|Frontiers of Scientific Computing Lecture Series|
|Adaptive Multiscale Modeling of Large-Scale Molecular Systems|
|Tinsley Oden, Institute for Computational Engineering and Sciences, The University of Texas at Austin|
|Life Sciences Building Annex A101 Auditorium
September 12, 2007 - 03:00 pm
In his monumental work on the philosophy of science published in 1951, philosopher Hans Reichenbach observed that "If error is corrected whenever it is recognized as such, the path to error is the path of truth." Reichenbach thus laid the philosophical foundations of adaptive modeling: estimate the error and then proceed to correct it. A half-century passed before the mathematical basis and the computational power were in place to begin implementing methods of error estimation and control in complex systems. In this lecture, we explore a general method of estimating modeling and computational error in very general systems and in systematically correcting error by what we call the goals — algorithm, an adaptive method that generates a sequence of models with diminishing error in some sense. The error, in our case, is in certain "quantities of interest" and is actually a relative error, comparing the errors in a sequence of surrogate models with the solution of a well-defined base model. As an application of this philosophy, we consider a class of problems in molecular statics of polymers that is encountered in manufacturing nano-scale semiconductor devices. We give examples of modeling error estimation and adaptive modeling in which the sequences of surrogate models are generated using atomistic (molecular)-to-continuum scaling. Our methods provide a rigorous and systematic approach to methods of coarse-graining, dimensional reduction, homogenization, and averaging prevalent in literature on multiscale modeling.
Tinsley Oden is Associate Vice President for Research and Director of the Institute for Computational Engineering and Sciences (ICES) at The University of Texas at Austin. Oden holds the Cockrell Family Regents' Chair in Engineering and the Peter O'Donnell, Jr. Centennial Chair in Computer Systems. He is a Professor of Aerospace Engineering and Engineering Mechanics and a Professor of Mathematics. Professor Oden is a member of the U.S. National Academy of Engineering and the National Academies of Engineering of Mexico and of Brazil. He serves on numerous organizational, scientific and advisory committees for international conferences and symposiums. He is an Editor of Computer Methods in Applied Mechanics and Engineering and serves on the editorial board of 26 scientific journals. Oden has published extensively in computational science and in related areas over the last three decades. His current research focuses on the development of computational methods for multi-scale modeling, with applications to semi-conductor manufacturing and on computer models for the adaptive control of laser therapies for cancer.
|This lecture has a reception.|