Open Access

ARTICLE

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

Hao Dong¹, Yufeng Nie^1,2, Zihao Yang¹, Yang Zhang¹, Yatao Wu¹

1 Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an 710129, PR China. E-mail: yfnie@nwpu.edu.cn
2 Research Center for Computational Science, Northwestern Polytechnical University, Xi’an710129, PR China.

Computer Modeling in Engineering & Sciences 2016, 111(5), 395-419. https://doi.org/10.3970/cmes.2016.111.395

Abstract

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.

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Keywords

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