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

TL;DR

This paper introduces a Nesterov's acceleration-based method for level set structural optimization, deriving a nonlinear wave PDE to improve convergence speed in topology optimization problems.

Contribution

It develops a novel PDE derived from Nesterov's method for level set functions, enhancing convergence in topology optimization.

Findings

Faster convergence to optimal configurations compared to reaction-diffusion methods

Application to minimum mean compliance problem demonstrates effectiveness

Implementation provided in FreeFEM++ code

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.