This US-Bulgaria Joint Cooperative Research on Iterative Methods for Large-Scale Discretization Problems is between Dr. Tony F.- C. Chan and Dr. Barry F. Smith of the University of California, Los Angeles, and Dr. Panayot Vassilevski, Dr. Svetozar D. Margenov, and Dr. Oleg P. Iliev of the Center of Informatics & Computer Technology. The research topics will include computational study (performance and analysis) of efficient iterative methods, based on domain decomposition, multi-level, and on ILU techniques for solving discretized differential equations. Such a collaboration will benefit both sides which have different experience on various aspects of multi-level, domain decomposition and general preconditioning methods. The research will focus on anisotropic, nonsymmetric, indefinite and/or almost indefinite problems obtained when discretizing elliptic equations with strong anisotropy, convection-diffusion type problems, elasticity equations including the incompressible limit, and Navier-Stokes equations, for example in stream-function vorticity formulation. Advances in deriving efficient solution methods for problems such as Navier-Stokes equations should be applicable to a large class of important processes in, say, ecology, weather prediction, oil and gas recovery, design of new constructive elements and materials, and in fluid dynamics. This research in mathematics fulfills the program objective of advancing science by enabling leading experts in the United States and Bulgaria to combine complementary talents and pool research resources in areas of strong mutual interest and competence.
