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

虽然对于对称正定问题（或带有m矩阵的问题）有几种可接受的代数多网格算法，但对于一般的非对称、不确定问题，很少有已知的有效算法，更不用说鲁棒性了。事实上，除了在特殊情况下，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，我们将开发原则，算法，以及串行和并行代码，当提供很少或没有，一些或大量的应用信息时，这些代码可以很好地工作，以使多尺度和多层次的求解器鲁棒。符号和数字工具都将被开发，使原型新算法相对无痛。将可移植地利用内存缓存，用户几乎不需要进行调优。两种不同的应用将激发新的算法和软件：海洋和火焰建模。研究结果将对任何涉及不对称、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 CS521）中，供大四学生和研究生学习。少数民族学生已经占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研究生都是少数民族学生。将通过http://www.mgnet.org和道格拉斯的主页http://www.ccs.uky.edu/~douglas等网站进行宣传。

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.