Department of Mathematics
An adaptive time-stepping strategy for the molecular beam epitaxy models
This paper is concerned with the numerical simulations for the dynamics of the molecular beam epitaxy (MBE) model. The numerical simulations of the MBE models require long time computations, and therefore large time-stepping methods become necessary. In this work, we consider some unconditionally energy stable finite difference schemes, which will be used in the time adaptivity strategies. It is found that the use of the time adaptivity cannot only resolve the steady-state solutions but also the dynamical changes of the solution accurately and efficiently. The adaptive time step is selected based on the energy variation or the change of the roughness of the solution. The numerical experiments demonstrated that the CPU time is significantly saved for long time simulations. © 2011 Society for Industrial and Applied Mathematics.
Adaptive time-stepping method, Finite difference schemes, Molecular beam epitaxy, Unconditionally energy stable
Source Publication Title
SIAM Journal on Scientific Computing
Society for Industrial and Applied Mathematics
Link to Publisher's Edition
Qiao, Zhonghua, Zhengru Zhang, and Tao Tang. "An adaptive time-stepping strategy for the molecular beam epitaxy models." SIAM Journal on Scientific Computing 33.3 (2011): 1395-1414.