Parallel Algebraic Recursive Multilevel Solvers: Advances in Scalable and Robust High Performance Linear System Solution Methods
并行代数递归多级求解器:可扩展且鲁棒的高性能线性系统解决方法的进展
基本信息
- 批准号:0000443
- 负责人:
- 金额:$ 46.98万
- 依托单位:
- 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:
- 关键词:
项目摘要
Parallel iterative methods are leading candidates for solving large-scale engineering and scientific problems, which usually appear as sparse linear systems. However, their robustness and overall efficiency remain mixed and problem-specific. These characteristics are closely tied to the preconditioners used as inputs to these methods. Preconditioners for general sparse linear systems remain by far the biggest stumbling block to obtaining good performance for iterative solution methods on high-performance computers in engineering and scientific applications. Accordingly, the main thrust of this project is to develop a class of preconditioning techniques based on the researchers' Algebraic Recursive Multilevel Solver (ARMS) framework. The researchers will develop the new methods and test them on realistic problems arising from the researchers' collaborations.The project will develop a class of parallel multi-level ILU-type preconditioning techniques using ARMS methods. Recursive multi-level ILU methods allow the unification of many standard iterative solvers into a single generic code. Their multi-level nature allows them to bridge the gap between the excellent problem-specifc performance of multigrid methods and the general-purpose nature of preconditioned Krylov solvers. The project will examine performance and scalability for classes of existing and new procedures thus obtained, including Schwartz procedures, Schur complement methods, direct solvers, and multilevel techniques. It will also conduct extensive realistic tests. In summary, this work promises advances in three important components of developing parallel solution methods: effective and scalable algorithms, use of effective computer science tools and data structures, and testing and validation.
并行迭代方法是解决大规模工程和科学问题的首选方法,这些问题通常表现为稀疏线性系统。然而,它们的稳健性和整体效率仍然参差不齐,并因问题而异。这些特征与用作这些方法的输入的预条件密切相关。一般稀疏线性系统的预条件仍然是高性能计算机上迭代求解方法在工程和科学应用中获得良好性能的最大绊脚石。因此,本项目的主要目的是开发一类基于研究人员的代数递归多层求解器(ARMS)框架的预处理技术。研究人员将开发新方法,并在研究人员合作产生的实际问题上进行测试。该项目将开发一类使用ARM方法的并行多级别ILU类型的预处理技术。递归多层ILU方法允许将许多标准迭代求解器统一到单个通用代码中。它们的多层次性质使它们能够弥合多重网格法优秀的特定问题性能和预条件Krylov解算器的通用性质之间的差距。该项目将检查现有的和由此获得的新程序类别的性能和可扩展性,包括Schwartz程序、Schur补码方法、直接求解器和多层次技术。它还将进行广泛的现实测试。总之,这项工作有望在开发并行求解方法的三个重要组成部分方面取得进展:有效和可扩展的算法,使用有效的计算机科学工具和数据结构,以及测试和验证。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Yousef Saad其他文献
Randomized linear solvers for computational architectures with straggling workers
用于具有落后工人的计算架构的随机线性求解器
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
V. Kalantzis;Yuanzhe Xi;L. Horesh;Yousef Saad - 通讯作者:
Yousef Saad
Efficiently Generalizing Ultra-Cold Atomic Simulations via Inhomogeneous Dynamical Mean-Field Theory from Two- to Three-Dimensions
通过二维到三维的非齐次动态平均场理论有效推广超冷原子模拟
- DOI:
10.1109/hpcmp-ugc.2010.17 - 发表时间:
2010 - 期刊:
- 影响因子:0
- 作者:
James Freericks;H. R. Krishnamurthy;Pierre Carrier;Yousef Saad - 通讯作者:
Yousef Saad
Computing charge densities with partially reorthogonalized Lanczos
- DOI:
10.1016/j.cpc.2005.05.005 - 发表时间:
2005-10-01 - 期刊:
- 影响因子:
- 作者:
Constantine Bekas;Yousef Saad;Murilo L. Tiago;James R. Chelikowsky - 通讯作者:
James R. Chelikowsky
Algorithms for the evolution of electronic properties in nanocrystals
- DOI:
10.1016/j.cpc.2007.02.072 - 发表时间:
2007-07-01 - 期刊:
- 影响因子:
- 作者:
James R. Chelikowsky;Murilo L. Tiago;Yousef Saad;Yunkai Zhou - 通讯作者:
Yunkai Zhou
Yousef Saad的其他文献
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{{ truncateString('Yousef Saad', 18)}}的其他基金
Collaborative Research: Robust Acceleration and Preconditioning Methods for Data-Related Applications: Theory and Practice
协作研究:数据相关应用的鲁棒加速和预处理方法:理论与实践
- 批准号:
2208456 - 财政年份:2022
- 资助金额:
$ 46.98万 - 项目类别:
Standard Grant
Multilevel Graph-Based Methods for Efficient Data Exploration
基于多级图的高效数据探索方法
- 批准号:
2011324 - 财政年份:2020
- 资助金额:
$ 46.98万 - 项目类别:
Standard Grant
Advances in Robust Multilevel Preconditioning Methods for Sparse Linear Systems
稀疏线性系统鲁棒多级预处理方法的进展
- 批准号:
1912048 - 财政年份:2019
- 资助金额:
$ 46.98万 - 项目类别:
Standard Grant
AF: Small: Collaborative Research: Effective Numerical Algorithms and Software for Nonlinear Eigenvalue Problems
AF:小型:协作研究:非线性特征值问题的有效数值算法和软件
- 批准号:
1812695 - 财政年份:2018
- 资助金额:
$ 46.98万 - 项目类别:
Standard Grant
Tenth International Conference on Preconditioning Techniques for Scientific and Industrial Applications
第十届科学和工业应用预处理技术国际会议
- 批准号:
1735572 - 财政年份:2017
- 资助金额:
$ 46.98万 - 项目类别:
Standard Grant
AF: Medium: Collaborative research: Advanced algorithms and high-performance software for large scale eigenvalue problems
AF:中:协作研究:大规模特征值问题的先进算法和高性能软件
- 批准号:
1505970 - 财政年份:2015
- 资助金额:
$ 46.98万 - 项目类别:
Continuing Grant
Advances in Robust Multilevel Preconditioning Methods for Sparse Linear Systems
稀疏线性系统鲁棒多级预处理方法的进展
- 批准号:
1521573 - 财政年份:2015
- 资助金额:
$ 46.98万 - 项目类别:
Standard Grant
AF: small: Numerical Linear Algebra Methods for Efficient Data Exploration
AF:小:高效数据探索的数值线性代数方法
- 批准号:
1318597 - 财政年份:2013
- 资助金额:
$ 46.98万 - 项目类别:
Standard Grant
Advances in robust multilevel preconditioning methods for sparse linear systems
稀疏线性系统鲁棒多级预处理方法的进展
- 批准号:
1216366 - 财政年份:2012
- 资助金额:
$ 46.98万 - 项目类别:
Standard Grant
Collaborative research: Development of efficient petascale algorithms for inhomogeneous quantum-mechanical systems
合作研究:开发非齐次量子力学系统的高效千万亿级算法
- 批准号:
0904587 - 财政年份:2009
- 资助金额:
$ 46.98万 - 项目类别:
Standard Grant
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