An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models

Zhonghua Qiao, Zhengru Zhang*, Tao Tang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

174 Citations (Scopus)
31 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)1395-1414
Number of pages20
JournalSIAM Journal on Scientific Computing
Issue number3
Publication statusPublished - 14 Jun 2011

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Adaptive time-stepping method
  • Finite difference schemes
  • Molecular beam epitaxy
  • Unconditionally energy stable


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