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

被引：123

作者：

Choi, Jeong-Whan ^{[1
]}

Lee, Hyun Geun ^{[1
]}

Jeong, Darae ^{[1
]}

Kim, Junseok ^{[1
]}

机构：

[1] Korea Univ, Dept Math, Seoul 136701, South Korea

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2009年 / 388卷 / 09期

基金：

新加坡国家研究基金会;

关键词：

Allen-Cahn equation; Nonlinear multigrid; Finite difference; Unconditionally gradient stable; ADAPTIVE MESH REFINEMENT; PROJECTION METHOD;

D O I：

10.1016/j.physa.2009.01.026

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：1791 / 1803

页数：13

共 19 条

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