Diffusion generated motion for grain growth in two and three dimensions

An efficient algorithm for accurately simulating curvature flow for large networks of curves in two dimensions and surfaces in three dimensions on uniform grids is proposed. This motion arises in the technologically important problem of simulating grain boundary motion in polycrystalline materials. In this formulation grains are zero level sets of signed distance functions. Curvature motion is achieved by first diffusing the signed distance functions followed by a reinitialization step. A technique is devised to allow a single signed distance function to represent many grains allowing the simulation of a very large number (hundreds of thousands) of grains using modest computational hardware.