Nesterov?s acceleration for level set-based topology optimization using reaction-diffusion equations

This paper discusses level set-based structural optimization. Level set-based structural op-timization is a method used to determine an optimal configuration for minimizing objec-tive functionals by updating level set functions characterized as solutions to partial dif-ferential equations (PDEs) (e.g., Hamilton-Jacobi and reaction-diffusion equations). In this study, based on Nesterov's accelerated gradient method, a nonlinear (damped) wave equa-tion 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 con-vergence to an optimal configuration faster than methods using only a reaction-diffusion equation, and moreover, its FreeFEM++ code will also be described.(c) 2023 Elsevier Inc. All rights reserved.