A simple scheme for volume-preserving motion by mean curvature

In this article, we present a diffusion-generated approach for evolving volume-preserving motion by mean curvature. Our algorithm alternately diffuses and sharpens characteristic functions to produce a normal velocity which equals the mean curvature minus the average mean curvature. This simple algorithm naturally treats topological mergings and breakings and can be made very fast even when the volume constraint is enforced to double precision (or more). Two dimensional numerical studies are provided to demonstrate the convergence of the method for smooth and nonsmooth problems.