Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations

被引：154

作者：

Guan, Zhen ^{[1
]}

Lowengrub, John S. ^{[1
]}

Wang, Cheng ^{[2
,3
]}

Wise, Steven M. ^{[4
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[2] Univ Massachusetts Dartmouth, Dept Math, N Dartmouth, MA 02747 USA

[3] Soochow Univ, Sch Math Sci, Suzhou 215006, Jiangsu, Peoples R China

[4] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2014年 / 277卷

基金：

美国国家科学基金会;

关键词：

Nonlocal Cahn-Hilliard equation; Energy stability; Unique solvability; Multigrid; DENSITY-FUNCTIONAL THEORY; FINITE-ELEMENT APPROXIMATION; PHASE SEGREGATION DYNAMICS; LONG-RANGE INTERACTIONS; NONLINEAR TUMOR-GROWTH; MESOSCOPIC MODELS; PARTICLE-SYSTEMS; BOUNDARY-PROBLEM; INTERFACE; DIFFERENCE;

D O I：

10.1016/j.jcp.2014.08.001

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We devise second-order accurate, unconditionally uniquely solvable and unconditionally energy stable schemes for the nonlocal Cahn-Hilliard (nCH) and nonlocal Allen-Cahn (nAC) equations for a large class of interaction kernels. We present numerical evidence that both schemes are convergent. We solve the nonlinear equations resulting from discretization using an efficient nonlinear multigrid method and demonstrate the performance of our algorithms by simulating nucleation and crystal growth for several different choices of interaction kernels. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：48 / 71

页数：24

共 58 条

[1] Long-time integration methods for mesoscopic models of pattern-forming systems [J].