发表机构
Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE); Institute of Mathematics, École polytechnique fédérale de Lausanne（工程数值方法国际中心; 洛桑联邦理工学院数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于降阶建模和预处理技术的参数化拓扑优化框架，利用EIFEM和DEIM构造降阶算子，以不精确梯度加速收敛，并通过几何特征参数化提高可制造性，实验表明能显著加速在线优化并有时产生更刚设计。
AI 中文摘要
拓扑优化（TopOpt）是结构概念设计的标准工具，以极大的设计自由度提供最优结构。然而，由于需要重复评估高保真有限元模型，其计算成本高昂，并且经常产生复杂的几何形状，需要大量解释才能实现可制造性。作为替代方案，本工作提出了一种基于降阶建模（ROM）和预处理技术的参数化优化框架。我们采用经验跨尺度有限元方法（EIFEM）结合离散经验插值方法（DEIM）来构造局部的、参数相关的降阶算子。从优化的角度来看，这种方法可以解释为一种预处理策略，其中使用不精确梯度来加速收敛。此外，通过显式几何特征（如夹杂半径或晶格宽度）对设计空间进行参数化，显著提高了所得优化设计的可制造性。我们以拓扑优化为基准，针对三种不同的单胞几何形状和三个不同的基准测试，评估了该方法在计算时间、设计拓扑和结构性能方面的表现。虽然参数化ROM框架需要初始的离线训练阶段，但我们的比较分析表明，它极大地加速了在线优化循环，并且在我们的一些实验中能够产生更刚性的设计。
英文摘要
Topology optimization (TopOpt) is a standard tool for structural conceptual design, providing optimal structures with great design freedom. However, it has a high computational costs due to the repeated evaluation of high-fidelity finite element models and frequently produces complex geometries that require extensive interpretation for manufacturability. As an alternative, this work presents a parameterized optimization framework based on Reduced Order Modeling (ROM) and preconditioning techniques. We employ the Empirical Interscale Finite Element Method (EIFEM) coupled with the Discrete Empirical Interpolation Method (DEIM) to construct localized, parameter-dependent reduced operators. From an optimization perspective, this approach can be interpreted as a preconditioning strategy in which inexact gradients are used to accelerate convergence. Furthermore, parameterizing the design space in terms of explicit geometric features, such as inclusion radii or lattice widths, significantly improves the manu facturability of the resulting optimized designs. We assess the performance of the method in terms of computational time, design topology and structural performance with TopOpt as baseline for three differ ent unit cell geometries and three different benchmarks. While the parametric ROM framework requires an initial offline training phase, our comparative analysis demonstrates that it drastically accelerates the online optimization loop and that it can produce even stiffer design in some of our experiments.
