منابع مشابه
An Analysis of the Quasicontinuum Method
The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. [18, 19] and to analyze its accuracy and convergence characteristics. Specifically, we assess the effect of the summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong singularities, such as point loads; and we...
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We introduce an algorithm for treating growth on surfaces which combines important features of continuum methods ~such as the level-set method! and kinetic Monte Carlo ~KMC! simulations. We treat the motion of adatoms in continuum theory, but attach them to islands one atom at a time. The technique is borrowed from the dielectric breakdown model. Our method allows us to give a realistic account...
متن کاملAnalysis of a Quasicontinuum Method in One Dimension
Abstract. The quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we aim to give a detailed a priori and a posteriori error analysis for a quasicontinuum method in one dimension. We consider atomistic models with Lennard–Jones type long-range interactions and a QC formulation which incorpora...
متن کاملA $\Gamma$-Convergence Analysis of the Quasicontinuum Method
We present a Γ-convergence analysis of the quasicontinuum method focused on the behavior of the approximate energy functionals in the continuum limit of a harmonic and defectfree crystal. The analysis shows that, under general conditions of stability and boundedness of the energy, the continuum limit is attained provided that the continuum—e.g., finite-element— approximation spaces are strongly...
متن کاملA-Priori Analysis of the Quasicontinuum Method in One Dimension
The quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we give an a-priori error analysis for the quasicontinuum method in one dimension. We consider atomistic models with Lennard–Jones type long range interactions and a practical QC formulation. First, we prove the existence, the local uni...
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ژورنال
عنوان ژورنال: International Journal for Numerical Methods in Engineering
سال: 2018
ISSN: 0029-5981,1097-0207
DOI: 10.1002/nme.5991