2023 Volume 33 Issue 3 Pages 121-132
A level set approach for evolving spirals is introduced to handle merging spiral steps. For this purpose, the level set method is extended to describe curves by an auxiliary surface and a surface defined by a pre-determined multivalued function, like as a Riemann surface. Since the level set equation is a degenerate parabolic type, its solution is considered in the viscosity sense. The comparison principle or the existence and uniqueness of viscosity solution globally-in-time are explained as the results of the mathematical analysis. This method can be applied to compute the growth rate of a crystal surface that is evolving via spiral steps. As an application of this, the growth rate of a crystal surface with several screw dislocations is investigated numerically. We improved the estimate of the surface growth rate compared to that reported by Burton et al. (Philos. Trans. R. Soc. London A, 243(1951), 299–358).
