Domain Decomposition Methods: Algorithms and Theory

领域分解方法：算法和理论

• 批准号: 0513251
• 负责人: Olof Widlund
• 金额: $ 10万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0513251&HistoricalAwards=false
• 关键词: Domain; Decomposition; Methods; Algorithms; Theory

Large scale continuum mechanics simulations routinely requirethe efficient solution of very large linear or nonlinear systemsof algebraic equations as well as powerful computer systems.Such problems are increasingly solved on parallel or distributedcomputing systems which provide access to a large amount of memoryas well as a substantial number of fast processors. The goal ofthis project is to further develop solvers of domain decompositiontype, algorithms which respect the memory hierarchy of modern computing systems and allow for a performance which approaches peak floating pointperformance. There already exists a well developed mathematical theory and a good understanding of how to adjust these algorithms to problemsarising in different applications but there is also a real needto further extend our understanding and to improve and numericallytest new algorithms especially in view of emergence of parallelcomputing systems with very many powerful processors. A maingoal of this project is the further understanding of theFETI-DP and BDDC families of domain decomposition methods.The direction of the work in this field is strongly influencedby the interaction between academic computational scientistsand scientists at the US national laboratories and inthe engineering software industry. The connection to the SANDIA-Albuquerque laboratories is particularly strong. Domain decompositionmethods are used extensively in very large and important applicationsat these laboratories and the domain decomposition methods arealso making significant inroads in software systems that are usedby a large community of engineers for the design and checkingof machine parts and larger engineering structures. Particularly importantapplication areas are elasticity and electromagnetics. The latterfield helps create a foundation for improvements of cellularphone systems, other wire-less communication systems, as well asmicro electronics.

大规模连续介质力学模拟通常需要高效求解非常大的线性或非线性代数方程组以及强大的计算机系统。此类问题越来越多地在并行或分布式计算系统上解决，这些系统提供对大量内存的访问以及大量快速处理器。本项目的目标是进一步开发域分解类型的求解器，这些算法尊重现代计算系统的内存层次结构，并允许接近峰值浮点性能的性能。已经存在一个发达的数学理论和一个很好的理解如何调整这些算法在不同的应用中出现的问题，但也有一个真实的需要进一步扩大我们的理解，并改善和numericallytest新的算法，特别是在出现的并行计算系统，有很多强大的处理器.该项目的主要目标是进一步理解FETI-DP和BDDC族的区域分解方法。该领域的工作方向受到美国国家实验室和工程软件行业的学术计算科学家和科学家之间的相互作用的强烈影响。与桑迪亚-阿尔伯克基实验室的联系尤其紧密。域分解方法被广泛用于非常大的和重要的应用在这些实验室和域分解方法也取得了重大进展的软件系统是由一个大的社区的工程师使用的设计和检查的机器零件和较大的工程结构.特别重要的应用领域是弹性和电磁学。后一领域有助于为蜂窝电话系统、其他无线通信系统以及微电子技术的改进奠定基础。