A Second-Order Operator Splitting Fourier Spectral Method for Models of Epitaxial Thin Film Growth

In this paper, we develop an operator splitting Fourier spectral method for models of epitaxial thin film growth with and without slope selection. A main idea of the method is to split the original equation into linear and nonlinear parts, and then to evolve one step which consists of three substeps. The linear part is solved by the spectral method, which has a closed-form solution in the Fourier space. And the nonlinear part is also solved by the spectral method combined with the Crank–Nicolson type method. We numerically demonstrate that our method achieves spectral accuracy in space and second-order accuracy in time and alleviates restriction on the time step. We also perform long time simulations for the coarsening process to show the capability of the method.