The Numerical Accuracy Analysis of Asymptotic Homogenization Method and Multiscale Finite Element Method for Periodic Composite Materials  

作　　者：Hao Dong Yufeng Nie Zihao Yang Yang Zhang YataoWu 

机构地区：[1]Department of Applied Mathematics,School of Science,Northwestern Polytechnical University,Xi’an 710129,PR China [2]Research Center for Computational Science,Northwestern Polytechnical University,Xi’an 710129,PR China

出　　处：《Computer Modeling in Engineering & Sciences》2016年第5期395-419,共25页工程与科学中的计算机建模（英文）

基　　金：the National Natural Science Foundation of China(No.11501449 and 11471262);the Center for high performance computing of Northwestern Polytechnical University.

摘　　要：In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems for four kinds of typical periodic composite materials,the main factors to determine the accuracy of first-order AHM and second-order AHM are found,and the physical interpretation of these factors is given.Furthermore,the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed,and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions.Finally,numerical experiments verify that MsFEM is essentially a first-order multiscale method for periodic composite materials.

关 键 词：ASYMPTOTIC HOMOGENIZATION METHOD Multiscale finite element METHOD FIRST-ORDER AHM Slight FLUCTUATIONS SECOND-ORDER AHM Severe FLUCTUATIONS 

分 类 号：O17[理学—数学]