SEMINARIO DI MATEMATICA APPLICATA
Martedì 14 Luglio 2026, ore 14:00 precise,
nell'Aula C11, Via Mangiagalli 25, Milano
la Prof.ssa Rong Tang, della Hong Kong Polytechnic University
terrà un seminario dal titolo:
An inertial minimal-deformation-rate framework for shape optimization
Sunto:
We present a numerical framework for PDE-constrained shape optimization and Willmore-driven surface hole filling. The method is designed to address two difficulties that often arise in geometric evolution: slow convergence in flat energy landscapes, which may lead to premature stagnation, and deterioration of the computational mesh. The main idea is to combine a second-order inertial flow with a minimal-deformation-rate mesh motion strategy. This accelerates the evolution while maintaining good mesh quality, so that remeshing is not required. For non-smooth or non-convex initial geometries, we further incorporate surface-diffusion regularization in the Barrett–Garcke–Nürnberg framework. We also extend the inertial MDR approach to Willmore-type surface hole filling, where it produces smooth high-order reconstructions from incompatible initial data. Numerical experiments show faster convergence to lower objective values and consistently better mesh preservation during the evolution.