TY - JOUR
T1 - An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
AU - Qiao, Zhonghua
AU - Zhang, Zhengru
AU - Tang, Tao
N1 - Funding information:
Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong (zqiao@hkbu. edu.hk, [email protected]). The research of the first author was supported by the FRG grants of the Hong Kong Baptist University under grant FRG/08-09/II-35. The research of the third author was supported by the Hong Kong Research Grants Council and by the Collaborative Research Fund of National Science Foundation of China (NSFC) under grant G10729101.
^ Corresponding author. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China ([email protected]). The research of this author was supported by National NSF of China under grant 10601007.
Publisher copyright:
Copyright © 2011 Society for Industrial and Applied Mathematics
PY - 2011/6/14
Y1 - 2011/6/14
N2 - 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.
AB - 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.
KW - Adaptive time-stepping method
KW - Finite difference schemes
KW - Molecular beam epitaxy
KW - Unconditionally energy stable
UR - http://www.scopus.com/inward/record.url?scp=79960420807&partnerID=8YFLogxK
U2 - 10.1137/100812781
DO - 10.1137/100812781
M3 - Journal article
AN - SCOPUS:79960420807
SN - 1064-8275
VL - 33
SP - 1395
EP - 1414
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 3
ER -