On the use of Multigrid Preconditioners for Topology Optimization

Abstract: Topology optimization for large scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the Finite Element Analysis (FEA). However, the preconditioners used in these works vary, and in many cases are notably suboptimal. A handful of works have already demonstrated the effectiveness of Geometric Multigrid (GMG) preconditioners in topology optimization. Here, we show that Algebraic Multigrid (AMG) preconditioners offer superior robustness with only a small overhead cost. The difference is most pronounced when the optimization develops fine-scale structural features or multiple solutions to the same linear system are needed. We thus argue that the expanded use of AMG preconditioners in topology optimization will be essential for the optimization of more complex criteria in large-scale 3D domains.