Commun. Comput. Phys., 15 (2014), pp. 647-676.


On the Effect of Ghost Force in the Quasicontinuum Method: Dynamic Problems in One Dimension

Xiantao Li 1, Pingbing Ming 2*

1 Department of Mathematics, the Pennsylvania State University, University Park, Pennsylvania, 16802, USA.
2 LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, No. 55, East Road Zhong-Guan-Cun, Beijing, 100190, P.R. China.

Received 25 February 2013; Accepted (in revised version) 27 August 2013
Available online 1 November 2013
doi:10.4208/cicp.250213.270813a

Abstract

Numerical error caused by "ghost forces" in a quasicontinuum method is studied in the context of dynamic problems. The error in the discrete W^{1,\infty} norm is analyzed for the time scale O(\epsilon) and the time scale O(1) with \epsilon being the lattice spacing.

AMS subject classifications: 65N15, 74G15, 70E55

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Key words: Quasicontinuum methods, ghost force, dynamic problems.

*Corresponding author.
Email: xli@math.psu.edu (X. Li), mpb@lsec.cc.ac.cn (P. B. Ming)
 

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