Adaptive Modeling for Multi-scale Methods
J. Tinsley Oden, Paul T. Bauman, Leszek Demkowicz, and
Serge Prudhomme, (UT Austin)

In this work, we propose to apply the Goal-Oriented Adaptive Modeling method [1,2] to multiscale simulations that aim at coupling atomistic and continuum methods for the design of materials at the nanoscale. The method has been developed to control modeling errors measured in terms of quantities of interest. Goal Oriented Adaptive Modeling is a general framework based on an error estimation module that estimates the error between two different models, and an adaptive algorithm module that automatically selects the models to be used in the various regions of the computational domain. Our goal is to extend the techniques to the analysis of complex multi-scale behavior encountered in the nano-manufacturing of computer chips [3]. We will discuss practical issues associated with the development of the a
posteriori error estimators and the implementation of the adaptive scheme.

[1] J. T. Oden and S. Prudhomme. Estimation of modeling error in computational mechanics. Journal of Computational Physics, 182, 496–515, 2002.
[2] J. T. Oden, S. Prudhomme, A. Romkes, and P. Bauman. Multi-scale modeling of physical phenomena: Adaptive control of models. Submitted to SIAM Journal on Scientific Computing, 2005.
[3] D. J. Resnick, S. Sreenivasan, and C. G.Willson. Step and flash imprint lithography. Materials Today, p. 35, Feb. 2005.

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