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 grain boundaries are zero-level sets of signed distance functions. Curvature motion is achieved by first diffusing locally maintained signed distance functions followed by a reinitialization step. A technique is devised to allow a single signed distance function to represent a large subset of spatially separated grains. Hundreds of thousands of grains can be simulated using a small number of signed distance functions (in this work, 32 in two dimensions and 64 in three dimensions are more than sufficient) using modest computational hardware.