Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
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Differential Operators on a Triangular Mesh and Their Applications

삼각형 메쉬 상에서의 미분 연산자와 그 응용

  • Baek, Seung-Yeob (Institute of Advanced Machinery and Design, Seoul National University) ;
  • Kam, Dong-Uk (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Lee, Kunwoo (School of Mechanical and Aerospace Engineering, Seoul National University)
  • 백승엽 (서울대학교 정밀기계설계공동연구소) ;
  • 감동욱 (서울대학교 기계항공공학부) ;
  • 이건우 (서울대학교 기계항공공학부)
  • Received : 2014.09.16
  • Accepted : 2014.12.08
  • Published : 2015.03.01
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Abstract

Solving partial differential equations (PDEs) on a manifold setting is frequently faced problem in CAD, CAM and CAE. However, unlikely to a regular grid, solutions for those problems on a triangular mesh are not available in general, as there are no well-established intrinsic differential operators. Considering that a triangular mesh is a powerful tool for representing a highly-complicated geometry, this problem must be tackled for improving the capabilities of many geometry processing algorithms. In this paper, we introduce mathematically well-defined differential operators on a triangular mesh setup, and show some examples of their applications. Through this, it is expected that many CAD/CAM/CAE application will be benefited, as it provides a mathematically rigorous solution for a PDE problem which was not available before.

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References

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