SCAIM Seminar: Christoph Ortner

Abstract:

Continuum mechanics models generally have an astonishing range of validity. For example, nonlinear elasticity can accurately describe the elastic behaviour of crystals even at the sub-grain scale (see talk on Monday). However, crystal defects such as cracks and dislocations are difficult to model quantitatively within CM. By coupling atomistic models of defects with continuum models of elastic far fields one can, in principle, obtain models with near-atomistic accuracy at significantly reduced computational cost. That said, various pitfalls must be overcome in the construction of efficient and reliable coupling mechanisms. In this talk, I will take a numerical analysis approach to this problem  and analyze a sequence of coupling mechanisms in terms of their accuracy relative to their computational cost, which requires a thorough understanding of the consistency errors committed in the coupled models.