A simple and efficient finite difference method for the phase-field crystal equation on curved surfaces

Hyun Geun Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)

Abstract

We present a simple and efficient finite difference method for the phase-field crystal (PFC) equation on curved surfaces embedded in R3. We employ a narrow band neighborhood of a curved surface that is defined as a zero level set of a signed distance function. The PFC equation on the surface is extended to the three-dimensional narrow band domain. By using the closest point method and applying a pseudo-Neumann boundary condition, we can use the standard seven-point discrete Laplacian operator instead of the discrete Laplace-Beltrami operator on the surface. The PFC equation on the narrow band domain is discretized using an unconditionally stable scheme and the resulting implicit discrete system of equations is solved by using the Jacobi iterative method. Computational results are presented to demonstrate the efficiency and usefulness of the proposed method.

Original languageEnglish
Pages (from-to)32-43
Number of pages12
JournalComputer Methods in Applied Mechanics and Engineering
Volume307
DOIs
Publication statusPublished - 2016 Aug 1

Bibliographical note

Funding Information:
The authors thank the reviewers for the constructive and helpful comments on the revision of this article. The first author (H.G. Lee) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2014R1A2A2A01003683 ).

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

  • Closest point method
  • Curved surface
  • Finite difference method
  • Narrow band domain
  • Phase-field crystal equation

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications

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