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Introduction to Quasicontinuum Methods: Formulation, Classification, Analysis

Dr. Christoph Ortner ( Oxford University )
Quasicontinuum methods are a prototypical class of atomistic-to-continuum coupling methods. For example, we may wish to model a lattice defect (a vacancy or a dislocation) by an atomistic model, but the elastic far field by a continuum model. If the continuum model is consistent with the atomistic model (e.g., the Cauchy--Born model) then the main question is how the interface treatment affects the method. In this talk I will introduce three of the main ideas how to treat the interface. I will explain their strengths and weaknesses by formulating the simplest possible non-trivial model problem and then simply analyzing the two classical concerns of numerical analysis: consistency and stability.

 

 

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