Series: Mathematics Colloquium

Date: Thursday, January 24, 2002

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Jinchao Xu

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: Gunnar Martinsson, University of Texas 

Title: Model Selection in Problems Involving Multiple Length-Scales

Abstract: 

The core dilemma in the analysis of multiple-scale phenomena lies in
choosing a mathematical or computational model that is simple enough
to be readily solvable, yet captures enough of the fine scale that the
solution is accurate.  The selection of such a model is typically
characterized by a high degree of arbitrariness where the modeler
needs to rely on his experience and judgment to find a model that
works for a particular case.  In this lecture, I will demonstrate that
for conduction problems and elasto-static problems on certain
heterogeneous media, the selection of a simplified model, given a
fine-scale model, can be automated.  The simplified model is chosen
out of a large class of conceivable models in such a way that any
preset level of accuracy is guaranteed to be met.  Applications of
this work to the design of certain ultra-light materials will be
discussed.