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

被引：131

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

[1] MICROSCOPIC THEORY FOR ANTIPHASE BOUNDARY MOTION AND ITS APPLICATION TO ANTIPHASE DOMAIN COARSENING [J].

ALLEN, SM ;

CAHN, JW .

ACTA METALLURGICA, 1979, 27 (06) :1085-1095

[2] A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations [J].

Almgren, AS ;

Bell, JB ;

Colella, P ;

Howell, LH ;

Welcome, ML .

JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 142 (01) :1-46

[3] Geometrical image segmentation by the Allen-Cahn equation [J].

Benes, M ;

Chalupecky, V ;

Mikula, K .

APPLIED NUMERICAL MATHEMATICS, 2004, 51 (2-3) :187-205

[4] LOCAL ADAPTIVE MESH REFINEMENT FOR SHOCK HYDRODYNAMICS [J].

BERGER, MJ ;

COLELLA, P .

JOURNAL OF COMPUTATIONAL PHYSICS, 1989, 82 (01) :64-84

[5] Numerical solution of plasma fluid equations using locally refined grids [J].

Colella, P ;

Dorr, MR ;

Wake, DD .

JOURNAL OF COMPUTATIONAL PHYSICS, 1999, 152 (02) :550-583

[6]

COWAN C, 2005, THESIS S FRASER U CA

[7] Numerical study of the Cahn-Hilliard equation in one, two and three dimensions [J].

de Mello, EVL ;

Filho, OTD .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2005, 347 :429-443

[8] A wavelet-laplace variational technique for image deconvolution and inpainting [J].

Dobrosotskaya, Julia A. ;

Bertozzi, Andrea L. .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 2008, 17 (05) :657-663

[9] Unconditionally gradient stable time marching the Cahn-Hilliard equation [J].

Eyre, DJ .

COMPUTATIONAL AND MATHEMATICAL MODELS OF MICROSTRUCTURAL EVOLUTION, 1998, 529 :39-46

[10] Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows [J].

Feng, XB ;

Prohl, A .

NUMERISCHE MATHEMATIK, 2003, 94 (01) :33-65

← 1 2 →