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Positive definiteness of the blended force-based quasicontinuum method
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Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) Positive definiteness of the blended force-based quasicontinuum method. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 1023-1045. doi:10.1137/110859270
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Official URL: http://dx.doi.org/10.1137/110859270
Abstract
The development of consistent and stable quasicontinuum models for multidimensional crystalline solids remains a challenge. For example, proving the stability of the force-based quasicontinuum (QCF) model [M. Dobson and M. Luskin, M2AN Math. Model. Numer. Anal., 42 (2008), pp. 113--139] remains an open problem. In one and two dimensions, we show that by blending atomistic and Cauchy--Born continuum forces (instead of a sharp transition as in the QCF method) one obtains positive-definite blended force-based quasicontinuum (B-QCF) models. We establish sharp conditions on the required blending width.
| 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 > Mathematics | ||||||||||
| Library of Congress Subject Headings (LCSH): | Multiscale modeling, Continuum mechanics, Crystalline polymers -- Mathematical models | ||||||||||
| Journal or Publication Title: | Multiscale Modeling & Simulation | ||||||||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||||||
| ISSN: | 1540-3459 | ||||||||||
| Official Date: | 2012 | ||||||||||
| Dates: |
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| Volume: | Volume 10 | ||||||||||
| Number: | Number 3 | ||||||||||
| Page Range: | pp. 1023-1045 | ||||||||||
| DOI: | 10.1137/110859270 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||
| Funder: | National Science Foundation (U.S.) (NSF), United States. Department of Energy, United States. Air Force. Office of Scientific Research (AFOSR), University of Minnesota. Supercomputer Institute, Engineering and Physical Sciences Research Council (EPSRC) | ||||||||||
| Grant number: | DMS-0757355 (NSF), DMS-0811039 (NSF), OISE-0967140 (NSF), DE-SC0002085 (DOE), FA9550-12-1-0187 (AFOSR), EP/H003096 (EPSRC) |
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