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

虽然有几种可接受的代数多重网格算法用于对称正定问题(或具有M-矩阵的问题)，但对于一般的非对称、不定问题，很少有人知道它是有效的，更不用说稳健地工作了。事实上，除了特殊情况外，发展代数多重网格法的三个基本原则都不适用。对于非对称、不确定的问题，我们将开发原理、算法以及串行和并行代码，当提供很少或没有、一些或大量应用程序信息时，这些代码可以很好地与应用程序一起工作，以使多尺度和多级别解算器具有健壮性。符号和数字工具都将被开发出来，使新算法的原型制作相对容易。用户只需很少的调整即可利用内存缓存。两个不同的应用将推动新的算法和软件：海洋和火焰建模。研究结果应该对任何科学或工程领域产生不对称的、不确定的问题产生影响。同时，该项目的材料可以被整合到计算科学的第一门课程(UKY CS521)中，该课程由高年级学生和研究生选修。少数民族学生已经占到了国际学生联合会研究小组的一半(一半是女性，一个是有色人种)。几乎所有的UKY CS研究生都是少数族裔学生。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

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.