Iterative methods for the force-based quasicontinuum approximation : analysis of a 1D model problem
Dobson, M., Luskin, M. and Ortner, Christoph. (2011) Iterative methods for the force-based quasicontinuum approximation : analysis of a 1D model problem. Computer Methods in Applied Mechanics and Engineering, Vol.200 (No.37-40). pp. 2697-2709. ISSN 0045-7825Full text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.cma.2010.07.008
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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Computer Methods in Applied Mechanics and Engineering|
|Date:||1 September 2011|
|Page Range:||pp. 2697-2709|
|Access rights to Published version:||Restricted or Subscription Access|
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