Beyond multiscale and multiphysics: Multimaths for model coupling
X. Blanc, C. Le Bris, F. Legoll and T. Lelievre
Networks and Heterogeneous Media, 5, 423-460 (2010).

ABSTRACT
The purpose of this article is to present a unified view of some multiscale
models that have appeared in the past decades in computational materials
science. Although very different in nature at first sight, since they are
employed to simulate complex fluids on the one hand and crystalline solids on
the other hand, the models presented actually share a lot of similarities, many
of those being in fact also present in most multiscale strategies. The
mathematical and numerical difficulties that these models generate, the way in
which they are utilized (in particular as numerical strategies coupling
different models in different regions of the computational domain), the
computational load they imply, are all very similar in nature. In particular, a
common feature of these models is that they require knowledge and techniques
from different areas in Mathematics: theory of partial differential equations,
of ordinary differential equations, of stochastic differential equations, and
all the related numerical techniques appropriate for the simulation of these
equations. We believe this is a general trend of modern computational modelling.