Phase-field based topology optimization with polygonal elements: A finite volume approach for the evolution equation

Arun L. Gain, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


Uniform grids have been the common choice of domain discretization in the topology optimization literature. Over-constraining geometrical features of such spatial discretizations can result in mesh-dependent, sub-optimal designs. Thus, in the current work, we employ unstructured polygonal meshes constructed using Voronoi tessellations to conduct structural topology optimization. We utilize the phase-field method, derived from phase transition phenomenon, which makes use of the Allen-Cahn differential equation and sensitivity analysis to update the evolving structural topology. The solution of the Allen-Cahn evolution equation is accomplished by means of a centroidal Voronoi tessellation (CVT) based finite volume approach. The unstructured polygonal meshes not only remove mesh bias but also provide greater flexibility in discretizing complicated (e.g. non-Cartesian) domains. The features of the current approach are demonstrated using various numerical examples for compliance minimization and compliant mechanism problems.

Original languageEnglish (US)
Pages (from-to)327-342
Number of pages16
JournalStructural and Multidisciplinary Optimization
Issue number3
StatePublished - Sep 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Allen-Cahn equation
  • Phase-field method
  • Polygonal finite elements
  • Topology optimization
  • Voronoi tessellation


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