A level set formulation of Willmore flow is derived using the gradient flow perspective. Starting from single embedded surfaces and the corresponding gradient flow, the metric is generalized to sets of level set surfaces using the identification of normal velocities and variations of the level set function in time via the level set equation. The approach in particular allows to identify the natural dependent quantities of the derived variational formulation. Furthermore, spatial and temporal discretization are discussed and some numerical simulations are presented.
Marc Droske; Martin Rumpf. A level set formulation for Willmore flow. Interfaces and free boundaries, Tome 6 (2004) no. 3, pp. 361-378. doi: 10.4171/ifb/105
@article{10_4171_ifb_105,
author = {Marc Droske and Martin Rumpf},
title = {A level set formulation for {Willmore} flow},
journal = {Interfaces and free boundaries},
pages = {361--378},
year = {2004},
volume = {6},
number = {3},
doi = {10.4171/ifb/105},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/105/}
}
TY - JOUR
AU - Marc Droske
AU - Martin Rumpf
TI - A level set formulation for Willmore flow
JO - Interfaces and free boundaries
PY - 2004
SP - 361
EP - 378
VL - 6
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/105/
DO - 10.4171/ifb/105
ID - 10_4171_ifb_105
ER -
%0 Journal Article
%A Marc Droske
%A Martin Rumpf
%T A level set formulation for Willmore flow
%J Interfaces and free boundaries
%D 2004
%P 361-378
%V 6
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/105/
%R 10.4171/ifb/105
%F 10_4171_ifb_105
