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

Abstract

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.