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

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来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.

Abstract:

We use the blended force-based atomistic-continuum coupling (BQCF) method to solve a Frenkel-Kontorova model and consider its adaptivity problem. We give a posteriori error estimator based on the residual. Then, by using this estimator, we construct a model adaptive algorithm, which adaptively determines the domain decomposition of an atomistic system and characterize the partition of the atomistic domain and the continuous domain. Numerical experiments illustrate the validity of the estimator and algorithm.