Force-based atomistic/continuum blending for multilattices

We formulate the blended force-based quasicontinuum method for multilattices and develop rigorous error estimates in terms of the approximation parameters: choice of atomistic region, blending region, and continuum finite element mesh. Balancing the approximation parameters yields a convergent atomi...

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Bibliographic Details
Published in:Numerische Mathematik 2018-11, Vol.140 (3), p.703-754
Main Authors: Olson, Derek, Li, Xingjie, Ortner, Christoph, Van Koten, Brian
Format: Article
Language:English
Subjects:
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
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Summary:We formulate the blended force-based quasicontinuum method for multilattices and develop rigorous error estimates in terms of the approximation parameters: choice of atomistic region, blending region, and continuum finite element mesh. Balancing the approximation parameters yields a convergent atomistic/continuum multiscale method for multilattices with point defects, including a rigorous convergence rate in terms of the computational cost. The analysis is illustrated with numerical results for a Stone–Wales defect in graphene.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-018-0979-x