Numerical methods for geometric motion 

Brian R. Wetton, University of British Columbia

10/23, 2023 at 11:30am-12:30pm (HH312)

We consider the evolution of curves and curve networks in 2D. We describe it as geometric motion if the evolution only depends on the shape of the curve. There are applications in material science (the evolution of microstructure in materials), biochemistry, and image processing. An overview and comparison of several mathematical formulations of the geometric evolution of curves is given, including tracking and level sets, and their numerical approximation. Two new gradient flow models are derived and their numerical implementation in a general computational framework is described.