Wave-type threshold dynamics and the hyperbolic mean curvature flow

TL;DR

This paper presents a novel wave-equation-based thresholding algorithm for simulating curvature-driven interfacial motions, including volume-preserving and multiphase dynamics, offering an alternative to traditional diffusion-based methods.

Contribution

It introduces a new wave-type thresholding method for curvature-dependent interfacial motion, expanding computational tools beyond diffusion-based approaches.

Findings

Effective simulation of volume-preserving motions

Successful application to multiphase systems

Demonstrates stability and accuracy of the method

Abstract

We introduce a method for computing interfacial motions governed by curvature dependent acceleration. Our method is a thresholding algorithm of the BMO-type which, instead of utilizing a diffusion process, thresholds evolution by the wave equation to obtain the desired interfacial dynamics. We also develop the numerical method and present results of its application, including an investigation of the volume preserving and multiphase motions.