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An Efficient Multigrid Method for Molecular Mechanics Modeling in Atomic Solids

Published online by Cambridge University Press:  20 August 2015

Jingrun Chen  and
Pingbing Ming
Jingrun Chen*
Affiliation:
Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, Beijing 100190, China
Pingbing Ming*
Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, Beijing 100190, China
*
Email:chenjr@lsec.cc.ac.cn
Corresponding author.Email:mpb@lsec.cc.ac.cn
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Abstract

We propose a multigrid method to solve the molecular mechanics model (molecular dynamics at zero temperature). The Cauchy-Born elasticity model is employed as the coarse grid operator and the elastically deformed state as the initial guess of the molecular mechanics model. The efficiency of the algorithm is demonstrated by three examples with homogeneous deformation, namely, one dimensional chain under tensile deformation and aluminum under tension and shear deformations. The method exhibits linear-scaling computational complexity, and is insensitive to parameters arising from iterative solvers. In addition, we study two examples with inhomogeneous deformation: vacancy and nanoindentation of aluminum. The results are still satisfactory while the linear-scaling property is lost for the latter example.

Keywords

65B9965N3065Z0574G1574G6574S05Multigrid methodlinear-scaling algorithmCauchy-Born rulenanoindentation

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 1 , July 2011 , pp. 70 - 89
Copyright
Copyright © Global Science Press Limited 2011

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