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Positive-definiteness of the blended force-based quasicontinuum method
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Li, Xingjie Helen, Luskin, Mitchell and Ortner, Christoph (2011) Positive-definiteness of the blended force-based quasicontinuum method. Working Paper. ArXiv e-prints.
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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) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Series Name: | ArXiv e-prints |
| Publisher: | ArXiv e-prints |
| Date: | 12 December 2011 |
| Number: | No.1112.2528v1 |
| Number of Pages: | 21 |
| Status: | Not Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Open Access |
| Funder: | PIRE, Department of Energy, EPSRC |
| Grant number: | DMS-0757355, DMS-0811039, OISE-0967140, de-sc0002085, EP/H003096 |
| Related URLs: | |
| URI: | http://wrap.warwick.ac.uk/id/eprint/48642 |
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