Convex Splitting Method for Strongly Anisotropic Solid-State Dewetting Problems in Two Dimensions

Abstract

A novel sharp-interface model for the solid-state dewetting problem in the two-dimensional case is proposed. Instead of incorporating the Willmore energy or an $L_2$-curvature regularization term as is done in previous studies, we add an $L_1$-curvature regularization to the interfacial energy functional in order to make this problem well-posed. Experiments show that such regularization improves the computational efficiency. In strongly anisotropic case, we consider a new numerical scheme based on the convex-splitting idea. This approach remarkably relax the restriction on the time step. In addition, we present the theoretical analysis of the scheme. Numerical results demonstrate the high efficiency and accuracy of the method.