No. 2021.14
Sobolev Gradients for the Möbius Energy
Ph. Reiter and H. Schumacher
Subject:
Abstract
Aiming to optimize the shape of closed embedded curves within prescribed isotopy classes, we use a gradient-based approach to approximate stationary points of the Möbius energy. The gradients are computed with respect to Sobolev inner products similar to the $W^{3/2,2}$-inner product. This leads to optimization methods that are significantly more efficient and robust than standard techniques based on $L^2$-gradients.
Reference
Arch. Rational Mech. Anal (Sept. 2021)