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

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.