Embassy Suites
Albuquerque, New Mexico
March 20-21, 2006

The goal of our workshop is to bring together a group of scientists to understand and quantify the limits in Atomistic-to-Continuum (AtC) coupling and the resulting impact on multiscale simulations. AtC coupling has emerged as a critical component in computational materials science and other applications of interest to the DOE Office of Science. Past research in AtC model and algorithm development has been primarily driven by applications and has paid off in the formulation of procedures that address specific applications. This previous research has also begun to lead to some degree of generalization. However, much less effort has been directed at the fundamental mechanics and/or mathematical theory of AtC methods. For example, a rigorous mechanical formulation, and error, stability, convergence analysis and uncertainty quantification of coupling atomistic and continuum models is lacking. As a result, a mathematical and mechanical framework that can provide a unified theoretical foundation for the formulation, analysis, and implementation of AtC coupling methods is an important open problem.

The goal of our workshop is to understand and quantify the limits in AtC coupling and the resulting impact on multiscale simulations. In particular, the following questions serve to focus the workshop:

1. What are the pros and cons of the existing AtC coupling methods?
2. What are the fundamental mechanical distinctions between atomistic and continuum models and their impact upon AtC coupling methods?
3. What are the mechanical relationships that must hold for any AtC coupling method? What is the synthesis with a mathematical theory for AtC coupling methods?
4. Can we quantify the approximation made by any numerical scheme for AtC
   coupling? What are the mathematical abstractions needed for such a quantification?
5. What example problems and simulations best illustrate the underlying mathematical and mechanical issues?
6. To what extent can we leverage the existing mathematical approaches such as domain decomposition, approximation theory, and stochastic analysis for AtC methods?
   

• Claude Le Bris
• Pavel Bochev
• Jacob Fish
• Rich Lehoucq
• Greg Wagner

Researchers Discuss Atomistic-to-Continuum (AtC) Coupling
Michael L. Parks and Richard B. Lehoucq
Sandia National Laboratories
April 12, 2006