ALGORITHMS: Multiscale, Multicolor, Multigrid-Like Solvers for High Performance Technical Computing

算法：用于高性能技术计算的多尺度、多颜色、类多重网格求解器

• 批准号: 0305466
• 负责人: Craig Douglas
• 金额: --
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0305466&HistoricalAwards=false
• 关键词: ALGORITHMS; Multiscale; Multicolor; Multigrid; Like

While there are several acceptable algebraic multigrid algorithms for symmetric positive definite problems (or ones with an M-matrix), there is very little known that works, much less works robustly, for general nonsymmetric, indefinite problems. In fact, none of the three basic principles for developing algebraic multigrid methods apply except under special circumstances. For nonsymmetric, indefinite problems we will develop principles, algorithms, and serial and parallel codes that work well with applications when little or no, some, or a lot of application information is provided to make multiscale and multilevel solvers robust. Both symbolic and numeric tools will be developed to make prototyping new algorithms relatively painless. Memory caches will be exploited portably with little tuning necessary from the users. Two diverse applications will motivate the new algorithms and software: ocean and flame modeling. The results should have impact on any area of science or engineering in which nonsymmetric,indefinite problems result.At the same time, material from the project can be integrated into a first course in computational sciences (UKy CS521), which is taken by seniors and graduate students. Minority students already are half of the PI's research group (half are female, one is of color). Almost all of the UKy CS grad students are minority students. Dissemination will be through web sites including http://www.mgnet.org and Douglas' home page http://www.ccs.uky.edu/~douglas.

尽管有几种可接受的代数多机算法，这些算法用于对称积极的确定问题（或一个具有M-Matrix的问题），但鲜为人知的可行，更不用说是鲁棒的，对于一般的非对称，不确定的问题而言。 实际上，除在特殊情况下，开发代数多族方法的三个基本原则都不适用。 对于非对称，不确定的问题，我们将制定原理，算法以及串行和并行代码，这些代码与应用程序很少或否，某些或许多应用程序信息可与应用程序配合在一起，以使多尺度和多层次求解器可靠。 将开发符号和数字工具，以使原型化新算法相对无痛。 内存缓存将被严重利用，而用户几乎不需要调整。 两个不同的应用程序将激发新的算法和软件：海洋和火焰建模。 结果应影响非对称，无限问题的科学或工程领域。在同一时间，该项目的材料可以集成到由老年人和研究生所采用的计算科学课程（UKY CS521）中。 少数族裔学生已经是PI研究小组的一半（一半是女性，一个是有色的）。 几乎所有UKY CS的研究生都是少数学生。 传播将通过http://www.mgnet.org和道格拉斯的主页http://www.ccs.uky.edu/~douglas等网站进行传播。