An unconditionally gradient stable numerical method for solving the Allen-Cahn equation

Jeong Whan Choi, Hyun Geun Lee, Darae Jeong, Junseok Kim

Research output: Contribution to journalArticle

60 Citations (Scopus)

Abstract

We consider an unconditionally gradient stable scheme for solving the Allen-Cahn equation representing a model for anti-phase domain coarsening in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy functional. We also show the pointwise boundedness of the numerical solution for the Allen-Cahn equation. We describe various numerical experiments we performed to study properties of the Allen-Cahn equation.

Original languageEnglish
Pages (from-to)1791-1803
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Volume388
Issue number9
DOIs
Publication statusPublished - 2009 May 1

Keywords

  • Allen-Cahn equation
  • Finite difference
  • Nonlinear multigrid
  • Unconditionally gradient stable

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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