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.