Event Type:

Department Colloquium

Date/Time:

Tuesday, March 8, 2005 - 07:00

Location:

Kidd 364

Guest Speaker:

Institution:

Institute for Computational Engineering and Sciences, The University of Texas at Austin

Abstract:

It is common knowledge that the accuracy with which computer simulations can depict physical events depends strongly on the choice of the mathematical model of the events. Perhaps less appreciated is the notion that the error due to modeling can be defined, estimated, and used adaptively to control modeling error,provided one accepts the existence of a base model that can serve as a datum with respect to which other models can be compared. In this lecture, it is shown that the idea of comparing models and controlling model error can be used to develop a general approach for multi-scale modeling, a subject of growing importance in computational science. A posteriori estimates of modeling error in so-called quantities of interest are derived and a class of adaptive modeling algorithms is presented. Generalizations of the theory to the problem of adaptive calibration of models are presented for cases in which experimental data on certain quantities of interest are available and the base model itself is not well defined. Several applications of the theory and methodology are presented. These include the analysis of molecular statics models of nanoindentation, random multi-phase composite materials, modeling quantum mechanics, and the quantum mechanics-molecular dynamics interface.