Analysis of an optimization-based atomistic-to-continuum coupling method for point defects

Derek Olson, Alexander V. Shapeev, Pavel B. Bochev, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


We formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Application of a potential-based atomistic model near the defect core enables accurate simulation of the defect. Away from the core, where site energies become nearly independent of the lattice position, the method switches to a more efficient continuum model. The two models are merged by minimizing the mismatch of their states on an overlap region, subject to the atomistic and continuum force balance equations acting independently in their domains. We prove that the optimization problem is well-posed and establish error estimates.

Original languageEnglish
Pages (from-to)1-41
Number of pages41
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number1
Publication statusPublished - 1 Jan 2016


  • Atomic lattice
  • Atomistic-to-continuum coupling
  • Constrained optimization
  • Point defect


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