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Communications in Mathematics and Statistics

, Volume 7, Issue 4, pp 459–474 | Cite as

Numerical Integration Over Implicitly Defined Domains with Topological Guarantee

  • Tianhui Yang
  • Ammar Qarariyah
  • Hongmei Kang
  • Jiansong DengEmail author
Article
  • 88 Downloads

Abstract

Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting the correct topology of the domain. Furthermore, a geometry-based local error estimate is explored to guide the hierarchical subdivision and save the computation cost. Numerical experiments are presented to demonstrate the accuracy and the potential of the proposed method.

Keywords

Isogeometric analysis Numerical integration Implicitly defined domains Topological guarantee Interval arithmetic Local error estimate Hierarchical subdivision 

Mathematics Subject Classification

65D30 

Notes

Acknowledgements

We would like to thank the anonymous reviewers and our laboratory group for helpful discussions and comments. The work is supported by the National Natural Science Foundation of China (No. 11771420).

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Copyright information

© School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Tianhui Yang
    • 1
  • Ammar Qarariyah
    • 1
  • Hongmei Kang
    • 2
  • Jiansong Deng
    • 1
    Email author
  1. 1.School of Mathematical ScienceUniversity of Science and Technology of ChinaHefeiChina
  2. 2.School of Mathematical SciencesSoochow UniversitySuzhouChina

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