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On Level Set Formulations for Anisotropic Mean Curvature Flow and Surface Diffusion

  • Ulrich Clarenz
  • Frank Haußer
  • Martin Rumpf
  • Axel Voigt
  • Ulrich Weikard
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 149)

Abstract

Anisotropic mean curvature motion and in particular anisotropic surface diffusion play a crucial role in the evolution of material interfaces. This evolution interacts with conservations laws in the adjacent phases on both sides of the interface and are frequently expected to undergo topological chances. Thus, a level set formulation is an appropriate way to describe the propagation. Here we recall a general approach for the integration of geometric gradient flows over level set ensembles and apply it to derive a variational formulation for the level set representation of anisotropic mean curvature motion and anisotropic surface flow. The variational formulation leads to a semi-implicit discretization and enables the use of linear finite elements.

Keywords

level set method anisotropic mean curvature flow anisotropic surface diffusion semi-implicit time discretization 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Ulrich Clarenz
    • 1
  • Frank Haußer
    • 2
  • Martin Rumpf
    • 1
  • Axel Voigt
    • 2
  • Ulrich Weikard
    • 1
  1. 1.Numerical Analysis and Scientific ComputingUniversität Duisburg-EssenDuisburgGermany
  2. 2.Crystal Growth groupresearch center caesarBonnGermany

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