Approximation of the mean curvature flow of thin structures

par Chih-Kang Huang (LJAD)

mardi 17 févr. 2026, 11:00 → 12:15 Europe/Paris

Salle de Conference (LJAD)

We address the approximation of the mean curvature flow of thin structures, for which classical phase-field methods are not adapted. By thin structures, we refer to surfaces that are not domain boundaries, typically higher codimension objects such as filaments in 3D or non-orientable surfaces. We propose a new approach that introduces a localized penalization term into the Allen-Cahn equation around the skeleton of the evolving set. This approximation guarantees a minimum thickness during evolution, thereby prohibiting self intersections.

The numerical efficiency of our approach is illustrated by approximations of the mean curvature flow of filaments. We also demonstrate its application to the Steiner problem and the Plateau problem. This is joint work with Elie Bretin (INSA Lyon) and Simon Masnou (Lyon 1). Finally, we also discuss perspectives on the controllability of the Allen-Cahn equation.