Memory-Efficient Implementation of Sparse Linear Solvers

稀疏线性求解器的内存高效实现

• 批准号: 0072119
• 负责人: Elizabeth Jessup
• 金额: $ 26.34万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-15 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072119&HistoricalAwards=false
• 关键词: Memory; Efficient; Implementation; Sparse; Linear

Solving many important problems in science and engineering depends on efficiently solving sparse linear systems, that is, sets of equations with many zero entries in the coefficients. This project will study techniques for creating sparse linear solvers that make efficient use of the memory hierarcy on single processor computers. It will concentrate on methods that reformulate the original system as a blocked system, with careful choices of the blocks to speed up convergence. Performance programming techniques will reduce the costs of the extra matrix-vector operations needed by the blocked version.There are three technical goals of this work. The first is to contribute to the understanding of the numerical behavior of memory-efficient sparse linear solvers through analysis and experiment. The second is to identify at least one robust, memory-efficient sparse linear solver for inclusion in the Portable Extensible Toolkit for Scientific Computation (PETSc) library. The final goal is to develop a memory-centric performance metric for evaluating the memory traffic requirements of linear algebra algorithms.

解决科学和工程中的许多重要问题取决于有效求解稀疏线性系统，即系数中有许多零条目的方程组。该项目将研究用于创建稀疏线性求解器的技术，从而有效利用单个处理器计算机上的存储器层。它将集中于将原始系统重新制定为阻塞系统的方法，并仔细选择块以加快收敛性。性能编程技术将降低阻塞版本所需的额外矩阵向量操作的成本。这项工作有三个技术目标。首先是通过分析和实验有助于理解记忆有效的稀疏线性求解器的数值行为。第二个是至少识别一个稳健的，记忆效率的稀疏线性求解器，以包含在可移植的可扩展工具包中用于科学计算（PETSC）库。最终目标是开发以内存为中心的性能度量标准，以评估线性代数算法的内存流量要求。