论文标题
Nesterov使用反应扩散方程的基于水平集的拓扑优化的加速度
Nesterov's acceleration for level set-based topology optimization using reaction-diffusion equations
论文作者
论文摘要
本文讨论了基于级别的结构优化。基于级别集的结构优化是一种方法，用于确定最佳配置，以通过更新为部分微分方程（PDES）的解决方案（例如Hamilton-Jacobi和Reaction-diffusion-fiffusion方程）来最大程度地降低目标函数。在这项研究中，基于Nesterov的加速方法，非线性（阻尼）波方程将作为PDE得出，以通过级别集合函数满足，并应用于最小平均依从性问题。从数值上讲，本研究中开发的方法将收敛到最佳配置比仅使用反应扩散方程更快的方法，此外，还将描述其FreeFem ++代码。
This paper discusses level set-based structural optimization. Level set-based structural optimization is a method used to determine an optimal configuration for minimizing an objective functional 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 method, a nonlinear (damped) wave equation will be derived as a PDE satisfied by level set functions and applied to a minimum mean compliance problem. 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.
