Fast and stable explicit operator splitting methods for phase-field models

Yuanzhen Cheng, Alexander Kurganov*, Zhuolin Qu, Tao Tang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

35 Citations (Scopus)
20 Downloads (Pure)


Numerical simulations of phase-field models require long time computations and therefore it is necessary to develop efficient and highly accurate numerical methods. In this paper, we propose fast and stable explicit operator splitting methods for both one- and two-dimensional nonlinear diffusion equations for thin film epitaxy with slope selection and the Cahn-Hilliard equation. The equations are split into nonlinear and linear parts. The nonlinear part is solved using a method of lines together with an efficient large stability domain explicit ODE solver. The linear part is solved by a pseudo-spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size. We demonstrate the performance of the proposed methods on a number of one- and two-dimensional numerical examples, where different stages of coarsening such as the initial preparation, alternating rapid structural transition and slow motion can be clearly observed.

Original languageEnglish
Pages (from-to)45-65
Number of pages21
JournalJournal of Computational Physics
Publication statusPublished - 15 Dec 2015

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Adaptive time-stepping
  • Cahn-Hilliard equation
  • Large stability domain explicit Runge-Kutta methods
  • Molecular beam epitaxy equation
  • Operator splitting methods
  • Phase-field models
  • Pseudo-spectral methods
  • Semi-discrete finite-difference schemes


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