(untitled) (Journal of Computational Mathematics, 2025)
This paper presents various acceleration techniques tailored for the traditional 3D topology optimization problem. Firstly, the adoption of the finite difference method leads to a sparser stiffness matrix, resulting in more efficient matrix-vector multiplication. Additionally, a fully matrix-free technique is proposed, which only assembles stiffness matrices at the coarsest grid level and does not require complex node numbering. Moreover, an innovative N-cycle multigrid (MG) algorithm is proposed to act as a preconditioner within conjugate gradient (CG) iterations. Finally, to further enhance the optimization process on high-resolution grids, a progressive strategy is implemented. The numerical results confirm that these acceleration techniques are not only efficient, but also capable of achieving lower compliance and reducing memory consumption. MATLAB codes complementing the article can be downloaded from Github.