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

9220287陈 这个美国和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Tony F. C. Chan和巴里F. 加州洛杉矶大学的史密斯博士和帕纳约特·瓦西列夫斯基博士、斯韦托扎尔·D·Margenov和信息学计算机技术中心的Oleg P. Iliev博士。 研究课题将包括有效的迭代方法的计算研究（性能和分析），基于区域分解，多级和ILU技术解决离散微分方程。 这种合作将有利于双方在多层次，区域分解和一般预处理方法的各个方面有不同的经验。 研究将集中在各向异性，非对称，不确定和/或几乎不确定的问题时，离散椭圆方程与强各向异性，对流扩散型问题，弹性方程，包括不可压缩的限制，和Navier-Stokes方程，例如在流函数涡公式。 在导出诸如Navier-Stokes方程之类的问题的有效求解方法方面的进展应该适用于生态学、天气预报、石油和天然气开采、新结构元件和材料的设计以及流体动力学中的一大类重要过程。 这项数学研究通过使美国和保加利亚的领先专家能够联合收割机互补人才并在共同感兴趣和能力强的领域汇集研究资源，实现了推进科学的计划目标。 ***

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. ***