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

作　　者：何杰 王皓[2] 秦飞龙 He Jie;Wang Hao;Qin Feilong(Chengdu,Technological University,Information and Computing Science,Chengdu 611730,China;SiChuan University,mathematics college,Chengdu 610065,China)

机构地区：[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

出　　处：《计算数学》2023年第1期74-92,共19页Mathematica Numerica Sinica

基　　金：国家自然科学基金项目(11971336);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。

摘　　要：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(QCE)、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.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.

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 

分 类 号：O411.1[理学—理论物理]