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论文摘要

基于能量多体作用的原子/连续耦合方法的后验误差估计

A posteriori error estimates for energy-based atomistic/continuum method for multi-body interaction systems

作者:何杰(四川大学数学学院);王皓(四川大学数学学院);胡兵(四川大学数学学院);刘少晖(四川大学数学学院)

Author:HE Jie(College of Mathematics, Sichuan University);WANG Hao(College of Mathematics, Sichuan University);HU Bing(College of Mathematics, Sichuan University);LIU Shao-Hui(College of Mathematics, Sichuan University)

收稿日期:2017-04-06          年卷(期)页码:2017,54(5):895-904

期刊名称:四川大学学报: 自然科学版

Journal Name:Journal of Sichuan University (Natural Science Edition)

关键字:原子/连续耦合方法;粗粒化;后验误差估计;自适应算法

Key words:Atomistic/continuum coupling method, coarse-graining, a posteriori error analysis,adaptive algorithm

基金项目:国家自然科学基金

中文摘要

本文研究了一维情形下基于能量多体作用的原子/连续耦合方法的后验误差估计,得到基于能量的后验误差估计子.基于理论结果,我们还设计了一个不依赖于原子节点自适应网格加密算法。实验结果显示本文的算法是有效的。

英文摘要

We derive the a posterior error estimate for an energy-based atomistic/continuum method for a one-dimensional periodic chain with multi-body interactions. The current extends previous results by eliminating the requirement that the computational nodes in the continuum region coincide with the lattice sites and providing a thorough stability analysis. Based on the estimator, we design an adaptive refinement algorithm which produces the optimal convergence rate. We also show numerically that error estimator is efficient.

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