An unconditionally gradient stable numerical method for solving the Allen-Cahn equation

Jeongwhan Choi, Hyun Geun Lee, Darae Jeong, Junseok Kim

Research output: Contribution to journalArticle

49 Citations (Scopus)

Abstract

We consider an unconditionally gradient stable scheme for solving the Allen-Cahn equation representing a model for anti-phase domain coarsening in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy functional. We also show the pointwise boundedness of the numerical solution for the Allen-Cahn equation. We describe various numerical experiments we performed to study properties of the Allen-Cahn equation.

Original languageEnglish
Pages (from-to)1791-1803
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Volume388
Issue number9
DOIs
Publication statusPublished - 2009 May 1

Fingerprint

Allen-Cahn Equation
Numerical Methods
Gradient
gradients
Hessian matrices
Hessian matrix
antiphase boundaries
Binary Mixtures
Coarsening
Energy Functional
binary mixtures
Boundedness
eigenvalues
Numerical Experiment
Numerical Solution
Eigenvalue
energy
Energy
Model

Keywords

  • Allen-Cahn equation
  • Finite difference
  • Nonlinear multigrid
  • Unconditionally gradient stable

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

An unconditionally gradient stable numerical method for solving the Allen-Cahn equation. / Choi, Jeongwhan; Lee, Hyun Geun; Jeong, Darae; Kim, Junseok.

In: Physica A: Statistical Mechanics and its Applications, Vol. 388, No. 9, 01.05.2009, p. 1791-1803.

Research output: Contribution to journalArticle

@article{e2da414552e3442d8ffd346ec85a4fca,
title = "An unconditionally gradient stable numerical method for solving the Allen-Cahn equation",
abstract = "We consider an unconditionally gradient stable scheme for solving the Allen-Cahn equation representing a model for anti-phase domain coarsening in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy functional. We also show the pointwise boundedness of the numerical solution for the Allen-Cahn equation. We describe various numerical experiments we performed to study properties of the Allen-Cahn equation.",
keywords = "Allen-Cahn equation, Finite difference, Nonlinear multigrid, Unconditionally gradient stable",
author = "Jeongwhan Choi and Lee, {Hyun Geun} and Darae Jeong and Junseok Kim",
year = "2009",
month = "5",
day = "1",
doi = "10.1016/j.physa.2009.01.026",
language = "English",
volume = "388",
pages = "1791--1803",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",
number = "9",

}

TY - JOUR

T1 - An unconditionally gradient stable numerical method for solving the Allen-Cahn equation

AU - Choi, Jeongwhan

AU - Lee, Hyun Geun

AU - Jeong, Darae

AU - Kim, Junseok

PY - 2009/5/1

Y1 - 2009/5/1

N2 - We consider an unconditionally gradient stable scheme for solving the Allen-Cahn equation representing a model for anti-phase domain coarsening in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy functional. We also show the pointwise boundedness of the numerical solution for the Allen-Cahn equation. We describe various numerical experiments we performed to study properties of the Allen-Cahn equation.

AB - We consider an unconditionally gradient stable scheme for solving the Allen-Cahn equation representing a model for anti-phase domain coarsening in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy functional. We also show the pointwise boundedness of the numerical solution for the Allen-Cahn equation. We describe various numerical experiments we performed to study properties of the Allen-Cahn equation.

KW - Allen-Cahn equation

KW - Finite difference

KW - Nonlinear multigrid

KW - Unconditionally gradient stable

UR - http://www.scopus.com/inward/record.url?scp=60349114175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=60349114175&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2009.01.026

DO - 10.1016/j.physa.2009.01.026

M3 - Article

VL - 388

SP - 1791

EP - 1803

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 9

ER -