This research focuses on the development of geometric methods and their numerical applications. The project involves the design of efficient algorithms for a variety of fundamental problems in parallel geometric and numerical computing and the implementation of these algorithms on both modern supercomputers and workstation clusters. The research has two principal directions. Geometric Methods for Unstructured Mesh Partitioning and Generation: The main theoretical and software question is how to make use of underlying geometric structures and numerical conditions to generate an unstructured finite element mesh and partition it for subsequent parallel numerical simulations. Parallel Numerical and Applications: The primary goal is to apply geometric mesh techniques to the parallel solution of large sparse linear systems, to adaptive and hierarchical computations, to distributed COSMOS circuit simulation, and to dynamic load balancing for parallel N-body simulations. The companion education plan is to design and teach courses in computer science, in the newly introduced Scientific Computation Program at the University of Minnesota, and in the areas that bridge the two. It involves the development of research programs and projects for graduate and undergraduate students who are interested in interdisciplinary research. It also involves the development of summer professional programs for professionals from industry companies, government research labs, and other universities, to initiate the collaboration between universities and industry.
