TY - JOUR
T1 - Efficient Acceleration Strategies for Multigrid Preconditioned Conjugate Gradients in Fast 3D Topology Optimization
AU - Zhou , Bingzhen
AU - Zhu , Zixian
AU - Wang , Xiaoping
JO - Journal of Computational Mathematics
VL - 5
SP - 1063
EP - 1091
PY - 2025
DA - 2025/09
SN - 43
DO - http://doi.org/10.4208/jcm.2508-m2025-0035
UR - https://global-sci.org/intro/article_detail/jcm/24471.html
KW - Topology optimization, Linear elasticity, Fully matrix-free, Multigrid preconditioned conjugate gradient, Finite difference method.
AB - <p style="text-align: justify;">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.</p>