Postdoc: Portable Parallel Preconditioning

博士后：便携式并行预处理

• 批准号: 9626298
• 负责人: John Gilbert
• 金额: $ 4.62万
• 依托单位: Palo Alto Research Center Incorporated
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-09-01 至 1998-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626298&HistoricalAwards=false
• 关键词: Postdoc; Portable; Parallel; Preconditioning

This project will study parallel preconditioners used by iterative methods to solve general sparse linear systems of equations. The new preconditioning algorithms will be based on Incomplete Factorization of Complete Matrices (IFCM; for example, ILU) and Complete Factorization of Incomplete Matrices (CFIM). The latter approach is rather new. The PI plans to extend the combinatorial algorithms developed in the parallel direct methods to the construction of parallel preconditioners. By exploiting both structural and algebraic features of the original matrix, they will design parallel linear solvers with a blend of techniques along the continuous spectrum from pure iterative to pure direct methods. The new preconditioners are independent of problem domain, and hence are suitable to be used in general-purpose library software. Besides fundamental algorithms research, the PI will produce widely usable parallel libraries and tools for computational scientists and engineers. The preconditioning software will be based on and augment the best available parallel direct-method software and tools, some of which is being developed in the PIs thesis work. The new algorithms and libraries will be bench marked in several applications, such as unsymmetric sparse eigenvalue computation, groundwater remediation modeling, and Stokesian dynamics models of colloidal suspensions.

本计画将研究平行预条件子用于迭代法求解一般稀疏线性方程组。 新的预处理算法将基于完全矩阵的不完全因子分解（IFCM;例如，ILU）和不完全矩阵的完全因子分解（CX）。 后一种方法是相当新的。 PI计划将并行直接方法中开发的组合算法扩展到并行预处理器的构建。 通过利用原始矩阵的结构和代数特征，他们将设计并行线性求解器，并将沿着从纯迭代到纯直接方法的连续谱技术混合在一起。 新的预条件子与问题域无关，因此适合于在通用图书馆软件中使用。 除了基础算法研究，PI还将为计算科学家和工程师提供广泛可用的并行库和工具。预处理软件将基于和增强最好的并行直接法软件和工具，其中一些正在开发的PI论文工作。 新的算法和库将基准标记在几个应用程序中，如非对称稀疏特征值计算，地下水修复建模，和斯托克斯动力学模型的胶体悬浮液。