Multiscale Modelling Methods for Applications in Materials Science

Current advances in multiscale modelling of materials promise scientific and practical
benefits including simple physical interpretation based on analysis of the underlying submodels,
as well as an improved computational scaling and acceptable amount of produced
data, which make the simulation of large and complex real-world materials feasible. These
developments give rise to an unprecedented predictive power of multiscale models allowing
a reliable computation of macroscopic materials properties from first principles with
sufficient accuracy. However, the development of methods which efficiently couple multiple
scales in materials science is still a challenge, since (i) proper coupling schemes have to
be developed which respect the physical and chemical descriptions on the different scales;
(ii) boundary conditions for e. g. mechanics, thermodynamics or hydrodynamics have to
be respected and (iii) error control and numerical stability have to be guaranteed. In addition
to these physical and numerical requirements, multiscale modelling poses serious
challenges to the practical realization of coupled applications due to the complex organization
of interfaces between the sub-models and heterogeneity of computational environments.
Therefore, both integrative and coordination actions, such as the Max-Planck
Initiative Multiscale Materials Modelling of Condensed Matter, FP7 projects MAPPER
and MMM@HPC, or the CECAM node MM1P Multiscale Modelling from First Principles,
have been initiated which bundle the expertise of different groups (in fields such as
quantum chemistry, molecular dynamics, coarse-grained modelling methods and finite element
analysis) and move forward both the theoretical understanding as well as the practical
implementation of a multiscale simulation environment.
The knowledge of and the experience with novel multiscale techniques, such as sequential/
hierarchical modelling or hybrid methods, as well as modelling tools should be
disseminated to a larger number of groups in the materials science and physics community.
Since the topic of multiscale modelling in materials science is still underdeveloped in
university courses, it is essential to provide tutorials by established experts to young scientists
working in multiscale simulations or starting in the field. In particular, postgraduate
students and postdoctoral researchers entering the field are addressed by this tutorial.
Past winter schools like Multiscale Simulation Methods in Molecular Sciences (2009)
or Hierarchical Methods for Dynamics in Complex Molecular Systems (2012), organized at
Forschungszentrum J¨ulich focused on dynamical aspects in molecular systems on different
time scales. They addressed non-adiabatic quantum dynamics, including descriptions of
photo-induced processes, up to non-equilibrium dynamics of complex fluids, while still
keeping the atomistic scale in the classical, quantum mechanical and mixed quantumclassical
descriptions. In the present tutorial Multiscale Modelling Methods for Applications
in Materials Science we emphasize on methodologies encompassing not only the
dynamical aspects but also steady-state or/and equilibrium properties on the meso- and
macroscopic scales treated for example by coarse-grained and finite-elements methods.
Moreover, this tutorial predominantly addresses modelling of systems with modern highprofile
applications with industrial importance, such as materials for energy conversion and
storage and for next generation electronics, which are not restricted to molecular systems.
The lecture notes collected in this book reflect the course of lectures presented in the tutorial
and include twelve chapters subdivided into two parts.