An efficient linear second order unconditionally stable direct discretization method for the phase-field crystal equation on surfaces

Yibao Li, Chaojun Luo, Binhu Xia, Junseok Kim

Research output: Contribution to journalArticle

5 Citations (Scopus)


We develop an unconditionally stable direct discretization scheme for solving the phase-field crystal equation on surfaces. The surface is discretized by using an unstructured triangular mesh. Gradient, divergence, and Laplacian operators are defined on triangular meshes. The proposed numerical method is second-order accurate in space and time. At each time step, the proposed computational scheme results in linear elliptic equations to be solved, thus it is easy to implement the algorithm. It is proved that the proposed scheme satisfies a discrete energy-dissipation law. Therefore, it is unconditionally stable. A fast and efficient biconjugate gradients stabilized solver is used to solve the resulting discrete system. Numerical experiments are conducted to demonstrate the performance of the proposed algorithm.

Original languageEnglish
Pages (from-to)477-490
Number of pages14
JournalApplied Mathematical Modelling
Publication statusPublished - 2019 Mar 1



  • Laplace–Beltrami operator
  • Phase-field crystal equation
  • Triangular surface mesh
  • Unconditionally stable

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

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