By Xiao-Ping Wang, Hong Kong University of Science and Technology

The threshold dynamics method developed by Merriman, Bence and Osher(MBO) is an efficient method for simulating the motion by mean curvature flow when the interface is away from the solid boundary.  Direct generalization of the MBO type method to the wetting problems with interface intersecting the solid boundary is not easy because solving heat equation on general domain with wetting boundary condition is not as efficient as that for the original MBO method. The dynamics of the contact point also follows a different dynamic law compared to interface dynamics away from the boundary. We develop an efficient volume preserving threshold dynamics (MBO) method for drop spreading on rough surfaces. The method is based on minimization of the weighted surface area functional over a extended domain that includes the solid phase.   
The method is  simple, stable with the complexity O (N log N) per time step and it is not sensitive to the inhomogeneity or roughness of the solid boundary. We also extend the idea to an efficient method for image segmentation.