Title: Benchmarking Multiscale Methods

Speaker: Ronald Miller, Mechanical and Aerospace Engineering, Carleton University

Date/Time: Tuesday, Sept. 22, 2008, 9:30 – 10:30 am MT

Location: CSRI/279 (NM), Videoconference to 915/W133 (CA)

Brief Abstract: In recent years there has been a multitude of new methods developed to couple an atomistic model to a continuum-based approximation (such as finite elements).  The goal of these methods is to be able to reproduce the results of a fully atomistic simulation at a reduced computational cost.  Naturally each of these methods has associated with it an inherent accuracy and efficiency, however it is difficult to compare these attributes between methods for three reasons.  First, it is necessary to spell out what is a suitably rigorous yet sufficiently simple and controllable test problem to study as a benchmark for these methods.  Second, it is necessary to implement all these methods within a unified overall framework.  This eliminates any differences between elements that are common across methods (such as, for instance, routines to compute atomic forces or solver algorithms), and thus permits a fair comparison.  Third, a common numerical analysis of the methods is required to clearly identify the differences between the methods and how their accuracy and efficiency can be controlled.

In this work, we move towards overcoming these difficulties.  We present a 2D implementation of a large number of the methods taken from the literature.  This allows quantitative comparison between their accuracy and efficiency in modeling a problem involving the structure and motion of a dislocation dipole in a single crystal. Finally, a complementary numerical analysis is used to improve the efficiencies in the 2D implementation.  Specifically, the analysis suggests ways to control errors in the methods, to understand how the error converges with model size and to improve solver algorithms.

CSRI POC: Mike Parks, (505) 845-0512