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 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.