Iterative Solvers on Parallel Architectures for Partial Differential Equations

偏微分方程并行结构的迭代求解器

• 批准号: 8917592
• 负责人: David Young
• 金额: $ 39.86万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-02-15 至 1993-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8917592&HistoricalAwards=false
• 关键词: Iterative; Solvers; Parallel; Architectures; Partial

The proposed work is concerned with the development, evaluation and testing of iterative algorithms and programs for solving large sparse systems of linear algebraic equations that typically arise in the numerical solution of partial differential equations by finite difference methods or by finite element methods. The main emphasis is on the efficient use of vector and parallel computer architectures. The research studies focus on parallel iterative algorithms designed for several types of computer architectures. General research studies on certain aspects of iterative algorithms including convergence rates, determination of iterative algorithms, and the treatment of nonsymmetric systems will also be made. A novel feature of the work is the development of hybrid iterative/direct methods designed to combine the best features of both types of methods. Computational kernels and research-oriented software will be developed for parallel architectures. The algorithms and software will be evaluated using a class of test problems and also using linear systems derived from biomedical problems and other physical applications. An important aspect of the work is the collaboration with researchers at other institutions. This will be especially important for the work on hybrid methods.//

这项工作涉及开发、评估和测试用于求解大型稀疏线性代数方程组的迭代算法和程序，这些算法和程序通常出现在用有限差分法或有限元方法数值求解偏微分方程组时。主要的重点是有效地使用矢量和并行计算机体系结构。研究集中在为几种类型的计算机体系结构设计的并行迭代算法上。还将对迭代算法的某些方面进行一般性研究，包括收敛速度、迭代算法的确定以及非对称系统的处理。这项工作的一个新特点是开发了混合迭代/直接方法，旨在结合两种方法的最佳特征。将为并行体系结构开发计算内核和面向研究的软件。算法和软件将使用一类测试问题进行评估，还将使用源自生物医学问题和其他物理应用的线性系统进行评估。这项工作的一个重要方面是与其他机构的研究人员合作。这对于混合方法的工作尤其重要。//