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International Journal for Multiscale Computational Engineering

ISSN for PRINT: 1543-1649

Institutional price:	$747.00
Issues per year:	6

Best Paper Award Selection - Editorial Board Site

2007, Volume5

83 pages

DOI: 10.1615/IntJMultCompEng.v5.i5

Issue price - $138.00

Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation

Marcel Arndt
School of Mathematics, University of Minnesota, 206 Church St., SE Minneapolis, MN 55455, USA

Mitchell Luskin
School of Mathematics, University of Minnesota, 206 Church St., SE Minneapolis, MN 55455, USA

ABSTRACT

We give a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method, and we use this estimator to design an adaptive algorithm to compute a quantity of interest to a given tolerance by using a nearly minimal number of atomistic degrees of freedom. We present computational results that demonstrate the effectiveness of our algorithm for a periodic array of dislocations described by a Frenkel-Kontorova-type model.