Geometric simulation and surface statistics of coarsening faceted surfaces

We introduce a general-purpose computational geometry tool for simulating the evolution of single-crystal, threefold-symmetric, 2 + 1D coarsening faceted surfaces z = h(x, y, t). By explicitly tracking the interface with an efficient three-component facet/edge/junction structure, rapid simulations of tens of thousands of facets are realized. Topological rearrangements of the surface, including coarsening events caused by facets merging or vanishing, are treated explicitly using a priori knowledge of the outcome of each event. The speed and flexibility of the resulting method allows the easy extraction of reliable surface statistics describing complex interface morphology. The method is demonstrated using a sample facet dynamics, under which surfaces totaling one million facets are simulated to study the statistics of the emerging dynamically scaling state.