Commun. Comput. Phys., 10 (2011), pp. 70-89.


An Efficient Multigrid Method for Molecular Mechanics Modeling in Atomic Solids

Jingrun Chen 1, Pingbing Ming 2*

1 Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, Beijing 100190, China.
2 LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, Beijing 100190, China.

Received 27 September 2010; Accepted (in revised version) 13 November 2010
Available online 7 March 2011
doi:10.4208/cicp.270910.131110a

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.

AMS subject classifications: 65B99, 65N30, 65Z05, 74G15, 74G65, 74S05

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Key words: Multigrid method, linear-scaling algorithm, Cauchy-Born rule, nanoindentation.

*Corresponding author.
Email: chenjr@lsec.cc.ac.cn (J. Chen), mpb@lsec.cc.ac.cn (P. B. Ming)
 

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