Speaker: Christoph Ortner (University of Oxford)
Title: Introduction to Quasicontinuum Methods: Formulation, Classification, Analysis
Abstract:In the first part of the talk I will, in general terms, motivate the need and the potential for coupling models of increasing complexity to describe materials at the atomistic scale. One of the simplest examples is the quasicontinuum method for coupling classical molecular mechanics (statics!) to nonlinear elasticity finite element methods. In the second part of my talk, I will derive two QC methods for a simple 1D model problem and show some recent analytic results about their properties. In the third part of the talk, I will give a more detailed analysis of a third QC method (the quasi-nonlocal coupling method of Shimokava et al). For this method, it is possible to prove that "local minimizers" of the atomistic model and the QNL model correspond 1-1.