也适用于稀疏线性求解器。这种组合在数值上显示为有效地减少了计算成本。给出了有关拓扑优化的几个基准问题的数字插图，例如悬臂和MBB问题。与传统的有限元计算相比，