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Carnegie Mellon Center for Nonlinear Analysis
The Role of the Patch Test in Atomistic-to-Continuum Coupling Methods


Christoph Ortner
University of Oxford
Mathematical Institute

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.