Prudhomme 200710

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Speaker: Serge Prudhomme, University of Texas at Austin, USA

Title: Estimation and Control of Approximation Errors for Atomistic-to-Continuum Coupling Methods

When: The NA seminar meets on Oct 25 at 15:15 in D4523


Abstract

In this talk, we present an ongoing effort geared toward the development of an adaptive error control strategy for multi-scale problems solved by atomistic-to-continuum coupling methods. The main chal- lenges in using such coupling methods are to make sure that the models are compatible, that the regions where the continuum and atomistic models should be used are properly determined, and that the over- lapping region between the two models of different scales are appropriately constructed. Our goal is to develop an approach that automatically selects the position and size of the overlapping region so as to control the modeling error within preset levels of accuracy. We extend here the so-called goal-oriented adaptive modeling theory and methodology to complex molecular-continuum systems such as those encountered in polymer materials of interest to the nano-manufacturing industry. The key idea of the approach is to upgrade the surrogate model, provided by the coupling method, by automatically enlarg- ing the atomistic region so as to systematically reduce the modeling error with respect to quantities of interest. Theoretical and practical issues associated with the implementation of such a strategy will be discussed.

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