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Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2011

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

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Résumé

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.

Dates et versions

hal-00676436 , version 1 (05-03-2012)

Identifiants

Citer

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, 2011, 200 (37-40), pp.2697-2709. ⟨10.1016/j.cma.2010.07.008⟩. ⟨hal-00676436⟩
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