*The Role of the Patch Test in Atomistic-to-Continuum Coupling Methods*

**Christoph Ortner**

University of Oxford

Mathematical Institute

`ortner@maths.ox.ac.uk`

**Abstract**: Low energy equilibria of crystalline materials are
typically characterized by localized defects that interact with their
environment through long-range elastic fields. By coupling atomistic models of
the defects with continuum models for the elastic far field one can, in
principle, obtain models with near-atomistic accuracy at significantly reduced
computational cost. Several pitfalls need to be overcome to construct a
reliable coupling mechanism. Possibly the most widely discussed among these
are the so-called ghost forces that typically arise in energy-based A2C
coupling mechanisms.

In this talk I will first describe the construction of energy-based A2C coupling methods, how ghost forces arise, and present some ideas how to avoid them. I will then explain the resulting modelling errors due to different types of interface treatment. I will give partial answers to the fundamental theoretical question whether absence of ghost forces automatically implies ``high accuracy''. of the coupling scheme.