U.S.-Bulgaria Research Project on Block Factorization Preconditioners

9220287 Chan这项美国-保加利亚关于大规模离散化问题迭代方法的联合合作研究是由加州大学洛杉矶分校的Tony F.-C.Chan博士和Barry F.Smith博士，以及信息学和计算机技术中心的Panayot Vassilevski博士、Svetzar D.Margenov博士和Oleg P.Iliev博士共同完成的。研究主题将包括高效迭代方法的计算研究(性能和分析)，基于区域分解，多层，以及求解离散微分方程的ILU技术。这种合作将使双方受益，因为双方在多层次、区域分解和一般预条件方法的各个方面都有不同的经验。研究的重点将集中在当离散具有强各向异性的椭圆型方程、对流扩散型问题、包括不可压缩极限的弹性方程和流函数涡度公式中的Navier-Stokes方程时所获得的各向异性、非对称、不定和/或几乎不定问题。在推导Navier-Stokes方程等问题的有效解方法方面的进展应该适用于一大类重要的过程，如生态学、天气预报、油气开采、新结构元素和材料的设计以及流体力学。这项数学研究通过使美国和保加利亚的顶尖专家能够将互补的人才结合在一起，并在相互感兴趣和能力很强的领域汇集研究资源，从而实现了推动科学发展的计划目标。***

9220287 Chan 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, multilevel, 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. ***