论文标题
关于使用多移民预调节器进行拓扑优化
On the use of Multigrid Preconditioners for Topology Optimization
论文作者
论文摘要
大规模问题的拓扑优化仍然是一项计算挑战。文献中存在一些解决该主题的作品，所有作品都利用迭代求解器来处理有限元分析（FEA）引起的线性系统。但是，这些作品中使用的预处理各不相同，在许多情况下，次优于次优。少数作品已经证明了几何多格里德（GMG）预处理在拓扑优化中的有效性。在这里，我们表明代数跨国公司（AMG）的预处理提供了出色的鲁棒性，只有很小的高架成本。当优化开发出精细的结构特征或需要对同一线性系统的多个解决方案时，差异最为明显。因此，我们认为，在拓扑优化中扩展的AMG预订器的使用对于优化大规模3D域中更复杂的标准至关重要。
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.
