Plenary and Semi-Plenary Lectures
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| Title: |
| Adaptive Multi-scale Modeling of Complex Systems |
| Lecturer: |
| J. Tinsley Oden |
| Abstract: |
| In recent work, we have introduced the notion of a posteriori estimation of error due to the choice of mathematical models of physical events. Modeling error can then be controlled through an adaptive process that employs so-called goal-oriented adaptive methods. The theory is based on the idea that a base model can be identified that serves as a datum with respect to which other models can be compared. We demonstrate that this process of model comparison, error estimation, and error control can be used to compare models exhibiting different spatial and temporal scales, and therefore provide a powerful framework for multi-scale modeling. We describe the theory of adaptive control of models, present relevant mathematical results, and demonstrate the approach as it applies to problems in nano-manufacturing where combined quantum-molecular dynamics-continuum models are encountered. It is shown that, given a base model of target quantities of interest, the adaptive goals algorithms lead automatically to hybrid models of possibly many scales, tuned so that key features are modeled within preset levels of accuracy. |
 J. Tinsley Oden is Associate Vice President for Research and the Director of the Institute for Computational Engineering and Sciences (ICES) at The University of Texas at Austin. Oden holds the Cockrell Family Regents Chair #2 in Engineering and the Peter O'Donnell Chair in Computer Systems. He is a Professor of Aerospace Engineering and Engineering Mechanics and a Professor of Mathematics. A member of the U. S. National Academy of Engineering, Oden has worked extensively on the mathematical theory and implementation of numerical methods applied to problems in solid and fluid mechanics. Oden is an Editor of Computer Methods in Applied Mechanics and Engineering. He has received numerous awards in recognition of his research accomplishments, including the IACM Congress Medal and four honorary doctorates. He was a founding member and first President of the USACM and founding member and past President of the IACM. |
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