Iterative solution of the quasicontinuum equilibrium equations with continuation

Matthew Dobson, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We give an analysis of a continuation algorithm for the numerical solution of the force-based quasicontinuum equations. The approximate solution of the force-based quasicontinuum equations is computed by an iterative method using an energy-based quasicontinuum approximation as the preconditioner. The analysis presented in this paper is used to determine an efficient strategy for the parameter step size and number of iterations at each parameter value to achieve a solution to a required tolerance. We present computational results for the deformation of a Lennard-Jones chain under tension to demonstrate the necessity of carefully applying continuation to ensure that the computed solution remains in the domain of convergence of the iterative method as the parameter is increased. These results exhibit fracture before the actual load limit if the parameter step size is too large.

Original languageEnglish (US)
Pages (from-to)19-41
Number of pages23
JournalJournal of Scientific Computing
Issue number1
StatePublished - Oct 2008

Bibliographical note

Funding Information:
This work was supported in part by DMS-0304326, by the University of Minnesota Supercomputing Institute and by the Department of Energy under Award Number DE-FG02-05ER25706.


  • Atomistic to continuum
  • Continuation
  • Fracture
  • Quasicontinuum


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