This Presidential Young Investigator (PYI) Award will be devoted to computational engineering, in particular, the following three areas will be examined: algorithmic enhancements, applications to computational fluid dynamics and other convective-diffusive systems, and implementation on parallel supercomputers. For field problems with in two or more dimensions, domain decom- position is a natural way to partition operations across proces- sors and to partition data across memories, since both the data structures and the algorithms employed in a proven serial code can be carried over to the parallel case with special code to treat the artificially introduced partitioning boundaries. The principal bottleneck to parallelizing iterative schemes is the preconditioning. The goal of preconditioning in domaindecom- position is to create independent or nearly independent threads of execution and optimal memory management of problems too large to fit in active core. Some of the issues to be examined under algorithmic include: 1. adaptive gridding and transition between levels of refinements occurring at subdomain boundaries. 2. adaptive updates of preconditioning and active control of local convergence rates. 3. transitional regions between subdomain boundaries for three dimensional problems. The implementation issues to be addressed are: 1. complex domain geometry. 2. characterizing the performance of supercomputers (Cray, etc) on domain-decomposed applications. 3. comparison between domain-decomposed out-of-core solution techniques with traditional techniques. Some of the test problems for which domain decomposition will be applied are: aerodynamics modeling. oil reservoir modeling, semi- conductor device physics modeling, and detailed kinetics combustion modeling.
