First and second order operator splitting methods for the phase field crystal equation

Hyun Geun Lee, Jaemin Shin, June Yub Lee

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


In this paper, we present operator splitting methods for solving the phase field crystal equation which is a model for the microstructural evolution of two-phase systems on atomic length and diffusive time scales. A core idea of the methods is to decompose the original equation into linear and nonlinear subequations, in which the linear subequation has a closed-form solution in the Fourier space. We apply a nonlinear Newton-type iterative method to solve the nonlinear subequation at the implicit time level and thus a considerably large time step can be used. By combining these subequations, we achieve the first- and second-order accuracy in time. We present numerical experiments to show the accuracy and efficiency of the proposed methods.

Original languageEnglish
Pages (from-to)82-91
Number of pages10
JournalJournal of Computational Physics
StatePublished - 5 Oct 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.


  • First and second order convergences
  • Fourier spectral method
  • Operator splitting method
  • Phase field crystal


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