Numerical methods for multilattices

Assyr Abdulle, Ping Lin, Alexander V Shapeev

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)


    Among the efficient numerical methods based on atomistic models, the quasi-continuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to multilattices [Tadmor et al., Phys. Rev. B, 59 (1999), pp. 235--245]. Another existing numerical approach to modeling multilattices is homogenization. In the present paper we review the existing numerical methods for multilattices and propose another concurrent macro-to-micro method in the numerical homogenization framework. We give a unified mathematical formulation of the new and the existing methods and show their equivalence. We then consider extensions of the proposed method to time-dependent problems and to random materials.

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    Original languageEnglish
    Pages (from-to)696-726
    Number of pages31
    JournalMultiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
    Issue number3
    Publication statusPublished - 2012


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