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

DOI10.1016/j.apm.2023.03.024zbMath1525.35222arXiv2205.14780WikidataQ123014042 ScholiaQ123014042MaRDI QIDQ6072675

Ryota Misawa, Tomoyuki Oka, Takayuki Yamada

Publication date: 13 October 2023

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.14780

zbMATH Keywords

level set methodreaction-diffusion equationtopology optimizationNesterov's accelerated gradient methodnonlinear (damped) wave equation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Optimization problems in thermodynamics and heat transfer (80M50) Nonlinear evolution equations (47J35) PDEs in connection with control and optimization (35Q93)

Related Items

Topology optimization with geometric constraints for additive manufacturing based on coupled fictitious physical model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On projection methods, convergence and robust formulations in topology optimization
• Structural optimization with FreeFem++
• A topology optimization method based on the level set method incorporating a fictitious interface energy
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Generating optimal topologies in structural design using a homogenization method
• Structural optimization using sensitivity analysis and a level-set method.
• A level-set method for shape optimization.
• Analysis of meshless weak and strong formulations for boundary value problems
• A boundary element and level set based bi-directional evolutionary structural optimisation with a volume constraint
• A level set method for structural topology optimization.
• Topological derivatives in shape optimization
• Structural optimization based on meshless element free Galerkin and level set methods
• A parametrized level set based topology optimization method for analysing thermal problems
• The localized radial basis functions for parameterized level set based structural optimization
• A new algorithm for topology optimization using a level-set method
• A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
• New development in freefem++
• The Homogenization Method for Topology Optimization of Structures: Old and New
• Shape optimization by the homogenization method