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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 (2011) Positive-definiteness of the blended force-based quasicontinuum method. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1112.2528v1).
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Official URL: http://arxiv.org/pdf/1112.2528v1.pdf
Abstract
The development of consistent and stable quasicontinuum models for multi-dimensional crystalline solids remains a challenge. For example, proving stability of the force-based quasicontinuum (QCF) model [8] remains an open problem. In 1D and 2D, 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: | Working or Discussion Paper (Working Paper) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Series Name: | ArXiv e-prints | ||||
Publisher: | ArXiv e-prints | ||||
Official Date: | 12 December 2011 | ||||
Dates: |
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Number: | No.1112.2528v1 | ||||
Number of Pages: | 21 | ||||
Institution: | University of Warwick | ||||
Status: | Not Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Funder: | PIRE, Department of Energy, EPSRC | ||||
Grant number: | DMS-0757355, DMS-0811039, OISE-0967140, de-sc0002085, EP/H003096 | ||||
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