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Abstract: A common problem of atomistic materials modelling is to determine properties of
crystalline defects, such as structure, energetics, mobility, from which
meso-scopic material properties or coarse-grained models can be derived (e.g.,
Kinetic Monte-Carlo, Discrete Dislocation Dynamics, Griffith-type fracture
laws). In this talk I will focus on one the most basic tasks, computing the
equilibrium configuration of a crystalline defect, but will also also comment on
free energy and transition rate computations.
A wide range of numerical strategies, including the classical supercell method
(periodic boundary conditions) or flexibe boundary conditions (discrete BEM),
but also more recent developments such as atomistic/continuum and QM/MM hybrid
schemes, can be interpreted as Galerkin discretisations with variational crimes,
for an infinite-dimensional nonlinear variational problem. This point of view is
effective in studying the structure of exact solutions, identify approximation
parameters, derive rigorous error bounds, optimise and construct novel schemes
with superior error/cost ratio.
Time permitting I will also discuss how this framework can be used to analyse
model errors in interatomic potentials and how this can feed back into the
developing of new interatomic potentials by machine learning techniques.