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.

虽然有几个可接受的代数多重网格算法的对称正定问题（或一个M-矩阵），有很少知道的作品，更不用说强大的作品，一般非对称，不确定的问题。 事实上，除非在特殊情况下，否则开发代数多重网格方法的三个基本原则都不适用。 对于非对称的，不确定的问题，我们将开发的原则，算法，串行和并行代码，以及与应用程序时，很少或没有，一些，或大量的应用程序的信息提供，使多尺度和多级求解器的鲁棒性。 符号和数字工具都将被开发出来，以使新算法的原型相对轻松。 内存缓存将被利用可移植的小调整需要从用户。 两种不同的应用将激发新的算法和软件：海洋和火焰建模。 结果应该对任何产生非对称、不确定问题的科学或工程领域产生影响。同时，该项目的材料可以整合到计算科学的第一门课程（UKy CS 521）中，该课程由高年级学生和研究生学习。 少数民族学生已经是PI研究小组的一半（一半是女性，一个是有色人种）。 几乎所有的英国CS格拉德生都是少数民族学生。 将通过包括http://www.mgnet.org和道格拉斯主页http://www.ccs.uky.edu/~douglas在内的网站进行传播。