Consistent boundary conditions for PDE filter regularization in topology optimization

Mathias Wallin, Niklas Ivarsson, Oded Amir, Daniel Tortorelli

Research output: Contribution to journalArticlepeer-review


Design variables in density-based topology optimization are typically regularized using filtering techniques. In many cases, such as stress optimization, where details at the boundaries are crucially important, the filtering in the vicinity of the design domain boundary needs special attention. One well-known technique, often referred to as “padding,” is to extend the design domain with extra layers of elements to mitigate artificial boundary effects. We discuss an alternative to the padding procedure in the context of PDE filtering. To motivate this augmented PDE filter, we make use of the potential form of the PDE filter which allows us to add penalty terms with a clear physical interpretation. The major advantages of the proposed augmentation compared with the conventional padding is the simplicity of the implementation and the possibility to tune the boundary properties using a scalar parameter. Analytical results in 1D and numerical results in 2D and 3D confirm the suitability of this approach for large-scale topology optimization.

Original languageEnglish (US)
Pages (from-to)1299-1311
Number of pages13
JournalStructural and Multidisciplinary Optimization
Issue number3
StatePublished - Sep 1 2020


  • Boundary effects
  • PDE filter
  • Topology optimization

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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