Level set calculations of the evolution of boundaries on a dynamically adaptive grid

We present a general algorithm for the study of the evolution of interfaces in growth processes based on the level set method, using the narrow band and the fast marching approximations, applied on a dynamically adaptive grid. A novel construction of a dynamical adaptive grid is presented. One important feature is that we establish a controllable nite-width region of the highest resolution straddling the physically important boundary. This high-resolution stripe provides a better description of the important physical variables. An e cient and robust coupling of a hierarchical space description structure with the state-of-the-art level set method is established