Higher-order meshing of implicit geometries—Part I: Integration and interpolation in cut elements

T. P. Fries*, Samir Omerovic, D. Schöllhammer, Jakob Steidl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An accurate implicit description of geometries is enabled by the level-set method. Level-set data is given at the nodes of a higher-order background mesh and the interpolated zero-level sets imply boundaries of the domain or interfaces within. The higher-order accurate integration of elements cut by the zero-level sets is described. The proposed strategy relies on an automatic meshing of the cut elements. Firstly, the zero-level sets are identified and meshed by higher-order surface elements. Secondly, the cut elements are decomposed into conforming sub-elements on the two sides of the zero-level sets. Any quadrature rule may then be employed within the sub-elements. The approach is described in two and three dimensions without any requirements on the background meshes. Special attention is given to the consideration of corners and edges of the implicit geometries.

Original languageEnglish
Pages (from-to)759-784
Number of pages26
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Jan 2017


  • Fictitious domain method
  • GFEM
  • Interface capturing
  • Level-set method
  • Numerical integration
  • XFEM

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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