Introduction to Quasicontinuum Methods: Formulation, Classification, Analysis
|
Thu, 21/05/2009 14:00 |
Dr. Christoph Ortner (Computing Laboratory, Oxford) |
Computational Mathematics and Applications  |
Comlab |
| 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. | |||