U. Clarenz, F. Haußer, M. Rumpf, A. Voigt, and U. Weikard.
On level set formulations for anisotropic mean curvature flow and
In A. Voigt, editor, Multiscale Modeling in Epitaxial Growth,
volume 149 of International Series of Numerical Mathematics, pages
227-238. Birkhäuser, 2004.
[ bib | .pdf 1 ]
Anisotropic mean curvature motion and in particular anisotropic surface diffusion play a crutial role in the evolution of material interfaces on microdevices. 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.