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A level set method using the signed distance function

Dedicated to Professors Masayasu Mimura and Takaaki Nishida on the occasion of their sixtieth birthdays
  • Masato Kimura
  • Hirofumi Notsu
Article

Abstract

A level set method based on the piecewise linear finite element approximation of the signed distance function is proposed for several moving boundary problems. As a prototype of our level set method, we consider a level set discretization of the mean curvature flow problem and give an effective algorithm guaranteed by the maximum principle. Two-phase generalized Stefan problem and one-phase Hele-Shaw problem are also solved as applications of our level set method. Through the simulations of these moving boundary problems, we check the reliability, practicality and applicability of our methods, in particular, we observe good experimental orders of convergence.

Key words

numerical analysis finite element method level set method moving boundary problem signed distance function 

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Copyright information

© JJIAM Publishing Committee 2002

Authors and Affiliations

  1. 1.Graduate School of MathematicsKyushu UniversityFukuokaJapan
  2. 2.Graduate School of ScienceHiroshima UniversityHigashi-HiroshimaJapan

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