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Talk Abstract
Analysis and Adaptive Modeling of Highly Heterogeneous Materials

J. Tinsley Oden, University of Texas

An adaptive method for hierarchical modeling of highly heterogeneous materials is presented. The goal is to resolve a classical paradox in the analysis of structures with complex microstructures: how can the effects of fine-scale components of the microstructure on macroscopic response be determined without exhausting computational capacities and resources? The approach is based on a-posteriori error estimates and an adaptive process in which error in traditional homogenized characterizations is estimated and corrected in an adaptive process so as to produce results which have a specified level of accuracy. A manageable computational process is produced based on our Homogenized Dirichlet Projection Method, which updates model accuracy by incorporating fine-scale effects when needed. Several numerical experiments are described.

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1996-1997 Mathematics in High Performance Computing

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