## IMA Postdoc Seminar (April 14, 2009)

**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.