On the inclusion of damping terms in the hyperbolic MBO algorithm

TL;DR

This paper introduces a damping term into the hyperbolic MBO algorithm, develops numerical methods for it, and demonstrates its ability to approximate standard mean curvature flow.

Contribution

The paper generalizes the hyperbolic MBO algorithm by incorporating damping terms and provides numerical methods and validation for this extension.

Findings

The generalized hyperbolic MBO can approximate standard mean curvature flow.

Numerical methods for the damped hyperbolic MBO are constructed and tested.

The damping term improves the algorithm's flexibility in modeling interfacial motion.

Abstract

The hyperbolic MBO is a threshold dynamic algorithm which approximates interfacial motion by hyperbolic mean curvature flow. We introduce a generalization of this algorithm for imparting damping terms onto the equation of motion. We also construct corresponding numerical methods, and perform numerical tests. We also use our results to show that the generalized hyperbolic MBO is able to approximate motion by the standard mean curvature flow.