Multiscale random-walk algorithm for simulating interfacial pattern formation

We present a novel computational method to simulate accurately a wide range of interfacial patterns whose growth is limited by a large-scale diffusion field. To illustrate the computational power of this method, we demonstrat e that it can be used to simulate three-dimensional dendritic growth in a p reviously unreachable range of low undercoolings that is of direct experime ntal relevance.