Title: Theory and Algorithms for the Quasicontinuum Method

Speaker: Mitchell Luskin, School of Mathematics University of Minnesota

Date/Time: Monday, March 17, 2008, 10:00am – 11:00am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: The quasicontinuum approximation is a method to reduce the atomistic degrees of freedom of a crystalline solid by piecewise linear interpolation from representative atoms. The coarsened triangles can be further approximated by a strain energy density based on the Cauchy-Born rule to obtain the finite element approximation in the continuum region.

The forces on all of the representative atoms are determined except for those representative atoms in an atomistic-continuum interfacial region, where it is not known how to model the forces to simultaneously satisfy conditions of accuracy, efficiency, and conservation. We will present a theoretical framework for evaluating the goal-oriented accuracy of the atomistic-continuum interface, and we will apply this theory to analyze several quasicontinuum approximations.

We will also present an a posteriori goal-oriented error estimator and a corresponding adaptive atomistic-continuum modeling and mesh refinement algorithm to enable a quantity of interest to be efficiently computed to a predetermined accuracy.

Joint work with Marcel Arndt and Matthew Dobson

CSRI POC: Richard Lehoucq, (505) 845-8929