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International Journal for Multiscale Computational Engineering
Facteur d'impact: 1.016 Facteur d'impact sur 5 ans: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v4.i5-6.60
pages 647-662

Error Control for Molecular Statics Problems

Serge Prudhomme
The University of Texas at Austin
Paul T. Bauman
Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712
J. Tinsley Oden
Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA

RÉSUMÉ

In this paper, we present an extension of goal-oriented error estimation and adaptation to the simulation of multiscale problems of molecular statics. Computable error estimates for the quasicontinuum method are developed with respect to specific quantities of interest, and an adaptive strategy based on these estimates is proposed for error control. The theoretical results are illustrated on a nanoindentation problem in which the quantity of interest is the force acting on the indenter. The promising capability of such error estimates and adaptive procedure for the solution of multiscale problems is demonstrated on numerical examples.


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