Convexity splitting in a phase field model for surface diffusion
This work addresses the need for efficient numerical methods for phase field simulations of surface diffusion, which is relevant for materials science applications like solid state dewetting.
The authors propose convexity splitting schemes with improved accuracy for a phase field model of surface diffusion, enabling large-scale 3D simulations of solid state dewetting. They demonstrate that a Rosenbrock method increases the maximal numerical timestep by at least one order of magnitude.
Convexity splitting like schemes with improved accuracy are proposed for a phase field model for surface diffusion. The schemes are developed to enable large scale simulations in three spatial dimensions describing experimentally observed solid state dewetting phenomena. We introduce a first and a second order unconditionally energy stable scheme and carefully elaborate the loss in accuracy associated with large time steps in such schemes. We then present a family of Rosenbrock convex splitting schemes. We show the existence of a maximal numerical timestep and demonstrate the increase of this maximal numerical time step by at least one order of magnitude using a Rosenbrock method. This scheme is used to study the effect of contact angle on solid state dewetting phenomena.