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

2022/05/29 by Tomoyuki Oka, Oka, Tomoyuki, Ryota Misawa +3
Computer Science · Engineering · #35Q93 #47J35 (Secondary) #80M50 (Primary) #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2205.14780

openalex publication_date 2022/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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