求解Frenkel-Kontorova模型自适应问题的混合力平衡型原子/连续耦合方法  

Blended force-based atomistic-continuum coupling method for the model adaptivity of a Frenkel-Kontorova model

作　　者：廖明杰 王皓[2] LIAO Ming-Jie;WANG Hao(School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083,China;School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]北京科技大学数理学院,北京100083 [2]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2019年第5期802-812,共11页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(91430106,11501389)

摘　　要：本文利用混合力平衡型原子/连续耦合方法求解Frenkel-Kontorova模型并考虑模型的自适应问题,给出了基于残量的后验误差估计子.基于这个估计子,本文建立了自适应算法对原子系统进行自适应区域的分解,确定了原子区域和连续区域的划分.数值实验验证了后验误差估计子和算法的可行性.We use the blended force-based atomistic-continuum coupling(BQCF)method to solve a Frenkel-Kontorova model and consider its model adaptivity problem.We give a posteriori error estimator based on the residual.Then,by using such estimator,we construct the model adaptive algorithm,which adaptively determines the domain decomposition of an atomistic system,characterizes the partition of the atomistic domain and the continuous domain.The numerical experiments illustrate the validity of our estimator and algorithm.

关 键 词：原子/连续耦合方法 后验误差估计 模型自适应 FRENKEL-KONTOROVA模型 

分 类 号：O241.82[理学—计算数学]