The operator splitting method with semi-implicit spectral deferred correction for molecular beam epitaxial growth models

Abstract

This paper presents a high order time discretization method by combining the time splitting method with semi-implicit spectral deferred correction method to simulate the molecular beam epitaxial growth models with and without slope selection. The original problem is split into linear and nonlinear subproblems. The Fourier spectral method is adopted for the linear part, and a second-order SSP-RK method together with the Fourier spectral method is used for the nonlinear part. The scheme takes advantage of avoiding nonlinear iteration. However, the temporal error is dominated by the operator splitting error, which is second order for Strang splitting. In order to achieve higher order numerical algorithm in time, we consider a semi-implicit spectral deferred correction (SDC) method to reduce the splitting error. Specifically, the temporal order is increased by one with each correction loop in the SDC framework. Numerical results are given to illustrate that the high order temporal algorithm is a practical, accurate and efficient simulation tool for molecular beam epitaxial growth models.