Geometric integration over irregular domains with application to level-set methods

Chohong Min, Frédéric Gibou

Research output: Contribution to journalArticlepeer-review

90 Scopus citations


We present a geometric approach for calculating integrals over irregular domains described by a level-set function. This procedure can be used to evaluate integrals over a lower dimensional interface and may be used to evaluate the contribution of singular source terms. This approach produces results that are second-order accurate and robust to the perturbation of the interface location on the grid. Moreover, since we use a cell-wise approach, this procedure can be easily extended to quadtree and octree grids. We demonstrate the second-order accuracy and the robustness of the method in two and three spatial dimensions.

Original languageEnglish
Pages (from-to)1432-1443
Number of pages12
JournalJournal of Computational Physics
Issue number2
StatePublished - 1 Oct 2007


  • Integration
  • Isosurfacing
  • Level-set methods
  • Quadtree/octree data structures


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