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.

Back to Workshop Schedule

1996-1997 Mathematics in High Performance Computing