Accéder directement au contenu Accéder directement à la navigation
Article dans une revue

Iterative methods for the force-based quasicontinuum approximation: Analysis of a 1D model problem

Abstract : Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite-element continuum model. For this reason, and due to their algorithmic simplicity, force-based coupling methods have become a popular class of atomistic-continuum hybrid models as well as other types of multiphysics models. However, the recently discovered unusual stability properties of the linearized force-based quasicontinuum (QCF) approximation, especially its indefiniteness, present a challenge to the development of efficient and reliable iterative methods. We present analytic and computational results for the generalized minimal residual (GMRES) solution of the linearized QCF equilibrium equations. We show that the GMRES method accurately reproduces the stability of the force-based approximation and conclude that an appropriately preconditioned GMRES method results in a reliable and efficient solution method.
Type de document :
Article dans une revue
Liste complète des métadonnées

https://hal-enpc.archives-ouvertes.fr/hal-00676436
Contributeur : Cermics Hal <>
Soumis le : lundi 5 mars 2012 - 12:57:47
Dernière modification le : mercredi 7 août 2019 - 15:34:13

Lien texte intégral

Identifiants

Collections

Citation

Matthew Dobson, M. Luskin, C. Ortner. Iterative methods for the force-based quasicontinuum approximation: Analysis of a 1D model problem. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2011, 200 (37-40), pp.2697-2709. ⟨10.1016/j.cma.2010.07.008⟩. ⟨hal-00676436⟩

Partager

Métriques

Consultations de la notice

153