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Mathematical Problems in Engineering
Volume 2015, Article ID 834517, 10 pages
Research Article

Challenges in Atomistic-to-Continuum Coupling

1Institute for Mathematics, TU Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany
2Zuse Institute Berlin (ZIB), Takustrasse 7, 14195 Berlin, Germany

Received 18 March 2015; Revised 31 May 2015; Accepted 1 June 2015

Academic Editor: Xiao-Qiao He

Copyright © 2015 Konstantin Fackeldey. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the design, analysis, and implementation of concurrent coupling approaches where different (atomic and continuous) models are used simultaneously within a single simulation process. Thereby, several problems or pitfalls can happen, for example, the reflection of molecular movements at the “boundary” between the atomic and continuum regions which leads to an unphysical increase in energy in the atomic model. We investigate the problems with the aim of giving an introduction into this field and preventing errors for scientists starting their research towards multiscale methods.