ALGORITHMS: New Concept and Parallel Algorithms for Robust Preconditioning in Large Scale Parallel Matrix Computation

算法：大规模并行矩阵计算中鲁棒预处理的新概念和并行算法

• 批准号: 0202934
• 负责人: Jun Zhang
• 金额: $ 17.24万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-01 至 2006-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0202934&HistoricalAwards=false
• 关键词: ALGORITHMS; New; Concept; Parallel; Algorithms

Large sparse unstructured matrices arising from various computer simulation and modeling are commonly solved by preconditioned iterative methods. This research project will study and design robust high performance preconditioners for parallel solution of large sparse linear systems, based on a class of multistep successive sparse approximate inverse preconditioning techniques.We will develop new concept and parallel algorithms of multistep successive preconditioning for enhancing the robustness of standard sparse approximate inverse preconditioning techniques, and generalize this concept to the context of other preconditioning techniques. Study will be conducted to show the advantages of such approach to enhance both preconditioning accuracy and factorization stability. We will build portable software packages to implement new preconditioning strategies for solving unstructured general sparse linear systems on high performance parallel computers.The general purpose high performance preconditioned iterative solvers from this research project are expected to make significant impact in the field of applied scientific computing. Our experience and existing strength will ensure that theproject be carried out fully as proposed. As U.S. industry is more and more relying on computer aided design and manufacturing, large scale computer simulation and modeling will be a vital component in new products research and development. The outcome of this research will benefit U.S. industry as well as scientific research community by providing more efficient kernel software forlarge scale computer simulations.

通常通过预处理的迭代方法解决了由各种计算机模拟和建模产生的大稀疏非结构矩阵。该研究项目将基于一类多阶段连续的稀疏近似近似逆向预处理技术来研究和设计可靠的高性能预处理，以实现大型稀疏线性系统的平行解决方案。我们将开发新的概念和多步骤连续的算法连续的算法，以增强标准跨度近似临近技术的稳健性，并在这些概念中增强了这些概念，并在这些概念上加强了这些概念的稳健性。将进行研究以显示这种方法的优势，以提高预处理准确性和分解稳定性。我们将构建便携式软件包，以实施新的预处理策略，以在高性能平行计算机上解决非结构化的一般稀疏线性系统。该研究项目的通用高性能预处理迭代求解器有望在应用科学计算领域产生重大影响。我们的经验和现有的力量将确保按照提议进行全面执行。由于美国行业越来越依赖计算机辅助设计和制造，因此大规模的计算机模拟和建模将是新产品研发中的重要组成部分。这项研究的结果将通过提供更有效的内核软件范例计算机模拟来使美国行业和科学研究社区受益。