Convex Splitting Method For Strongly Anisotropic Solid-State Dewetting Problems

In many engineering fields such as materials science,solid-state thin films are affected by surface potential,and they disperse or aggregate into isolated islands.This phenomenon is known as the solid-state problem.The problem of dewetting is widely used in nanomaterials.For the study of solid-state dewetting,especially when the surface density is strongly anisotropic,numerical simulations encounter great challenges in terms of accuracy and efficiency.Some numerical schemes may destroy the mesh quality during evolution,rendering the calculation impossible.For the two-dimensional solid-state dewetting problem,we first design a L1 curvature regularization method when the anisotropy is strong,which can allow a larger time step than the traditional L2 regularization method.Since the regularization method is limited to the time step △t=O(h2),we further develop the algorithm of the convex splitting scheme under strong anisotropy.Numerical experiments show that our method can achieve Δt=O(h).At the same time,for the convex split numerical scheme,We also demonstrate results such as well-posedness and area preservation for the discrete method.For the three-dimensional solid-state dewetting problem,it is more difficult to construct a robust numerical method under strong anisotropy.The main difficulty is that the grid properties will be greatly deformed during the evolution process.We generalize the two-dimensional convex splitting scheme to the sharp-interface model in the threedimensional case,and derive the variational problem corresponding to the weak solution using integration by parts on the manifold.The algorithm has good numerical stability even under strong anisotropy,and we demonstrate the stability of the numerical method,the existence and uniqueness of the solution,the volume retention and the energy dissipation.