基于反应扩散方程的水平集拓扑optimization的Nesterov加速
Nesterov's acceleration for level set-based topology optimization using reaction-diffusion equations
摘要：
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用于通过更新表征为偏微分方程（PDE）（例如，Hamilton-Jacobi和反应扩散方程）。本文基于Nesterov的加速方法，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，并应用于最小平均柔度问题。在数值上，在这项研究中开发的方法将产生收敛到最佳配置比只使用一个反应扩散方程的方法更快，而且，它的FreeFEM++代码也将被描述。
英文摘要：
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.
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