  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.
