2017-12-06
10:15 at HCP F 43.4

Atomistic and multi-scale simulation of crystalline defects - From the perspective of numerical analysis

Christoph Ortner

Mathematics Institute, University of Warwick, United Kingdom

A key problem of atomistic materials modelling is to determine properties of lattice defects, such as geometries, formation energies, or mobility, from which meso-scopic material properties or coarse-grained models (e.g., Kinetic Monte-Carlo, Discrete Dislocation Dynamics, Griffith-type fracture laws) can be derived. Their multi-scale nature (complex defect cores coupled to long-range elastic fields) often makes it a subtle (and sometimes highly non-trivial) task to develop accurate and efficient numerical schemes. For example, QM/MM hybrid methods have become a popular tool in this field. The key challenge in the construction of QM/MM schemes is the interface condition coupling quantum chemistry to atomistic mechanics. A poor choice of interface condition can lead to uncontrollable simulation errors. In this talk I will describe an emerging mathematical / numerical analysis approach to multi-scale modelling which leads to the construction of several new multi-scale schemes, including new QM/MM type schemes, for which rigorous error estimates and convergence rates with respect to computational cost can be established.