求解Cahn-Hilliard方程非线性项的两种数值格式对比  

COMPARISON OF TWO NUMERICAL SCHEMES FOR THE NONLINEAR TERM IN THE CAHN-HILLIARD EQUATION

作　　者：卿欢 李晓[1] 纪光华[1] 张辉[1] 

机构地区：[1]北京师范大学数学科学学院,北京100875

出　　处：《数值计算与计算机应用》2016年第2期95-115,共21页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11261160486;11471046;11571045);教育部新世纪优秀人才支持计划(NCET-12-0053)

摘　　要：基于快速显式算子分裂方法，将Cahn-Hilliard方程与分子束外延（MBE）方程分裂为非线性与线性两个部分．对非线性部分，采用中心差分与半离散有限差分两种格式进行数值计算；线性部分通过拟谱方法进行精确求解．在两种格式下，通过对数值解的全局Lo。误差估计，比较分析了两种格式的数值解差异以及运行效率．对于Cahn—Hilliard方程与MBE方程，两种格式的数值解一致；对Cahn—Hilliard方程的数值求解，中心差分格式的效率是半离散有限差分格式的3到6倍；在MBE方程的数值求解中，半离散有限差分格式的效率是中心差分格式的2倍．Based on the fast explicit operator splitting （FEOS） method, Cahn-Hilliard equation and Molecular Beam Epitaxy （MBE） equation are split into nonlinear and linear parts. The nonlinear parts are approximated numerically by two different schemes： center-difference scheme and semi-discrete finite-difference scheme. The linear part is solved by a pseudo- spectral method based on the exact solution. The global discrete L~ error estimate is verified numerically. Comparing the numerical results and operating efficiency of the two schemes, we find that the results of the two schemes are highly consistent with each other for either the Cahn-Hilliard equation or the MBE equation. For the Cahn-Hilliard equation, center-difference scheme is 3-6 times more efficient, while for the MBE equation, semi-discrete finite-difference scheme is 2 times more efficient.

关 键 词：CAHN-HILLIARD方程 快速显式算子分裂 中心差分格式 半离散有限差分格式 运行效率. 

分 类 号：O241.8[理学—计算数学]