Volume 10, Issue 1
An Efficient Multigrid Method for Molecular Mechanics Modeling in Atomic Solids

Jingrun Chen & Pingbing Ming

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

Published online: 2011-10

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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.

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@Article{CiCP-10-70, author = {}, title = {An Efficient Multigrid Method for Molecular Mechanics Modeling in Atomic Solids}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {1}, pages = {70--89}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.270910.131110a}, url = {http://global-sci.org/intro/article_detail/cicp/7435.html} }
TY - JOUR T1 - An Efficient Multigrid Method for Molecular Mechanics Modeling in Atomic Solids JO - Communications in Computational Physics VL - 1 SP - 70 EP - 89 PY - 2011 DA - 2011/10 SN - 10 DO - http://doi.org/10.4208/cicp.270910.131110a UR - https://global-sci.org/intro/article_detail/cicp/7435.html KW - AB -

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.

Jingrun Chen & Pingbing Ming. (2020). An Efficient Multigrid Method for Molecular Mechanics Modeling in Atomic Solids. Communications in Computational Physics. 10 (1). 70-89. doi:10.4208/cicp.270910.131110a
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