Volume 46, Number 6, November-December 2012
|Page(s)||1509 - 1526|
|Published online||13 June 2012|
Phase field method for mean curvature flow with boundary constraints
CMAP, École Polytechnique, 91128
2 Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, UMR 5224, B.P. 53, 38041 Grenoble Cedex 9, France
Received: 14 April 2011
Revised: 9 January 2012
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a Γ-convergence result and then show some numerical comparisons of these two different models.
Mathematics Subject Classification: 49Q / 35B / 35K
Key words: Allen Cahn equation / mean curvature flow / boundary constraints / penalization technique / gamma-convergence / Fourier splitting method
© EDP Sciences, SMAI, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.