Preconditioned Interative Methods for Large Linear Systems

大型线性系统的预条件交互方法

• 批准号: 9802919
• 负责人: Anne Greenbaum
• 金额: $ 6.22万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9802919&HistoricalAwards=false
• 关键词: Preconditioned; Interative; Methods; Large; Linear

The numerical solution of large sparse linear algebraic equationsrepresents a very significant portion of scientific computing.Such linear systems arise from the discretization of partialdifferential equations as well as in many other contexts, such asthe numerical solution of nonlinear equations and optimizationproblems. Over the past two decades, significant progress hasbeen made in the development and analysis of iterative Krylovsubspace methods. This project will address a number of theoreticaland practical issues associated with the use of Krylov spacemethods for solving linear systems.One of the large remaining open problems in this field is the development of a clear method of choice for nonsymmetric problems.Analysis of nonsymmetric Krylov space methods will be a componentof this project. It is also important to understand the effect ofrounding errors on the performance of both symmetric and nonsymmetriciterative methods and this topic will also be addressed. Finally,from a practical point of view, it is most often the preconditionerthat has the greatest effect on the performance of an iterative method. Ideas developed in this research will be applied in problems involving neutron transport and ground-water flow simulationto test their practicality. Parallelism will be a considerationin all of the work.

大型稀疏线性代数方程的数值解决方案表达了科学计算的很大一部分。类似的线性系统是由partialDifference方程的离散化以及许多其他情况下引起的，例如非线性方程和优化问题的数值解决方案。在过去的二十年中，在迭代krylovsubspace方法的开发和分析中取得的重大进展。 该项目将解决与使用Krylov空间方法来求解线性系统有关的许多理论和实际问题。该领域中剩余的大问题之一是开发出一种清晰的非对称问题方法，以解决非对称的问题。方法将是该项目的组成部分。 还要理解误差对对称和非对称方法的性能的影响也很重要，并且该主题也将得到解决。 最后，从实际的角度来看，这通常是对迭代方法的性能的最大影响。 这项研究中提出的想法将应用于涉及中子运输和地下水流量模拟的问题，以测试其实用性。 并行性将是所有工作中的考虑。