Convergence of a fast explicit operator splitting method for the epitaxial growth model with slope selection

Xiao Li, Zhonghua Qiao, Hui Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

21 Citations (Scopus)

Abstract

A fast explicit operator splitting method for the epitaxial growth model with slope selection has been presented in [Cheng et al., J. Comput. Phys., 303 (2015), pp. 45-65]. The original problem is split into linear and nonlinear subproblems. For the linear part, the pseudospectral method is adopted; for the nonlinear part, a 33-point difference scheme is constructed. Here, we give a compact center-difference scheme involving fewer points for the nonlinear subproblem. In addition, we analyze the convergence rate of the algorithm. The global error order O(τ2+ h4) in discrete L2-norm is proved theoretically and verified numerically. Some numerical experiments show the robustness of the algorithm for small coefficients of the fourth-order term for the one-dimensional case. In addition, coarsening dynamics are simulated in large domains and the 1/3 power laws are observed for the two-dimensional case.
Original languageEnglish
Pages (from-to)265-285
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume55
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • Convergence
  • Epitaxial growth
  • Fast explicit operator splitting
  • Finite difference method
  • Pseudospectral method
  • Stability

ASJC Scopus subject areas

  • Numerical Analysis

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