基于多体作用的原子/连续耦合方法的先验误差估计

doi:10.12286/jssx.j2021-0831

计算数学 ›› 2023, Vol. 45 ›› Issue (1): 74-92.DOI: 10.12286/jssx.j2021-0831

基于多体作用的原子/连续耦合方法的先验误差估计

何杰¹, 王皓², 秦飞龙³

1. 成都工业学院大数据与人工智能学院, 成都 611730;
2. 四川大学数学学院, 成都 610065;
3. 成都工业学院大数据与人工智能学院, 成都 611730

收稿日期:2021-07-01 出版日期:2023-02-14 发布日期:2023-02-13
基金资助:
国家自然科学基金项目(11971336)和融合5G-V2X通信的智慧交通云服务平台的研发与应用(2021YFG0170)资助.

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何杰, 王皓, 秦飞龙. 基于多体作用的原子/连续耦合方法的先验误差估计[J]. 计算数学, 2023, 45(1): 74-92.

He Jie, Wang Hao, Qin Feilong. A PROIOR ERROR ESTIMATES FOR ENERGY-BASED ATOMISTIC/CONTINUUM METHOD FOR MULTI-BODY INTERACTION SYSTEMS BASED ON FRENKEL-KONFOROVA MODEL[J]. Mathematica Numerica Sinica, 2023, 45(1): 74-92.

A PROIOR ERROR ESTIMATES FOR ENERGY-BASED ATOMISTIC/CONTINUUM METHOD FOR MULTI-BODY INTERACTION SYSTEMS BASED ON FRENKEL-KONFOROVA MODEL

He Jie¹, Wang Hao², Qin Feilong³

1. Chengdu, Technological University, Information and Computing Science, Chengdu 611730, China;
2. SiChuan University, mathematics college, Chengdu 610065, China;
3. Chengdu, Technological University, Information and Computing Science, Chengdu 611730, China

Received:2021-07-01 Online:2023-02-14 Published:2023-02-13
Supported by:
The project was supported by the National Key Research and Development Program of China (2019YFC1905301);National Natural Science Foundation of China (22078115,21776108,21690083,22008078).

本文研究理想晶体发生位错时如何发生形变, 应用本地化拟连续方法(QCL)、基于能量的拟连续方法(Q CE)、非本地化拟连续方法(QNL), 分析了多体作用下Frenkel-Kontorova模型在一维情形中先验误差分析, 推导了该误差估计与原子模型解的光滑性的关系, 并且由于考虑的是一维原子链, 该误差还具备超收敛性.本文将一致性误差分析分解为模型误差和粗粒化误差, 并推导出基于负范数的误差估计, 稳定性分析将均匀应变扩充为非线性应变.最后利用数值实验说明了本文的分析结果.

关键词： 拟连续方法, 原子/连续耦合方法, 粗粒化, 先验误差分析

In this paper, we analyzed the deformation of ideal crystal when dislocation occurs. By using the localized quasi-continuous method (QCL), energy based quasi-continuous method (QCE) and nonlocal quasi-continuous method (QNL), we analyze the prior error of Frenkelkontorova model under multi-body interaction in one-dimensional case, and derive the relationship between the error estimate and the smoothness of the solution of atomic model, In this paper, the consistent error analysis is decomposed into model error and coarse-grained error, and the error estimation based on negative norm is derived. The stability analysis extends the uniform strain to nonlinear strain. Finally, numerical experiments are used to illustrate the analysis results.

Key words: Quasicontinuum method, atomistic/continuum coupling, coarse-graining, proior estimates analysis

MR(2010)主题分类:

65D17

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摘要

基于多体作用的原子/连续耦合方法的先验误差估计

A PROIOR ERROR ESTIMATES FOR ENERGY-BASED ATOMISTIC/CONTINUUM METHOD FOR MULTI-BODY INTERACTION SYSTEMS BASED ON FRENKEL-KONFOROVA MODEL

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