A critical comparative assessment of differential equation-driven methods for structural topology optimization

Arun L. Gain, Glaucio Paulino

Research output: Contribution to journalReview article


In recent years, differential equation-driven methods have emerged as an alternate approach for structural topology optimization. In such methods, the design is evolved using special differential equations. Implicit level-set methods are one such set of approaches in which the design domain is represented in terms of implicit functions and generally (but not necessarily) use the Hamilton-Jacobi equation as the evolution equation. Another set of approaches are referred to as phase-field methods; which generally use a reaction-diffusion equation, such as the Allen-Cahn equation, for topology evolution. In this work, we exhaustively analyze four level-set methods and one phase-field method, which are representative of the literature. In order to evaluate performance, all the methods are implemented in MATLAB and studied using two-dimensional compliance minimization problems.

Original languageEnglish (US)
Pages (from-to)685-710
Number of pages26
JournalStructural and Multidisciplinary Optimization
Issue number4
StatePublished - Jul 3 2013



  • Allen-Cahn equation
  • Compliance minimization
  • Differential equation-driven methods
  • Hamilton-Jacobi equation
  • Level-set method
  • Phase-field method

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization

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