Section: New Results

Willmore flow simulation with diffusion-redistanciation numerical schemes

Participant : Thibaut Metivet.

In collaboration with Arnaud Sengers (Université Claude Bernard), Emmanuel Maitre (Laboratoire Jean Kuntzmann, Grenoble INP) and Mourad Ismail (Laboratoire Interdisciplinaire de Physique, UGA), we have proposed original diffusion-redistanciation numerical schemes to compute the static shapes of elastic membranes with bending stiffness under constant area constraints. This numerical method relies on an implicit representation of the surface which is used as an initial condition for diffusion-like equations. This allows to circumvent the usual difficulties pertaining to the high geometrical order and non-linearities of the bending energy and to benefit from the robustness of discretised diffusion operators. We have implemented the schemes within the finite element library Feel++ and studied the numerical convergence properties in 2D and 3D. We have also validated our method using comparative benchmarks computed with standard approaches. This work has led to the PhD defense of Arnaud Sengers [35] and a publication is under preparation.