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

Abstract

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.

LanguageEnglish
Pages477-490
Number of pages14
JournalApplied Mathematical Modelling
Volume67
DOIs
Publication statusPublished - 2019 Mar 1

Fingerprint

Phase Field
Triangular Mesh
Discretization Method
Unconditionally Stable
Linear Order
Direct Method
Crystal
Gradient
Crystals
Discretization Scheme
Unstructured Mesh
Energy Dissipation
Discrete Systems
Elliptic Equations
Linear equation
Numerical methods
Energy dissipation
Divergence
Numerical Methods
Numerical Experiment

Keywords

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

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

Cite this

An efficient linear second order unconditionally stable direct discretization method for the phase-field crystal equation on surfaces. / Li, Yibao; Luo, Chaojun; Xia, Binhu; Kim, Junseok.

In: Applied Mathematical Modelling, Vol. 67, 01.03.2019, p. 477-490.

Research output: Contribution to journalArticle

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