Nesterov's acceleration for level set-based topology optimization using reaction-diffusion equations
Nesterov's acceleration for level set-based topology optimization using reaction-diffusion equations
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Nesterov 使用反应扩散方程加速基于水平集的拓扑优化
DOI：
10.1016/j.apm.2023.03.024
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发表时间：
2023
影响因子：
5
通讯作者：
Yamada Takayuki
中科院分区：
文献类型：
--
作者：
Oka Tomoyuki;Misawa Ryota;Yamada Takayuki
本文讨论了基于水平集的结构优化问题。基于水平集的结构优化是一种通过更新以偏微分方程（例如，Hamilton-Jacobi和反应-扩散方程）的解为特征的水平集函数来确定最小化目标函数的最优配置的方法。本研究基于Nesterov加速梯度法，将非线性（阻尼）波动方程导出为水平集函数满足的偏微分方程，并将其应用于最小平均柔度问题。在数值上，本研究中开发的方法将比仅使用反应扩散方程的方法更快地收敛到最佳配置，而且，它的FreeFEM++代码也将被描述。
This paper discusses level set-based structural optimization. Level set-based structural optimization is a method used to determine an optimal configuration for minimizing objective functionals by updating level set functions characterized as solutions to partial differential equations (PDEs) (e.g., Hamilton-Jacobi and reaction-diffusion equations). In this study, based on Nesterov’s accelerated gradient method, a nonlinear (damped) wave equation will be derived as a PDE satisfied by level set functions and applied to minimum mean compliance problems. Numerically, the method developed in this study will yield convergence to an optimal configuration faster than methods using only a reaction-diffusion equation, and moreover, its FreeFEM++ code will also be described.