An adaptive strategy for the control of modeling error in two-dimensional atomic-to-continuum coupling simulations

DOI10.1016/j.cma.2008.12.026zbMath1227.74089OpenAlexW2062698844MaRDI QIDQ649436

Hachmi Ben Dhia, Serge Prudhomme, Ludovic Chamoin, Paul T. Bauman

Publication date: 30 November 2011

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2008.12.026

zbMATH Keywords

a posteriori estimationArlequin frameworkatomic-to-continuum coupling methodsgoal-oriented error estimation and adaptivity

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15) Molecular, statistical, and kinetic theories in solid mechanics (74A25)

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Cites Work

• Unnamed Item
• Adaptive multiscale modeling of polymeric materials with Arlequin coupling and goals algorithms
• An introduction to computational nanomechanics and materials
• A bridging domain method for coupling continua with molecular dynamics
• On the application of the Arlequin method to the coupling of particle and continuum models
• Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method
• Analysis and adaptive modeling of highly heterogeneous elastic structures
• Coupling of atomistic and continuum simulations using a bridging scale decomposition.
• Adaptive modeling of wave propagation in heterogeneous elastic solids.
• Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. I: Error estimates and adaptive algorithms
• Estimation of modeling error in computational mechanics.
• Validity and failure of the Cauchy-Born hypothesis in a two-dimensional mass-spring lattice
• Analyse mathématique de la méthode Arlequin mixte
• An optimal control approach to a posteriori error estimation in finite element methods
• On Atomistic-to-Continuum Coupling by Blending
• Problèmes mécaniques multi-échelles: la méthode Arlequin
• MultiScale Modeling of Physical Phenomena: Adaptive Control of Models
• The Arlequin method as a flexible engineering design tool
• Estimation of local model error and goal-oriented adaptive modeling of heterogeneous materials. II: A computational environment for adaptive modeling of heterogeneous elastic solids
• Goal-oriented error estimation and adaptivity for the finite element method