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(In-)stability and stabilisation of QNL-type atomistic-to-continuum coupling methods
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Ortner, Christoph, Shapeev, A. V. and Zhang, L. (2014) (In-)stability and stabilisation of QNL-type atomistic-to-continuum coupling methods. Multiscale Modeling & Simulation: a SIAM Interdisciplinary Journal , 12 (3). pp. 1258-1293. doi:10.1137/130933873 ISSN 1540-3459.
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Official URL: https://doi.org/10.1137/130933873
Abstract
We study the stability of ghost force-free energy-based atomistic-to-continuum coupling methods. In 1D we essentially complete the theory by introducing a universally stable a/c coupling as well as a stabilisation mechanism for unstable coupling schemes.
We then present a comprehensive study of a two-dimensional scalar planar interface setting, as a step towards a general 2D/3D vectorial analysis. Our results point out various new challenges. For example, we find that none of the ghost force-free methods known to us are universally stable (i.e., stable under general interaction and general loads). We then explore to what extent our 1D stabilisation mechanism can be extended.
| Item Type: | Journal Article | ||||
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| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Multiscale modeling, Crystalline polymers -- Defects -- Mathematical models, Continuum mechanics | ||||
| Journal or Publication Title: | Multiscale Modeling & Simulation: a SIAM Interdisciplinary Journal | ||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
| ISSN: | 1540-3459 | ||||
| Official Date: | 9 September 2014 | ||||
| Dates: |
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| Volume: | 12 | ||||
| Number: | 3 | ||||
| Page Range: | pp. 1258-1293 | ||||
| DOI: | 10.1137/130933873 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Date of first compliant deposit: | 1 January 2016 | ||||
| Date of first compliant Open Access: | 1 January 2016 | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), United States. Air Force. Office of Scientific Research (AFOSR) | ||||
| Grant number: | EP/H003096 (EPSRC), FA9550-12-1-0187 (AFOSR) |
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