An analysis of node-based cluster summation rules in the quasicontinuum method

Mitchell Luskin, Christoph Ortner

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We investigate two examples of node-based cluster summation rules that have been proposed for the quasicontinuum (QC) method: a force-based approach and an energy-based approach which is a generalization of the nonlocal QC method. We show that, even for the case of nearest-neighbor interaction in a one-dimensional 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.

Original languageEnglish (US)
Pages (from-to)3070-3086
Number of pages17
JournalSIAM Journal on Numerical Analysis
Issue number4
StatePublished - 2009

Bibliographical note

Funding Information:
This author's research was supported by EPSRC Critical Mass Project "New Frontiers in the Mathematics of Solids."

Publisher Copyright:
© 2009 Society for Industrial and Applied Mathematics.


  • Atomistic-to-continuum coupling
  • Cluster summation rule
  • Coarse-graining
  • Quasicontinuum method


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