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An analysis of nodebased cluster summation rules in the quasicontinuum method
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Luskin, Mitchell Barry and Ortner, Christoph. (2009) An analysis of nodebased cluster summation rules in the quasicontinuum method. SIAM Journal on Numerical Analysis, Volume 47 (Number 4). pp. 30703086. ISSN 00361429

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Official URL: http://dx.doi.org/10.1137/080743391
Abstract
We investigate two examples of nodebased cluster summation rules that have been proposed for the quasicontinuum (QC) method: a forcebased approach and an energybased approach which is a generalization of the nonlocal QC method. We show that, even for the case of nearestneighbor interaction in a onedimensional periodic chain, both of these approaches create large errors that cannot be removed by increasing the cluster size when used with graded and, more generally, nonsmooth meshes. We offer some suggestions for how the accuracy of (cluster) summation rules may be improved.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) 

Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Multiscale modeling, Continuum mechanics, Crystalline polymers  Defects  Mathematical models  
Journal or Publication Title:  SIAM Journal on Numerical Analysis  
Publisher:  Society for Industrial and Applied Mathematics  
ISSN:  00361429  
Official Date:  4 September 2009  
Dates: 


Volume:  Volume 47  
Number:  Number 4  
Page Range:  pp. 30703086  
Identifier:  10.1137/080743391  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
Funder:  National Science Foundation (U.S.) (NSF), United States. Department of Energy, Institute for Mathematics and Its Applications (IMA), University of Minnesota. Supercomputer Institute, Engineering and Physical Sciences Research Council (EPSRC)  
Grant number:  DMS 0757355 (NSF), DMS0811039 (NSF), DEFG0205ER25706 (DOE)  
References:  [1] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, Classics Appl. Math. 40, 

URI:  http://wrap.warwick.ac.uk/id/eprint/43811 
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