A Level Set Method Using the Signed Distance Function

Masato Kimura, Hirofumi Notsu

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)415-446
Number of pages32
JournalJapan Journal of Industrial and Applied Mathematics
Volume19
Issue number3
Publication statusPublished - 2002 Oct
Externally publishedYes

Keywords

  • Finite element method
  • Level set method
  • Moving boundary problem
  • Numerical analysis
  • Signed distance function

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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