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Analysis of blended atomistic/continuum hybrid methods
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Li, Xingjie Helen, Ortner, Christoph, Shapeev, Alexander V. and Van Koten, Brian (2016) Analysis of blended atomistic/continuum hybrid methods. Numerische Mathematik, 134 (2). pp. 275-326. doi:10.1007/s00211-015-0772-z
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Official URL: http://doi.org/10.1007/s00211-015-0772-z
Abstract
We present a comprehensive error analysis of two prototypical atomistic-to-continuum coupling methods of blending type: the energy-based and the force-based quasicontinuum methods. Our results are valid in two and three dimensions, for finite range many-body interactions (e.g., EAM type), and in the presence of lattice defects (we consider point defects and dislocations). The two key ingredients in the analysis are (1) new force and energy consistency error estimates; and (2) a new technique for proving energy norm stability of a/c couplings that requires only the assumption that the exact atomistic solution is a stable equilibrium.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QP Physiology |
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| Divisions: | Faculty of Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Molecular dynamics, Continuum mechanics | ||||||||
| Journal or Publication Title: | Numerische Mathematik | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0029-599X | ||||||||
| Official Date: | October 2016 | ||||||||
| Dates: |
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| Date of first compliant deposit: | 2 March 2017 | ||||||||
| Volume: | 134 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 275-326 | ||||||||
| DOI: | 10.1007/s00211-015-0772-z | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC), Leverhulme Trust (LT), United States. Air Force. Office of Scientific Research (AFOSR) | ||||||||
| Grant number: | EP/H003096 (EPSRC), Starting Grant 335120 (ERC) |
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