Iterative Methods for the Force-based Quasicontinuum Approximation. (arXiv:0910.2013v1 [math.NA])

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 approach for
atomistic-continuum hybrid methods as well as other types of multiphysics model
coupling. However, the recently discovered unusual stability properties of the
linearized force-based quasicontinuum approximation, especially its
indefiniteness, present a challenge to the development of efficient and
reliable iterative methods. Using a combination of rigorous analysis and
computational experiments, we present a systematic study of the stability and
rate of convergence of a variety of linear stationary iterative methods and
generalized minimal residual methods (GMRES) for the solution of the linearized
force-based quasicontinuum equations.

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Original source : http://arxiv.org/abs/0910.2013...