An efficient numerical method for evolving microstructures with strong elastic inhomogeneity

Darae Jeong, Seunggyu Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


In this paper, we consider a fast and efficient numerical method for the modified Cahn-Hilliard equation with a logarithmic free energy for microstructure evolution. Even though it is physically more appropriate to use a logarithmic free energy, a quartic polynomial approximation is typically used for the logarithmic function due to a logarithmic singularity. In order to overcome the singularity problem, we regularize the logarithmic function and then apply an unconditionally stable scheme to the Cahn-Hilliard part in the model. We present computational results highlighting the different dynamic aspects from two different bulk free energy forms. We also demonstrate the robustness of the regularization of the logarithmic free energy, which implies the time-step restriction is based on accuracy and not stability.

Original languageEnglish
Article number045007
JournalModelling and Simulation in Materials Science and Engineering
Issue number4
Publication statusPublished - 2015 Jun 1

Bibliographical note

Publisher Copyright:
© 2015 IOP Publishing Ltd.


  • CahnHilliard equation
  • elastic inhomogeneity
  • logarithmic free energy
  • multigrid
  • phase-field method
  • unconditionally gradient stable scheme

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Computer Science Applications


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