U.S.-Bulgaria Research on Iterative Methods for Large-Scale Discretization Problems

美国和保加利亚联合合作研究， 大规模迭代法 离散化问题是由Tony F. C. Chan和巴里F.的史密斯 加州大学，洛杉矶，博士。 Panayot Vassilevski，Svetozar D.马格诺夫， 和中心的奥列格·P·伊利耶夫博士 信息学计算机技术. 的 研究主题将包括计算 研究（性能和分析）效率 迭代方法，基于域 分解，多级，并在ILU上 离散微分求解技巧 方程 这样的合作将有利于 双方有不同的经验， 多层次、多领域的各个方面 分解和一般预处理 方法. 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，当 离散椭圆型方程 各向异性，对流扩散型问题， 弹性方程，包括 不可压缩极限和纳维尔-斯托克斯方程 方程，例如流函数 涡度公式 推导的进展 有效的解决方法，如 Navier-Stokes方程应适用于 一大类重要的过程，比如说， 生态学、天气预报、石油和天然气 恢复、设计新的建设性要素 材料和流体动力学。 这项数学研究满足了 科学发展的计划目标 让美国的顶尖专家 和保加利亚联合收割机互补人才 并将研究资源集中在 共同利益和能力。

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.