Predictive and efficient quasicontinuum methods

Wednesday, November 5, 2008 - 11:15am - 12:00pm
EE/CS 3-180
Mitchell Luskin (University of Minnesota, Twin Cities)
The development of predictive and efficient atomistic-to-continuum
computational methods requires both an analysis of the
error and efficiency of its many components (coupling method,
model and mesh adaptivity, solution methods) as well as its integration
into an efficient code capable of solving problems of technological interest.

There are many choices available for the interaction between the
representative atoms of the quasicontinuum method, especially between those in the atomistic
and continuum regions, which has led to the development of a
variety of quasicontinuum approximations.
We will present criteria for determining a good choice of quasicontinuum approximation that considers trade-offs between accuracy and
algorithmic efficiency. Our criteria are based on
the effect of the coupling error on the goal of
the computation, on the
integration of the quasicontinuum approximation with model and mesh adaptivity, and
on the development of efficient iterative solution methods.

Joint Work with Marcel Arndt, Matthew Dobson, Ron Miller, Christoph Ortner, and Ellad Tadmor.