A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods
R. E. Miller and E. B. Tadmor
Modelling and Simulation in Materials Science and Engineering, 17, 053001 (2009).

ABSTRACT
A partitioned-domain multiscale method is a computational framework in which
certain key regions are modeled atomistically while most of the domain is
treated with an approximate continuum model (such as finite elements). The goal
of such methods is to be able to reproduce the results of a fully atomistic
simulation at a reduced computational cost. In recent years, a large number of
partitioned-domain methods have been proposed. Theoretically, these methods
appear very different to each other making comparison difficult. Surprisingly,
it turns out that at the implementation level these methods are in fact very
similar. In this paper, we present a unified framework in which fourteen leading
multiscale methods can be represented as special cases.

We use this common framework as a platform to test the accuracy and efficiency
of the fourteen methods on a test problem; the structure and motion of a Lomer
dislocation dipole in face-centered cubic aluminum. This problem was carefully
selected to be sufficiently simple to be quick to simulate and straightforward
to analyze, but not so simple to unwittingly hide differences between methods.
The analysis enables us to identify generic features in multiscale methods that
correlate with either high or low accuracy and either fast or slow performance.

All tests were performed using a single unified computer code in which all
fourteen methods are implemented. This code is being made available to the
public along with this paper.