【作者】 肖珺； 唐少强；

【Author】 XIAO Jun,TANG Shao-qiang (College of Engineering,Peking University,Beijing 100871,China)

【机构】 北京大学工学院；

【摘要】 本文提出了一种基于PML算法的多尺度模拟方法。在本文的计算工作中,将被研究的区域分成三个部分:MD(Molecular Dynamics)区域、MC(MacrosCopic)区域、以及PML区域。粗网格方程用于整个区域中,而MD计算仅限于MD+PML区域。PML区域用于吸收MD区域与MC区域之间数值边界上的人为反射。对于粗网格计算,我们使用一种由匹配微分算子方法得到的方程作为粗网格的控制方程,理论上说,该粗网格方程可以达到直至谱精度任意精度。本文使用该算法模拟几个一维晶格系统,取得了比较满意的结果。更多还原

【Abstract】 In this paper,we shall propose a modified PML method to simulate multiscale problems.Within this method,the whole domain is devided into three subdomains,MD(Molecular Dynamic) region,MC (MacrosCopic) region and PML(Perfectly Matched Layer) region.We construct the coarse scale simulations over the whole damain,while MD simulations are only subjected to MD+PML region.The PML governing equations are obtained by stretching space coordinates,and damping terms are hence introduced into the equations,which are said to be able to damp waves of all frequencies except zero.Furthermore,PML region can"perfectly match"the rest region of the whole domain.For coarse scale simulations,instead of widely-used LE scheme,we employ a so-called MDO-k equation which is obtained by"matching differential operator method".Theoretically,MDO-k equation can reach any order of accuracy up to spectral accuracy.To couple simulations of two different scales,reassignments are attributed to both MD and coarse grid variables.In PML region,the coarse scale part of atom displacement is replaced by coarse grain displacement,and in pure MD region the latter is reassigned by the former.We simulate a few 1-D lattice models with the modified PML method,and reliable results are obtained.更多还原