Wave-type threshold dynamics and the hyperbolic mean curvature flow

2015/05/08 by Elliott Ginder, Ginder, Elliott, Karel Švadlenka +1
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Navier-Stokes equation solutions #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1505.01963

openalex publication_date 2015/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• On the inclusion of damping terms in the hyperbolic MBO algorithm
• Analysis of thresholding for codimension two motion by mean curvature: a gradient-flow approach
• The thresholding scheme for mean curvature flow and de Giorgi's ideas\n for minimizing movements
• Convergence of thresholding schemes incorporating bulk effects
• Convergence of the thresholding scheme for multi-phase mean-curvature\n flow