年間 6 号発行
ISSN 印刷: 1543-1649
ISSN オンライン: 1940-4352
Indexed in
Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation
要約
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.
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Dobson Matthew, Luskin Mitchell, Iterative Solution of the Quasicontinuum Equilibrium Equations with Continuation, Journal of Scientific Computing, 37, 1, 2008. Crossref
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Dobson Matthew, Luskin Mitchell, An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation, SIAM Journal on Numerical Analysis, 47, 4, 2009. Crossref
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Gunzburger Max, Zhang Yanzhi, A Quadrature-Rule Type Approximation to the Quasi-Continuum Method, Multiscale Modeling & Simulation, 8, 2, 2010. Crossref
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Prudhomme S., Ben Dhia H., Bauman P.T., Elkhodja N., Oden J.T., Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method, Computer Methods in Applied Mechanics and Engineering, 197, 41-42, 2008. Crossref
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Zhang Yanzhi, Gunzburger Max, Quadrature-rule type approximations to the quasicontinuum method for long-range interatomic interactions, Computer Methods in Applied Mechanics and Engineering, 199, 9-12, 2010. Crossref
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Prudhomme Serge, Chamoin Ludovic, Dhia Hachmi Ben, Bauman Paul T., An adaptive strategy for the control of modeling error in two-dimensional atomic-to-continuum coupling simulations, Computer Methods in Applied Mechanics and Engineering, 198, 21-26, 2009. Crossref
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Arndt Marcel, Luskin Mitchell, Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model, Computer Methods in Applied Mechanics and Engineering, 197, 49-50, 2008. Crossref
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Dobson Matthew, Luskin Mitchell, An analysis of the effect of ghost force oscillation on quasicontinuum error, ESAIM: Mathematical Modelling and Numerical Analysis, 43, 3, 2009. Crossref
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Wang Hao, Yang Siyao, Analysis of the Residual-Type and the Gradient Recovery-Type a Posteriori Error Estimators for a Consistent Atomistic-to-Continuum Coupling Method in One-Dimension, Multiscale Modeling & Simulation, 16, 2, 2018. Crossref
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Chung Eric, Pollock Sara, Pun Sai-Mang, Online basis construction for goal-oriented adaptivity in the generalized multiscale finite element method, Journal of Computational Physics, 393, 2019. Crossref
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Luskin Mitchell, Ortner Christoph, Atomistic-to-continuum coupling, Acta Numerica, 22, 2013. Crossref
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Wang Yangshuai, Zhang Lei, Wang Hao, A priori analysis of a higher-order nonlinear elasticity model for an atomistic chain with periodic boundary condition, IMA Journal of Numerical Analysis, 41, 2, 2021. Crossref
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Mikeš K., Bormann F., Rokoš O., Peerlings R.H.J., Comparative study of multiscale computational strategies for materials with discrete microstructures, Computer Methods in Applied Mechanics and Engineering, 382, 2021. Crossref
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Mikeš Karel, Jirásek Milan, Quasicontinuum method combined with microplane model, International Journal of Solids and Structures, 238, 2022. Crossref
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Chung Eric, Pollock Sara, Pun Sai-Mang, Goal-oriented adaptivity of mixed GMsFEM for flows in heterogeneous media, Computer Methods in Applied Mechanics and Engineering, 323, 2017. Crossref