Yet another parameter-free shape optimization method

Kenneth E. Swartz, Ketan Mittal, Mathias Schmidt, Jorge Luis Barrera, Seth Watts, Daniel A. Tortorelli

Research output: Contribution to journalArticlepeer-review


The use of node coordinates as design variables in shape optimization offers a larger design space than computer-aided design (CAD)-based shape parameterizations. It also allows for the optimization of legacy designs, i.e., a finite element mesh from an existing design can be readily optimized to meet new performance requirements without involving a CAD model. However, it is well known that the node coordinate parameterization method is fraught with numerical difficulties, which makes it impractical to use. This has led to several of “parameter-free” shape optimization methods that seek the advantages and avoid the pitfalls of the naïve node coordinate parameterization method. These methods come in two main varieties: sensitivity filtering (or gradient smoothing) and consistent filtering. The latter is analogous to the density filter method used in topology optimization (TO). Herein, we use the PDE filter from TO and energy-based filters to implement consistent shape optimization filtering schemes easily and efficiently. Numerical experiments demonstrate that consistent methods are more robust than sensitivity filtering methods.

Original languageEnglish (US)
Article number245
JournalStructural and Multidisciplinary Optimization
Issue number12
StatePublished - Dec 2023


  • Consistent filtering
  • Node coordinate parameterization
  • Shape optimization

ASJC Scopus subject areas

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


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