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A meshless quasicontinuum method based on local maximum-entropy interpolation

Kochmann, Dennis M. and Venturini, Gabriela N. (2014) A meshless quasicontinuum method based on local maximum-entropy interpolation. Modelling and Simulation in Materials Science and Engineering, 22 (3). Art. No. 034007 . ISSN 0965-0393.

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Coarse-graining atomistic ensembles can overcome the practical limitations of molecular statics and dynamics in order to facilitate simulations at much larger length scales than accessible by discrete atomistic techniques due to computational expense. The quasicontinuum (QC) method was introduced to reduce the number of degrees of freedom in crystalline solids by choosing a set of representative atoms from the fully atomistic ensemble and obtaining the positions and momenta of all remaining lattice sites by interpolation. Here, we present a new energy-based nonlocal meshless version of the QC method based on local maximum-entropy (max-ent) interpolation schemes instead of the traditional polynomial interpolation, which particularly promises advantages in model adaptation to tie atomistic resolution to crystal defects while efficiently coarse-graining away from these. To this end, we formulate the meshless QC representation and analyze its performance. One-dimensional chain problems allow for clean mathematical treatment and provide interesting insight, which allow us to quantify the approximation error as a function of representative atom distribution and support of meshless shape functions. A fully three-dimensional implementation then demonstrates the applicability of the new QC scheme and highlights its features. Overall, we show that local max-ent interpolation offers a number of advantages over previous QC realizations.

Item Type:Article
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Kochmann, Dennis M.0000-0002-9112-6615
Additional Information:© 2014 IOP Publishing Ltd. Received 4 September 2013, revised 4 February 2014; Accepted for publication 5 February 2014; Published 1 April 2014. The authors gratefully acknowledge financial support from the US Department of Energy National Nuclear Security Administration (under award number DE-FC52-08NA28613 through Caltech’s PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials).
Funding AgencyGrant Number
Department of Energy (DOE) National Nuclear Security AdministrationDE-FC52-08NA28613
Subject Keywords:molecular dynamics; crystalline solids; quasicontinuum; meshfree methods
Issue or Number:3
Classification Code:PACS: 65.40.G-; 62.20.D-; 81.70.Bt; 81.40.Jj; 61.72.J-
Record Number:CaltechAUTHORS:20140613-133404451
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Official Citation:A meshless quasicontinuum method based on local maximum-entropy interpolation Dennis M Kochmann and Gabriela N Venturini 2014 Modelling Simul. Mater. Sci. Eng. 22 034007
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:46267
Deposited By: Tony Diaz
Deposited On:13 Jun 2014 20:59
Last Modified:24 Nov 2020 00:42

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