A hybrid FEM for solving the Allen-Cahn equation

Jaemin Shin, Seong Kwan Park, Junseok Kim

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We present an unconditionally stable hybrid finite element method for solving the Allen-Cahn equation, which describes the temporal evolution of a non-conserved phase-field during the antiphase domain coarsening in a binary mixture. Its various modified forms have been applied to image analysis, motion by mean curvature, crystal growth, topology optimization, and two-phase fluid flows. The hybrid method is based on the operator splitting method. The equation is split into a heat equation and a nonlinear equation. An implicit finite element method is applied to solve the diffusion equation and then the nonlinear equation is solved analytically. Various numerical experiments are presented to confirm the accuracy and efficiency of the method. Our simulation results are consistent with previous theoretical and numerical results.

Original languageEnglish
Pages (from-to)606-612
Number of pages7
JournalApplied Mathematics and Computation
Volume244
DOIs
Publication statusPublished - 2014 Oct 1

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Allen-Cahn Equation
Hybrid Method
Nonlinear equations
Nonlinear Equations
Finite Element Method
Motion by Mean Curvature
Operator Splitting Method
Finite element method
Crystal Growth
Phase Field
Unconditionally Stable
Topology Optimization
Binary Mixtures
Shape optimization
Coarsening
Implicit Method
Two-phase Flow
Binary mixtures
Crystal growth
Image Analysis

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

A hybrid FEM for solving the Allen-Cahn equation. / Shin, Jaemin; Park, Seong Kwan; Kim, Junseok.

In: Applied Mathematics and Computation, Vol. 244, 01.10.2014, p. 606-612.

Research output: Contribution to journalArticle

Shin, Jaemin ; Park, Seong Kwan ; Kim, Junseok. / A hybrid FEM for solving the Allen-Cahn equation. In: Applied Mathematics and Computation. 2014 ; Vol. 244. pp. 606-612.
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