A Numerical Study of Anisotropic Crystal Growth with Bunching under Very Singular Vertical Diffusion

We study numerically the anisotropic bunching effect in crystal growth under curvature and a singular vertical diffusive regularization. Our assumption is that the mobility of the growth depends on the height of the given crystal. This assumption may result in overhanging crystals if approached in a naive way. Instead, we embed the profile of the crystal as the zero level set of a continuous function and study the corresponding level set evolution. To prevent “overhanging”, we regularize the equation with a singular diffusion that vanishes everywhere except at the formation of “overhanging”. In addition, we add the mean curvature regularization to keep the convexity of the level sets.