An unconditionally stable hybrid numerical method for solving the AllenCahn equation

Yibao Li, Hyun Geun Lee, Darae Jeong, Junseok Kim

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

We present an unconditionally stable second-order hybrid numerical method for solving the AllenCahn equation representing a model for antiphase domain coarsening in a binary mixture. The proposed method is based on operator splitting techniques. The AllenCahn equation was divided into a linear and a nonlinear equation. First, the linear equation was discretized using a CrankNicolson scheme and the resulting discrete system of equations was solved by a fast solver such as a multigrid method. The nonlinear equation was then solved analytically due to the availability of a closed-form solution. Various numerical experiments are presented to confirm the accuracy, efficiency, and stability of the proposed method. In particular, we show that the scheme is unconditionally stable and second-order accurate in both time and space.

Original languageEnglish
Pages (from-to)1591-1606
Number of pages16
JournalComputers and Mathematics with Applications
Volume60
Issue number6
DOIs
Publication statusPublished - 2010

Keywords

  • AllenCahn equation
  • Finite difference
  • Motion by mean curvature
  • Operator splitting
  • Unconditionally stable

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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