报告题目：Efficient acceleration strategies for multigrid preconditioned conjugate gradients

in fast 3D topology optimization

报 告 人：周丙臻 助理研究员 （宁德时代公司）

报告时间：2025年6月25 日（星期三）下午16:00-17:00

报告地点：数学研究中心528

报告摘要：

This work introduces a set of acceleration techniques designed to improve the efficiency of traditional 3D topology optimization. By adopting the finite difference method, we obtain a sparser stiffness matrix that enables faster matrix-vector multiplication. Building on this, we propose a fully matrix-free approach that assembles stiffness matrices only on the coarsest grid level, eliminating the need for complex node numbering and significantly reducing memory usage. To further enhance convergence, we introduce a novel N-cycle multigrid (MG) algorithm that serves as an effective preconditioner within Conjugate Gradient (CG) iterations. Additionally, a progressive resolution strategy is employed to enable efficient optimization on high-resolution grids. Numerical results demonstrate that these techniques not only accelerate the optimization process and reduce memory consumption but also achieve lower structural compliance. MATLAB codes supporting this work are publicly available on GitHub.

报告人简介：

周丙臻，宁德时代高通量计算助理研究员。2015-2022年硕士和博士就读于湖南师范大学计算数学专业，主要从事三角谱元方法与界面问题的求解和四面体谱元法研究。2018 年入选中国科协优秀中外青年交流计划, 2019 年赴新加坡南洋理工大学访问, 研究SAV方法求解非线性问题。2022-2024 年为香港中文大学(深圳)与中国科技大学联合培养博士后, 研究拓扑优化问题的快速求解算法。目前主要从事电池仿真研究工作。 获宁德市第三批省级创新实验室创新技术人才, 以及宁德市第十六批“天湖人才”。