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

This paper discusses level set-based structural optimization. Level optimization is a method used to determine an optimal configuration for minimizing objective functionals by updating set functions characterized as solutions partial differential equations (PDEs) (e.g., Hamilton-Jacobi and reaction-diffusion equations). In this study, based on Nesterov’s accelerated gradient method, nonlinear (damped) wave equation will be derived PDE satisfied applied minimum mean compliance problems. Numerically, the developed in study yield convergence faster than methods using only equation, moreover, its FreeFEM++ code also described.