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

[9220287]本文由Tony f . c .博士与美国-保加利亚联合开展的大规模离散化问题迭代方法研究。Chan和加州大学洛杉矶分校的Barry F. Smith博士，以及信息学和计算机技术中心的Panayot Vassilevski博士、Svetozar D. Margenov博士和Oleg P. Iliev博士。研究课题将包括计算研究（性能和分析）的有效迭代方法，基于域分解，多层次，和ILU技术解决离散微分方程。这种合作将使双方受益，双方在多层次、领域分解和一般预处理方法的各个方面都有不同的经验。研究将集中在各向异性、非对称、不定和/或几乎不定的问题上，这些问题是在对具有强各向异性的椭圆方程、对流扩散型问题、包括不可压缩极限的弹性方程以及流函数涡量公式中的Navier-Stokes方程进行离散时得到的。在求解诸如Navier-Stokes方程等问题的有效方法方面取得的进展应该适用于诸如生态学、天气预报、石油和天然气开采、新构造元素和材料的设计以及流体动力学等一系列重要过程。这项数学研究通过使美国和保加利亚的顶尖专家在共同感兴趣和能力强的领域结合互补的人才和集中研究资源，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. ***