A minimization-based finite element formulation for interface-preserving level set reinitialization

Abstract

This paper presents a new approach to reinitialization in finite element methods for the level set transport equation. The proposed variational formulation is derived by solving a minimization problem. A penalty term is introduced to preserve the shape of the free interface in the process of redistancing. In contrast to hyperbolic PDE reinitialization, the resulting boundary value problem is elliptic and can be solved using a simple fixed-point iteration method. The minimization-based approach makes it possible to define the desired geometric properties in terms of a suitable potential function. In particular, truncated distance functions can be generated using a double-well potential. The results of a numerical study indicate that the new methodology is a promising alternative to conventional reinitialization techniques.