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

Jeong Whan Choi; Hyun Geun Lee; Darae Jeong; Junseok Kim

doi:10.1016/j.physa.2009.01.026

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

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

Department of Mathematics

Korea University

Research output: Contribution to journal › Article › peer-review

135 Scopus citations

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 language	English
Pages (from-to)	1791-1803
Number of pages	13
Journal	Physica A: Statistical Mechanics and its Applications
Volume	388
Issue number	9
DOIs	https://doi.org/10.1016/j.physa.2009.01.026
State	Published - 1 May 2009

Keywords

Allen-Cahn equation
Finite difference
Nonlinear multigrid
Unconditionally gradient stable

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10.1016/j.physa.2009.01.026

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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.",

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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

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 9

ER -

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

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Keywords

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