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

  • Authors:

  • Chohong Min;Frédéric Gibou

  • Affiliations:

  • Mathematics Department, KyungHee University, Seoul, Republic of Korea;Mechanical Engineering Department & Computer Science Department, University of California, Santa Barbara, CA 93106, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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Abstract

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.